The shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.
How to find time ?To find the time it takes for the shell from the fireworks to reach the water, we need to solve the equation h = 0 for t.
The given equation for h is h = -16t^2 + 64t + 36, so we can substitute this into the equation h = 0 to get:
0 = -16t^2 + 64t + 36
To solve this equation, we can use the quadratic formula, which is:
t = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In this case, a = -16, b = 64, and c = 36, so the formula becomes:
t = (-64 +/- sqrt(64^2 - 4(-16)(36))) / (-32)
Simplifying this gives us:
t = (-64 +/- sqrt(4096 - 2304)) / (-32)
which simplifies to:
t = (-64 +/- sqrt(1792)) / (-32)
Finally, simplifying gives us:
t = (-64 +/- 44) / (-32)
t = (-20 or 24) / (-32)
t = -0.625 or 0.75
Thus, the shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.
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Solve the equation without using a calculator
[tex]\bf\\\\log^2x+log^2(x+10)=log^211\\\\log(x+10)\neq 0[/tex]
[tex]\bf\\(\ lgx=log_{10}x=logx\ )[/tex]
The solution to the logarithmic expression log²x + log²(x + 10) = log²11 is;
x = -11 and 1
How to solve logarithm expressions?We are given the logarithmic expression as;
log²x + log²(x + 10) = log²11
By the power rule of logarithm, we know that; log²x = 2log x
Thus;
log²x + log²(x + 10) = log²11 can be expressed as;
2log x + 2log (x + 10) = 2log 11
Divide through by 2 to get;
log x + log (x + 10) = log 11
We know from product rule of logarithm that log (ab) = log a + log b. Thus; log x + log (x + 10) = log 11 is;
log x(x + 10) = log 11
Log cancels out to get;
x² + 10x - 11 = 0
Using quadratic equation calculator gives;
x = -11 and 1
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If Corey scored higher than the mean on his SAT, but Jerry scored lower than the mean on his SAT, how will both Z scores differ? Jerry's Z score will be positive, while Corey's Zscore will be negative Jerry's Z score will be negative, while Corey's Z score will be positive Both Jerry and Corey's Z scores will be positive Both Jerry and Corey's Z scores will be negative
Based on the provided information, Jerry's Z score will be negative, while Corey's Z score will be positive.
A Z-score refers to a numerical measurement that defines the raw value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it means that the data point's score is identical to the mean score. A negative z-score indicates that the data point is below average or mean and a positive z-score indicates that the data point is above average or mean. Consider the formula for z score which is given by:
z = (x - µ)/σ where x is the given data value, µ is the mean, and σ is the standard deviation.
Hence, if the x < µ, the z score will be negative while if x > µ, the z score will be positive. As Corey scored higher than the mean on his SAT, his z score will be positive, and Jerry scored lower than the mean on his SAT, his z score will be negative.
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Three sides of a triangle have lengths 4, 5, and 6. The angle between the two sides 5 and 6 is nearest: a. 83° b. 56°C. 41° d. 32°
In the given triangle, the angle between the two sides 5 and 6 is nearest 41°.
The term triangle means the polygon which has three sides and three angles and three vertices,
Here we have given that three sides of a triangle have lengths 4, 5, and 6.
And here we need to find the angle between the two sides 5 and 6
According to the given values, let us consider a = 4, b = 5 and c = 6
So, the angle between 5 and 6 can be written as ∠b
And it can be calculated as the following is one way to perform the calculation and it may not be the best way.
∠B = arc cos(a² + c² - b²)/2ac
When we apply the values one the formula, then we get
=> 0.72273 rad
The approximate degree is written as
=> 41.41°
When we round off it then we get the resulting value,
=> 41°
Therefore, option (c) is correct.
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Find AE on the rhombus below when AD=4 x+2, DC=7 x-13 and BD=34 .
Note: Write your answer in simplest radical form. In the first blank put the number in front of the v. And in the second blank. put the number that is inside the . ** If there is no number in front of the v, enter a 1 in the blank **
The length AE of the rhombus is √195 units
How to determine the length AE of the rhombus?From the question, we have the following parameters that can be used in our computation:
AD = 4x + 2
DC = 7x - 13
BD = 34
All the four sides of a rhombus are congruent
This means that
DC = AD
Substitute the known values in the above equation, so, we have the following representation
7x - 13 = 4x + 2
Evaluate the like terms
3x = 15
Divide both sides by 3
x = 5
Substitute x = 5 in AD = 4x + 2
So, we have
AD = 4 x 5 + 2
AD = 22
The length AE of the rhombus is then calculated as
AE² = AD² - (BD/2)²
Substitute the known values in the above equation, so, we have the following representation
AE² = 22² - (34/2)²
Evaluate
AE² = 195
Take the square roots
AE = √195
Hence, the length is √195 units
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If a figure is translated 3 units left and 3 units up, which translation moves the image back to the original position?
A.3 units right and 3 units down
B.3 units left and 3 units up
C. 3 units up
D. 3 units left
Answer:
I believe it is A
Step-by-step explanation:
Just go backwards. translations on a graph are pretty simple once you understand left vs right and up vs down.
The required translation to move the image back to the original position is 3 units right and 3 units down. Option A is correct.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
What is translation?The translation processes in geometry enable the shift of figures from one location to other.
Here,
The given translation is ,
a figure is translated 3 units left and 3 units up,
(x' , y') ⇒ (x - 3 , y + 3 )
To shift back the image,
x' = x - 3 ⇒ x = x' + 3
y' = y + 3 ⇒ y = y' -3
Thus, the required translation to move the image back to the original position is 3 units right and 3 units down. Option A is correct.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The equation of the transformed graph will be y = -3(2ˣ) + 2.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
Suppose the equation of the given graph is y = A 2ˣ + k.
Substitute,(0,-1)
-1 = A 2⁰ + k
A + k = -1 (1)
Substitute, (1,-4)
-4 = A 2¹ + k
2A + k = -4
A + k/2 = -2 (2)
Subtract 1 - 2 as
k - k/2 = -1 + 2
k/2 = 1
k = 2
And, A = -2 - 2/2
A = -3
Thus y = -3(2ˣ) + 2
Hence "The equation of the transformed graph will be y = -3(2ˣ) + 2 ".
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"Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years."
After 11.61 years the given principal amount of $ 900 will be double.
What is Compound interest?
Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.
The formula for the Amount when compound interest is calculated is given by
Amount, A = P(1+r/n)^nt
P = Principal amount
r = Rate of interest
n = Number of compounds
t = Time period in years
Given:
Principal amount = $ 900
Rate of interest = 6% = 6/100 = 0.06
Number of compounds = 12 [ ∵ compounded monthly]
We need to find the time period
Assume that after 't' years the amount will be doubled
From the given data and formula,
Amount, A = 900(1+0.06/12)^12t
= 900(1+0.06/12)^12t
= 900(1 + 0.005)^12t
= 900 (1.005)^12t
As we assumed after 't' years the amount is double
=> 900 (1.005)^12t = 2 × 900
=> (1.005)^12t = 2
Applying log on both sides
=> log (1.005)^12t = log 2
=> 12t log(1.005) = log 2
=> 12t = log 2/log(1.005)
=> 12t = 0.30108/ 0.00216
=> 12t = 139.888
=> t = 11.61
Hence, after 11.61 years the given principal amount of $900 will be double.
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Find the most general antiderivative of the function f(x) = 7 sin(x) - 4 sec(x) tan(x) on the interval
[tex]( - \frac{\pi}{2} \: \: \frac{\pi}{2} )[/tex]
The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.
Given that,
We have a function f(x)=7sinx -4secx tanx.
We have to find the most general antiderivative of the function on the interval (-π/2, π/2).
We know that,
Take the function,
f(x)=7sinx -4secx tanx.
The antiderivative is
= [tex]\int {7sinx-4secxtanx} \, dx[/tex]
= [tex]7\int{sinx} \, dx -4\int {secxtanx} \, dx[/tex]
= 7(-cosx)-4[tex]\int {sinx/cos^{2}(x) } \, dx[/tex]
Take cosx =u
-sinxdx=du
= -7cosx-4[tex]\int {-1/u^{2} } \, du[/tex]
= -7cosx-4(1/u)+C
=-7cosx-4(1/cosx)+C ( since we know u=cosx)
= -7cosx-4secx+C
Now for the interval (-π/2,π/2)
= -7(cosπ/2-cos(-π/2))-4(secπ/2-sec(-π/2))+C
= -7(0-0)-4(∞-∞)+C
=not defined
Therefore, The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.
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Write the fractional values under each note. Verify that the sum of the fractions is 1 for each measure.
Answer:
1/8, 1/8, 1/4, 1/4, 1/16, 1/16, 1/16, 1/16 = 1
1/2, 1/2 = 1
Step-by-step explanation:
from left to right
is this music class or math class lol?
if the total profit per month of a company is Rs 200,000 and its revenue per month can be obtained by adding Rs. 20,000 to the twice the cost per month, find the revenue and cost per month. ..?
Answer:
okey baik dan sangat bagus
Suppose that $11,353 is invested at an interest rate of 5.7% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answer:
Step-by-step explanation:
1)11357*(105.7/100)^t
2)1 year 12000.121 2 year 12684 5 year 14979.1 10 years 19763.3
3)11357*(105.7/100)^t=22714 so t+12.5
what is 3/4 - 1/4ygkfmvkbkmbkvmmf
Answer:
1/2
Step-by-step explanation:
A toy company recently added some made-to-scale models of racecars to their product line. The length of a certain racecar is 17ft. Its width is 5ft . The width of the die-cast replica is 1,25 in.
Find the length of the model.
The model's length 1.4.To do this, I'm going to put up a proportion. This time period is excessively long when compared to how long it takes to whip.
Calculate the model's length?There is a race vehicle in this question, and it's length is 21 feet. Its width is 1.4 feet. We want to know if the replica is to scale, and if so, what is the length of the replica. To do this, I'm going to put up a proportion. This time period is excessively long when compared to how long it takes to whip.As a result, since the width was also measured in inches, I'm going to refer to the length that I'm looking for as X and this time, X will be one inch. Thus, length is to wit. With regard to the race car, 21 is 2 7 as long as X is to 1.4, thus I must now cross multiply to find X. Before I do that, though, I should realize that 21/7 can be boiled down to just three numbers.In order to retrieve X alone and reverse this division by 1.4, I will multiply by 1.4, which equals x when multiplied by three. Therefore, 21 7 is three, which is equal to two x over 1.4. "4.2, 4.2 is equal to three times 1.4.To learn more about Model's length refer to:
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An area near a forest was monitored by researchers. The first graph shows the change in the amount of ground shade during a five-year period. The second graph shows how the population of milkweed changed over the same period.
Which hypothesis is supported by the data?
A. The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, decreased.
B. The milkweed population is an abiotic factor that decreased as the amount of sunlight, a biotic factor, decreased.
C. The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, increased.
D. The milkweed population is an abiotic factor that decreased as the amount of sunlight, a biotic factor, increased.
Option A is correct.
What is increasing and decreasing graphs?
Generally speaking, we are aware that if something is growing, it is moving upward, and if it is shrinking, it is moving downward. As a result, if we talk about a function's graph, an increasing function is one that is moving upward, and a decreasing function is one that is moving downward.
From the graph, we infer that the sunlight, that is the shaded area increased in the given time. Which means that the sunlight was less.
From the milkweed population graph, we see that the milkweed population decreased over time.
Hence the most supportive hypothesis would be option A.
The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, decreases.
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Chloe needs a 1.25-meter piece of wood for a desk that she is building. How many centimeters need to be cut off a 2-meter piece of wood in order to use it for her desk.
Chloe needs to cut 75 centimetres after the unit conversion piece of wood in order to use it for her desk.
What is unit conversion?
Unit conversion is a multi-step process that includes rounding, selecting the appropriate number of significant digits, and multiplying or dividing by a numerical factor.
Given, Chloe needs a 1.25-meter piece of wood
Total available 2-meter piece of wood
So, the extra piece of wood = 2-1.25 = 0.75 meter
Convert meter to centimetres
Then, 1 meter = 100 centimetres
0.75 meter = 0.75*100 centimetres = 75 centimetres
Hence, she needs to cut 75 centimetres piece of wood.
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Which letter represents the mesosphere?
A
B
C
D
Answer:
A represents the mesosphere
50pts help. Please look at attached pic
Answer:
there is no attached picture...
Step-by-step explanation:
The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.
We want to study the population formula of a given US state according to exponential equation.
a) 23.1 millions.
b) in 2013 - 2014
What is exponential equation?
The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable
Main body:
The population state is:
A = 23.1*e^(0.0153*t)
In millions.
Where t represents the number of years after 2000.
a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).
A(0) = 23.1*e^(0.0153*0) = 23.1
The population at year 2000 was 23.1 millions.
b) Now we want to solve:
A(t) = 28.3 = 23.1*e^(0.0153*t)
28.3/23.1 = e^(0.0153*t)
1.23 = e^(0.0153*t)
Now we can apply the natural logarithm to both sides:
ln(1.23) = ln( e^(0.0153*t) )
ln(1.23) = 0.0153*t
ln(1.23)/0.0153 = t = 13.5
Hence, 13.5 years after 2000 the population will be 28.3 million.
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Question 1 One solution. 2x - 1 =_________x - 1
Answer:
2
Step-by-step explanation:
2x-1 = __x-1
Make both sides match to make the statement true.
2x-1 = 2x-1
PLEASE HELP!!!!
Which graph is linear?
Answer:
the second
Step-by-step explanation:
the second is a linear graph
Answer:
The second Graph
Step-by-step explanation:
The question is asking what graph is linear.
The first graph is of an absolute value function which is not linear.
The second is of a line. This is linear.
The third looks to be either an exponential or a logarithmic function. Both of which are not linear.
2 M 1 0 2 B 4 5 6 Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A'B'C'. What are the coordinates of triangle A'B'C'? OA) A'(0, 4), B'(4, 0), C´(8, 8) B) A'(4, 0), B'(0, 4), C'(8,8) C) A'(0, -4), B'(-4, 0), C'(-8, -8) OD) A'(0, 4), B'(4, 0), C'(16, 16) Mange a N not a fan o
The coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).
What are coordinates?
A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Here, we have
Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A'B'C'.
A = ( 0,2)
B = (2, 0)
C = (4,4)
After applying dilated by a factor of 2, we get
A' = (0,4)
B' = (4,0)
C' =(8,8)
Hence, the coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).
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What is the vertex of the graph f(z)= 2z² +82 +37
The vertex of the function is located at coordinates (119, 0).
Step-by-step explanation:1. Write the function and simplify it.[tex]f(z)= 2z^{2}+82+37\\ \\f(z)= 2z^{2}+119[/tex]
2. Find the derivative with respect to z.Check the attached image.
[tex]\frac{d}{dz} (2z^{2}+119)\\ \\f'(z)=2*2z^{2-1}\\ \\f'(z)=4z[/tex]
3. Find the roots of the resulting function.[tex]f'(z)=4z\\ \\4z=0\\ \\z=0[/tex]
4. Evaluate the calculated value in the original function.[tex]f(0)= 2(0)^{2}+119\\ \\f(0)=119[/tex]
5. Conclude.The vertex of the function is located at coordinates (0, 119).
Which operations involving complex numbers have solutions represented by (-6, 7)? 2(1 − 2i) − (4 + 3i), 2(1 + 2i) + (-4 − 3i), 2(-1 + 2i) − (4 − 3i), (-2 + 4i) + (-4 + 3i) , (-2 − 4i) + (4 − 3i)
Option 3 and 4 are the operations involving complex numbers have solutions represented by (-6, 7).
What is a complex number ?Every complex number can be expressed in the form displaystyle a+bia + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation displaystyle i2=-1. René Descartes referred to me as an imaginary number since no actual number can satisfy the aforementioned equation. The real component of the complex number displaystyle a+bia+bi is referred to as a, and the imaginary part is referred to as b. The symbols C or displaystyle "mathbb "C" are used to represent the set of complex numbers.Complex numbers are crucial to many parts of the scientific explanation of the natural world, despite the historical appellation "imaginary," and are recognized in the mathematical sciences as just as "real" as real numbers.Find the attachment answer
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if 1+1+10 x 34 what is it
Answer:
408
Step-by-step explanation:
1+1+10 equals 12, then do 12 x 34, which equals 408
9. Bob Rowinski made a $4,000 deposit to a
savings account paying 1.6% annual interest
compounded semiannually. If he kept the money
on deposit for 6 months, what would his account
balance be after the interest payment is made?
The account balance of Bob Rowinski if he kept the money on deposit for 6 months is $4,032.00.
What is Bob Rowinski account balance the interest payment is made?The compound interest formula can be expressed as;
A = P(1 + r/n)^(n*t)
Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.
Given the data in the question;
Principal P = $4,000Interest rate r = 1.6% = 1.6/100 = 0.016Compounded semi-annually n = 2Time t = 6 months = 0.5 yearAccrued amount A = ?Plug the given values into the above formula and solve for A.
A = P(1 + r/n)^(n*t)
A = $4000( 1 + 0.016/2 )^(2*0.5)
A = $4000( 1 + 0.008 )^(1)
A = $4000( 1.008 )
A = $4,032.00
Therefore, the accrued amount after half a year is $4,032.00
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It keeps saying I’m wrong
Answer:
translation of 2 squares left and 1 square down
Step-by-step explanation:
consider the top vertex of both figures
S → T
then shape T is a translation of shape S
by moving 2 squares to the left and 1 square down
help please thankssss
If the functions are combined using addition, which statements describe the resulting graph h(x)? Check two options. domain: x ≥ –2 domain: x ≥ 2 The point (2, 2) is on h(x). The point (–2, 0) is on h(x). The point (0, –3) is on h(x).
Answer:
(25,-5)
Step-by-step explanation:
I need help with my home work
Answer:
Below
Step-by-step explanation:
If congruent then
x = y+5 and
x+3 = 3y <======sub in the first equation for 'x'
y+5 +3 = 3y
8 = 2y then y = 4 x = y+5 = 9
( i only need number one and number 7 )
someone please i’m desperate i have so much work i need done by monday even if you only do one of them it is greatly appreciated
Answer:
1. x-intercept = (1, 0), y-intercept = (0, -2)
7. y + 4 = -6( x - 7)
Step-by-step explanation:
Question 1Given point-slope equation:
[tex]y-2=2(x-2)[/tex]
The x-intercept is when y = 0:
[tex]\begin{aligned}y=0\implies 0-2 &=2(x-2)\\-2&=2x-4\\2&=2x\\x&=1\end{aligned}[/tex]
The y-intercept is when x = 0:
[tex]\begin{aligned}x=0\implies y-2 &=2(0-2)\\y-2&=2(-2)\\y-2&=-4\\y&=-2\end{aligned}[/tex]
Therefore, the intercepts are:
x-intercept = (1, 0)y-intercept = (0, -2)To graph the equation, plot the intercepts and draw a straight line through them. (See attachment 1).
---------------------------------------------------------------------------------
Question 7[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Given:
m = -6(x₁, y₁) = (7, -4)Substitute the given slope and point (7, -4) into the formula to write the equation of the line in point-slope form:
[tex]\implies y-(-4)=-6(x-7)[/tex]
[tex]\implies y+4=-6(x-7)[/tex]
To graph the line, find the value of y when x = 6 and when x = 8:
[tex]\begin{aligned}x=6\implies y+4 &=-6(6-7)\\y+4 &=-6(-1)\\y+4&=6\\y&=2\end{aligned}[/tex]
[tex]\begin{aligned}x=8\implies y+4 &=-6(8-7)\\y+4 &=-6(1)\\y+4&=-6\\y&=-10\end{aligned}[/tex]
To graph the equation, plot the points (6, 2) and (8, -10) and draw a straight line through them. (See attachment 2).
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Please note that I have drawn the graphs using the same size 7x7 grids as shown in your question paper. If you wish to graph more of the line, please change the scale from those I have used.