The new angular speed, ω₂, is four times the initial angular speed, ω₁.
How to solveTo solve this problem, we can use the conservation of angular momentum. The initial and final angular momenta should be equal:
I₁ω₁ = I₂ω₂
Where I₁ and I₂ are the initial and final moments of inertia, respectively.
Assuming the particles are connected in a circular arrangement, the moment of inertia can be calculated using:
I = n * m * r²
Where n is the number of particles and r is the distance from the center of rotation.
Now we have:
(n * m * L²)ω₁ = (n * m * (0.5L)²)ω₂
Simplifying the equation, we get:
ω₂ = 4ω₁
So the new angular speed, ω₂, is four times the initial angular speed, ω₁.
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A system of small particles, each with mass m, is connected by light strings of length L. The system is rotating at an initial angular speed ω₁. If the strings are shortened to 0.5L, what is the new angular speed, ω₂?
The sample space for tossing a coin 4 times is {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}. Determine P(at least 3 heads). 12.5% 25% 31.25% 68.75%
Answer: a
Step-by-step explanation:
Theres 5 times that we could get at least 3 heads and were tossing the coin 4 times so 5/4. 5 divided 4 = 1.25 x100 =12.5 percent
The probability of P(at least 3 heads) is 31.25%
How to determine the probabilityProbability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
From the information given, we have that;
{HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}.
Count the number of events with 3 H's
Now, to determine the P(at least 3 heads).
We get;
P(at least 3 heads) = 5/16 × 100/1
Divide the values, we get;
P(at least 3 heads) = 0.3125×100/1
Multiply the values we get;
P(at least 3 heads) = 31.25%
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At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 2.5%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
If each year the population grows by 2.5%, then the "exponential-function" which shows the relationship between "y" and "t" is y = 300,000 × [tex](1.025)^t[/tex].
The "Exponential-Growth" is defined as a type of growth where the rate at which something grows is proportional to its current value. This results in a rapid and increasingly faster growth over time.
The relationship between "y" (population) and "t" (time in years) can be modeled by an "exponential-function" ;
⇒ y = a × [tex](1+r)^{t}[/tex],
where "a" is = initial population, "r" is = annual growth-rate (in decimal), and "t" is = time;
In this case, the "initial-population" is = 300,000, and
The annual growth rate is = 2.5% or 0.025,
So, we can write exponential function as : y = 300,000 × [tex](1+0.025)^{t}[/tex],
Simplifying the expression,
We get,
⇒ y = 300,000 × [tex](1.025)^t[/tex],
Therefore, the required exponential-function is y = 300,000 × [tex](1.025)^t[/tex].
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Help with this math please ..
A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The lengths of the corresponding segments are given as follows:
EH = 2.XW = 4.Hence the scale factor is given as follows:
k = 4/2
k = 2.
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61. You plan to save some money based on the following criteria. On day 1, you save $2, on day 2 you save $22, and on day 3 you save $2³. If you continue along the same pattern for one week, how much do you save in all?
You would save a total of $272 in one week if you continued along the same pattern.
What is pattern?
A pattern is a repeating or predictable sequence of events, numbers, shapes, or objects. In the context of the question you asked earlier, the pattern is the sequence of the amounts saved on each day, which follows a predictable rule: the amount saved doubles each day, starting with $2 on day 1. So the pattern is: $2, $22, $2³, $2⁴, $2⁵, $2⁶, $2⁷. Recognizing and understanding patterns is an important skill in many areas of life, from mathematics and science to language and music.
Based on the given pattern, on day 4, the amount saved would be $2⁴ = $16. On day 5, the amount saved would be $2⁵ = $32. On day 6, the amount saved would be $2⁶ = $64. And on day 7, the amount saved would be $2⁷ = $128.
To calculate the total amount saved for the week, we simply add up the amounts saved on each day:
Total amount saved = $2 + $22 + $2³ + $16 + $32 + $64 + $128
= $2 + $22 + $8 + $16 + $32 + $64 + $128
= $272
Therefore, you would save a total of $272 in one week if you continued along the same pattern.
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If cosθ = 0.2, find the value of cosθ + cos (θ + 2π) + cos (θ + 4π)
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
13. Tyra picked two numbers, x and y. She told her friend that the sum of the two numbers is 28
and the difference between the two numbers is 14.
a. Write two different linear equations that model what Tyra told her friend
b. Solve the system of linear equations using the elimination method. What two numbers
did Tyra pick?
a.
x + y = 28
x - y = 14
b.
Add the two equations:
2x = 42
x = 21
Substitute back into either original equation:
y = 28 - 21 = 7
Therefore, the two numbers Tyra picked are x = 21 and y = 7.
Please Help!!
There are a total of 32652 subscriptions to the local newspaper. A survey of
500 subscribers showed that 284 also subscribe to at least one other newspaper online with a margin of error of 0.017
Identify all true statements.
Answer:
Step-by-step explanation:
The true statements are B, D, E, and H for the given margin of error of 0.017.
What is the margin of error?The margin of error shows the range of values within which the real value of a population parameter is expected to reside, based on the findings of a sampling of that population.
To find the margin of error in terms of percentage, we need to divide the margin of error by the sample proportion and multiply by 100.
The sample proportion is 284/500 = 0.568, so the margin of error in terms of percentage is (0.017/0.568) × 100 ≈ 2.99%.
Therefore, the true statements are:
B. The margin of error is between 55.1% and 58.5%.
D. The margin of error is between 17,991 and 19,101 subscribers.
E. The results show 56% of the subscribers also subscribe to at least one other newspaper online.
H. It cannot be concluded that over half of the subscribers also subscribe to at least one other newspaper online.
Statement A is incorrect because the margin of error is less than 3%, which is outside the range of 54% to 58%.
Statement C is incorrect because the margin of error is less than 3%, which is outside the range of 17,632 to 18,938 subscribers.
Statement F is incorrect because the sample proportion is 0.568, which is not equal to 56.8%.
Statement G is incorrect because we cannot conclude that over half of the subscribers also subscribe to at least one other newspaper online due to the margin of error.
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What are the odds in favor of Dave selecting a gray t-shirt if he has 5 gray in his wardrobe of 16
Answer:
wouldn't it be 5/16
Step-by-step explanation:
honestly not sure but isn't this just a probability question?
Suppose it takes John 18 minutes to run 2 miles. How long would it take him to run 5 kilometers? Round your answer to the nearest minute.
The required it would take John 26.3 minutes to run 5 kilometers.
Since there are 1.60934 kilometers in a mile, we can first convert 2 miles to kilometers:
2 miles = 2 * 1.60934 kilometers = 3.21869 kilometers
Now we can use the formula for speed:
speed = distance/time.
time = distance/speed
We know the distance (5 kilometers), and we can find the speed by dividing the distance by the time it takes to run 2 miles:
speed = 3.21869 kilometers / 18 minutes
speed ≈ 0.19 kilometers per minute
Now we can use this speed to find the time it would take to run 5 kilometers:
time = 5 kilometers / 0.19 kilometers per minute
time ≈ 26.3 minutes
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A two-day environmental clean up started at 9AM on the first day. The number of workers fluctuated as shown in the following figure.
graph of number of workers vs. time; between t=0 hours and t=8 hours the graph behaves as a sine curve with centerline 30, amplitude 10 and period 16; between t=12 and t=20, the graph is constant at 20. Then, at t=20 the graph becomes a sine curve again, starting at its minimum and completing one period between t=20 and t=36. The graph is then constant at 20 until t=44, before increasing as a sine again until t=48.
Suppose that the workers were paid 15 dollars per hour for work during the time period 9 am to 5 pm and were paid 22.5 dollars per hour for work during the rest of the day. What would the total personnel costs of the clean up have been under these conditions?
total cost =
dollars
The total personnel costs of the cleanup would be $8,625.
How to determine?Between 9AM and 5PM, a total of 8 hours, the workers are present during the interval t=0 to t=8. During this interval, the number of workers is given by:
f(t) = 30 + 10sin((2π/16)t)
We can calculate the number of workers for each hour using this formula:
f(0) = 30 + 10sin(0) = 30
f(1) = 30 + 10sin(π/8) ≈ 38.66
f(2) = 30 + 10sin(π/4) = 40
f(3) = 30 + 10sin(3π/8) ≈ 38.66
f(4) = 30 + 10sin(π/2) = 40
f(5) = 30 + 10sin(5π/8) ≈ 38.66
f(6) = 30 + 10sin(3π/4) = 30
f(7) = 30 + 10sin(7π/8) ≈ 21.34
f(8) = 30 + 10sin(π) = 20
So, during the first 8 hours, the number of workers fluctuates between 20 and 40.
Between 5PM and 9AM the next day, a total of 16 hours, the workers are present during the intervals t=8 to t=12, t=20 to t=36, and t=44 to t=48. During these intervals, the number of workers is given by:
Between t=8 and t=12, the number of workers is decreasing from 40 to 20. We can approximate this by a linear function:
f(t) = 40 - 5t
Between t=20 and t=36, the number of workers is constant at 20.
Between t=44 and t=48, the number of workers is increasing from 20 to 40. We can use the same linear function as before, but with t shifted by 44:
f(t) = 40 - 5(t-44)
We can now calculate the total personnel costs by multiplying the number of workers at each time interval by the appropriate hourly rate:
From 9AM to 5PM (8 hours): 30 workers on average, at a rate of $15 per hour:
8 × 30 × 15 = $3,600
From 5PM to 9AM the next day (16 hours):
From t=8 to t=12 (4 hours): average of 30 workers, at a rate of $22.5 per hour:
4 × 30 × 22.5 = $2,700
From t=20 to t=36 (16 hours): constant 20 workers, at a rate of $22.5 per hour:
16 × 20 × 22.5 = $7,200
From t=44 to t=48 (4 hours): average of 30 workers, at a rate of $22.5 per hour:
4 × 30 × 22.5 = $2,700
The total cost is the sum of the costs for each time interval:
$3,600 + $2,700 + $7,200 + $2,700 = $16,200
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One can of soda has a capacity of 355mL. How may liters of soda does 12.
12 cans of soda hold 4.26 liters of soda.
The process for determining the total volume of soda would be the same using the specific capacity and number of cans.
We need to determine how many milliliters of soda 12 cans hold. We can do this by multiplying the capacity of one can (355 mL) by the number of cans (12):
355 mL/can x 12 cans = 4,260 mL
Now we need to convert this amount to liters. We know that 1 liter is equal to 1,000 milliliters, so we can divide the total volume in milliliters by 1,000:
4,260 mL ÷ 1,000 mL/L = 4.26 L
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A right triangle with legs of lengths x and y has a hypotenuse of length z. Write an expression for the length of the hypotenuse, z. Show your work.
An expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.
What is Pythagoras' theorem?
A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
Here, we have
Given: A right triangle with legs of lengths x and y has a hypotenuse of length z.
We have to write an expression for the length of the hypotenuse z.
By Pythagoras' theorem
x²+y² = z²
[tex]\sqrt{x^2 + y^2}[/tex] = z
Hence, an expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.
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Data should be analyzed using each of the following except:
A. population size
B. shape
C. spread
D. measures of central tendency
Population size is a characteristic of the data set and is not used to analyze the data. The correct option is A
What is Population size ?The quantity of an organisms belonging to a specific species is referred to as its population size.
Population size is a characteristic of the data collection that is therefore ignored when data analysis is performed. The population under investigation's size is merely described in terms of the number of individuals or data points.
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there are n people seated at a round table.
Step-by-step explanation:
circular permutations of n objects =(n-1)!
The volume of a cone is 678.24 cubic inches. What is the height of the cone?
The height of the cone is 18 inches.
How to find the height of a cone?The height of the cone can be found as follows:
volume of a cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
r = 6 inches
volume of the cone = 678.24
h = ?
Hence,
678.24 = 1 / 3 × 3.14 × 6² × h
678.24 = 1 / 3 × 3.14 × 36 × h
37.68h = 678.24
divide both sides of the equation by 37.68
h = 678.24 / 37.68
h = 18 inches
Therefore,
height of the cone = 18 inches
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The point N lies on the segment MP.
Find the coordinates of N so that the ratio of MN to NP is 3 to 5.
Check
M(-6,-3)
N (?.?)
P (26,13)
Coordinates of N:
4D
2023 McGraw Hill LLC. All Right
The coordinates of point N that divides the line segment formed joining points M(-6,-3) and P(26,13) in the ratio 3:5, evaluated using section-formula is (14,7)
What is section-formula?
The coordinates of the point that splits a specific line segment into two halves are given by the section formula. The line may be split at the point either internally or externally. Their lengths are divided in a way that keeps them in the m: n ratio. The ratio in which the line segment is divided and the coordinates of the points connecting it allow us to calculate the coordinates.
According to section-formula:
(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex]) {where (x,y)are coordinates of point which divides & (a,b) ; (c,d) are coordinates of points forming line segment.
Given P=(a,b) = (26,13)
M=(c,d) = (-6.-3)
m:n = 3 : 5
N=(x,y) = ?
N=(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex])
= {[tex]\frac{(-6)(3)+(26)(5)}{3+5}[/tex] ; [tex]\frac{(-3)(3)+(13)(5)}{3+5}[/tex] }
={ [tex]\frac{-18+130}{8}[/tex] ; [tex]\frac{-9+65}{8}[/tex] }
= {[tex]\frac{112}{8}[/tex] , [tex]\frac{56}{8}[/tex] }
={14 , 7}
The coordinates of point N are (14,7) which divides line joining P(26,13) and M(-6,-3) in ratio 3:5.
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Can someone help me with this thank you
Answer:
1. 4 tens 2 ones
2. 6 tens 5 ones
3. 3 tens 7 ones
4. 2 tens 6 ones
5. 7 tens 4 ones
6. 5 tens 9 ones
7. 8 tens 1 ones
8. 9 tens 9 ones
9. 1 tens 3 ones
Step-by-step explanation:
not sure if I did it right, lmk if im wrong. Think ur just suppsoed to count the number of boxes that make 10, and those that dont count up to 10, depending on the number, are seen as "ones".
solve 2.1*tan9 to 2d.p
Answer:
Correct question:-
Prove that tan9.tan17.tan45.tan73.tan81=1
LHS
Step-by-step explanation:
Find the perimeter of △JKL. Assume that segments that appear to be tangent are tangent.
perimeter =
(60 POINTs will give BRAINIEST FOR EFFORT)
The calculated value of the perimeter of △JKL is 88 units
Finding the perimeter of △JKL.Assuming that segments that appear to be tangent are tangent, we have
7y - 9 = 2y + 11
8x - 35 = 5x - 8
When the expressions are evaluated, we have
y = 4
x = 9
So, we have the following side lengths
OK = 2(4) + 11
OK = 19
Also, we have
JM = 5(4) - 8
JM = 12
Lastly, we have
LO = 32 - 19
LO = 13
The perimeter of △JKL is then calculated as
Perimeter = 2 * (OK + JM + LO)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (19 + 12 + 13)
Evaluate
Perimeter = 88
Hence, the perimeter is 88 units
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graph the function f(x)=x^2+6x+4 by starting with the graph of y=x^2 and using transformations
The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log3 3/8
The expression "log₃(3/8)" can be expressed in the form of "difference-of-logarithms" is log₃(3) - log₃(8), and it's simplified value is -0.89278.
The "Quotient-Property" states that logarithm of quotient of "two-numbers" is equal to the difference of logarithms of individual numbers. It is expressed as : logₐ(b/c) = logₐ(b) - logₐ(c);
Using the quotient property, we can write log₃(3/8) as:
⇒ log₃(3) - log₃(8)
We know that log₃(3) = and log₃(8) = ,
So, ⇒ log₃(3) - log₃(8),
⇒ 1 - 1.89278
⇒ -0.89278,
Therefore, the value of log₃(3/8) is -0.89278.
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The given question is incomplete, the complete question is
Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log₃(3/8).
Find the accumulated value of an investment of $15,000 for 5 years at an interest rate of 6.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly d. compounded continuously. Round answers to the nearest cent.
Answer:
a. Compounded semiannually: $19,216.67
b. Compounded quarterly: $19,338.56
c. Compounded monthly: $19,416.32
d. Compounded continuously: $19,451.08
Step-by-step explanation:
The formula for the accumulated value (A) of an investment with an initial principal (P), an interest rate (r) and a compounding period (n) for a number of years (t) is:
A = P(1 + r/n)^(n*t)
Using this formula, we can calculate the accumulated value for each of the compounding periods given:
a. Compounded semiannually:
A = $15,000(1 + 0.065/2)^(2*5) = $19,216.67
b. Compounded quarterly:
A = $15,000(1 + 0.065/4)^(4*5) = $19,338.56
c. Compounded monthly:
A = $15,000(1 + 0.065/12)^(12*5) = $19,416.32
d. Compounded continuously:
A = $15,000e^(0.0655) = $19,451.08
Therefore, the accumulated value of the investment varies depending on the compounding period, with more frequent compounding resulting in a higher accumulated value.
Maximiliano is making a quilt and he has determined he needs 474 square inches of burgundy fabric and 456 square inches of green. How many square yards of each material will he need? Round your answers up to the nearest quarter yard.
The burgundy fabric:
The green fabric:
How many total yards of fabric will she have to buy?
The distance between Anaheim, CA and Sacramento, CA is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles.
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.
Find the equation of a line perpendicular to y=-1/2x+4 that passes through the point (-2,8)
Answer:
y = 2x + 12.
Step-by-step explanation:
To find the equation of a line perpendicular to y=-1/2x+4 and passing through the point (-2,8), we can first determine the slope of the perpendicular line.
Recall that two lines are perpendicular if and only if their slopes are negative reciprocals of each other. Therefore, the slope of the line we want to find is the negative reciprocal of the slope of y=-1/2x+4.
The slope of y=-1/2x+4 is -1/2, so the slope of the line perpendicular to it is 2 (since the negative reciprocal of -1/2 is 2).
Next, we can use the point-slope form of the equation of a line to write the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8):
y - 8 = 2(x + 2)
Simplifying and putting the equation in slope-intercept form, we get:
y = 2x + 12
Therefore, the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8) is y = 2x + 12.
[tex]\sf y =2x+12.[/tex]
Step-by-step explanation:1. Find the slope of the given equation.The slope of any linear equation can be found just by taking a look at the equation when it's solved for "y".
[tex]\sf y=-\dfrac{1}{2} x+4[/tex]
Looking at the given equation, we can clearly tell that the value of slope is [tex]-\dfrac{1}{2}[/tex].
2. Find the slope of the perpendicular line.The slope of any linear equation that is perpendicular to another can be found by writting the multiplicative reciprocal of the original equation's slope, and changing the sign on it.
Let's do it step by step:
a) Write the slope of the original equation.
[tex]-\dfrac{1}{2}[/tex]
b) Write the multiplicative reciprocal.
For this, you just need to change the order in the fraction. In other words, switch places between the numerator and denominator.
[tex]-\dfrac{1}{2}\Longrightarrow-\dfrac{2}{1}=-2[/tex]
c) Change the symbol of the number.[tex]\sf -2\Longrightarrow2[/tex]
Therefore, the slope of the new equation will be 2, and it is perpendicular to the original equation ([tex]\sf y=-\dfrac{1}{2} x+4[/tex]).
3. Identify the values.With the given ordered pair (-2, 8) and the slope (2) we can calculate the formula of the new equation.
Formula to use: [tex]\sf y-y_{1} =m(x-x_{1} )[/tex]
[tex]\sf x_{1} =-2\\ \\\sf y_{1} =8\\ \\m=2[/tex]
4. Calculate.Now we substitute the variables in the equation by the identified values in step 3.
[tex]\sf y-(8) =(2)(x-(-2))\\ \\y-8 =(2)(x+2)\\ \\[/tex]
Use the distributive property of multiplication on the right side of the equation (check the attached image).
[tex]\sf y-8 =(2)(x)+(2)(2)\\\\y-8 =2x+4\\ \\y-8+8 =2x+4+8\\ \\y =2x+12[/tex]
5. Verify.a) Is it perpendicular?
According to the theory explained in step 2, it is, because the slope is 2.
b) Does it pass through point (-2, 8)?.
For this, simply substitute "x" by "-2" in the calculated equation. If y= 8, then the function also meets this requirement.
[tex]\sf y =2(-2)+12\\ \\y=-4+12\\ \\y=8[/tex]
That's correct. We have found the correct answer.
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15.3
21. A squirrel is standing on the branch of a tree. The angle of elevation from a point on the ground to the squirrel
is 48°. The ground distance from the point to the tree is 28ft. How high above the ground is the squirrel?
Round your answer to the nearest foot.
48⁰
28 ft
21
Answer:
The height of the squirrel is 31 feet.
Step-by-step explanation:
You need to know your Right Triangle Trigonometry to do this problem.
Rt Triangle trig is all about ratios. Angles and ratios.
In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.
tan Angle = opposite/adjacent
tan 48° = x/28
multiply both sides by 28
28•tan48° = x
You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"
Enter 28 × tan48° =
It will return 31.0971504152
Your question asks you to round to the nearest whole.
x = 31
The squirrel's height in the tree is 31ft.
4x + 3y = 18
4x - 2y = 18
Answer:
To solve the system of linear equations:
4x + 3y = 18
4x - 2y = 18
we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the equations in a way that eliminates one of the variables. Here's how we can do it:
Multiply the first equation by 2, and the second equation by 3 to eliminate x:
8x + 6y = 36
12x - 6y = 54
Now, subtract the second equation from the first:
8x + 6y - (12x - 6y) = 36 - 54
8x + 6y - 12x + 6y = -18
-4x + 12y = -18
Divide both sides by -4 to isolate x:
-4x/(-4) + 12y/(-4) = -18/(-4)
x - 3y = 4.5
Now, we can substitute this value of x into one of the original equations, let's use the first equation:
4(4.5) + 3y = 18
18 + 3y = 18
3y = 18 - 18
3y = 0
y = 0
So, the solution to the system of equations is x = 4.5 and y = 0.
Method 2: Substitution
In this method, we solve one of the equations for one variable and then substitute that expression into the other equation to solve for the other variable. Here's how we can do it:
Solve the first equation for x:
4x + 3y = 18
4x = 18 - 3y
x = (18 - 3y)/4
Now, substitute this expression for x into the second equation:
4[(18 - 3y)/4] - 2y = 18
18 - 3y - 2y = 18
-5y = 18 - 18
-5y = 0
y = 0
Now, substitute this value of y back into the expression for x:
x = (18 - 3(0))/4
x = 18/4
x = 4.5
So, the solution to the system of equations is x = 4.5 and y = 0, which is consistent with the solution obtained using the elimination method.
Answer:
(4.5,0)
Step-by-step explanation:
The point that makes this system of equations true is (4.5,0.
When x=4.5, and y=0 both of these equations equal each other.
You can find this point either by using your calculator, or graphing the equations and seeing where they intersect.
Classify the expression.
-3x4 + 9x² + 6
binomial
not a polynomial
trinomial
monomial
other polynomial
The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.
Classifying the expression.From the question, we have the following parameters that can be used in our computation:
-3x^4 + 9x² + 6
A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.
In this expression, we have three terms:
This means that it is a trinomial
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The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.
Classifying the expression.From the question, we have the following parameters that can be used in our computation:
-3x^4 + 9x² + 6
A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.
In this expression, we have three terms:
This means that it is a trinomial
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Ayuda porfavor , cuadros magicos de tal manera que al sumarlos horizontal y vertical den el resultado
hola te hice tres los otros no tuve tiempo espero te sirvan de ayuda :)