Using the concepts of Application of derivative, we got that 1657.92inches³/sec rate of the volume of the cone changing when the radius is 40 inches and the height is 40 inches for a right circular cone.
We know that volume of right circular cone is given by =(1/3πr²h)
We are given rate of change of radius(dr/dt) and rate of change of the height(dh/dt)
Therefore ,differentiating the volume with respect to time and applying the chain rule.
dV/dt = [(1/3)πr²×(dh/dt)+ (1/3)π·2·r·(dr/dt)·h]
=>dV/dt=[(1/3)× π×r × [(r×dh/dt)+2h×(dr/dt)]]
We are given that dr/dt=2inc/sec and dh/dt= -5inc/sec
So, on putting the values, we get
=>dV/dt=[ ( (1/3)×3.14×40)×[40×(-5)+2×40×2]]
=>dV/dt=[0.33×3.14×40×[-200+160]
=>dV/dt=[0.33×3.14×40×(-40)]
=>dV/dt= -1657.92inches³/sec(negative sign denote volume is decreasing)
Hence, if the radius of a right circular cone is increasing at the rate of 2 inches per second and its height is decreasing at the rate of 5 inches per second. the rate of the volume of the cone changing when the radius is 40 inches and the height is 40 inches is 1657.92inches³/sec.
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A person invests 5000 dollars in a bank. The bank pays 6.25% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 6500 dollars?
Based on the calculation below, the number of years the person must leave the money in the bank until it reaches 6500 dollars is 4.3 years.
How long must money be left in a bank to reach a particular amount?This can be calculated using the formula for calculating the future value (FV) as follows:
FV = PV(1 + r)^n ......................... (1)
Where:
FV = future value or the amount in the bank after certain years = 6500
PV = present value or the amount invested = 5000
r = quarterly interest rate = 6.25% / 4 = 0.0625 / 4 = 0.015625
n = number of quarters
Substituting relevant values into equation (1) and solve for n, we have:
6500 = 5000(1 + 0.015625)^n
6500 / 5000 = 1.015625^n
1.3 = 1.015625^n
Log linearize both sides, we have:
log1.3 = n * log1.015625
0.1139 = n0.0067
n = 0.1139 / 0.0067
n = 17 quarters
Number of years the money must be in the bank = n / number of quarters in a year = 17 / 4 = 4.25 years
To the nearest tenth of a year, we have:
Number of years the money must be in the bank = 4.3 years
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Answer:
Its actually 4.2
Step-by-step explanation:
saw it on delta
4 units squares each 5/7
Question:
4 unit squares each have 5/7 of their area shaded. What is the total area that is shaded?
The total area that is shaded=20/7 unit squares
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
The total area= 4*(5/7)=20/7
This cannot be simplified any more than it is
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Henry showed all the steps he took to solve the equation.
4 (negative one-half x + 7) + 5 x = 15
Step
Simplified Expression
1
-Negative 2 x + 28 + 5 x = 15
2
3 x + 28 = 15
3
3 x = 15
4
x = 5
Sammy tried to verify the solution by substituting x = 5 back into the original equation. It did not result in a true statement. Which explains why Henry’s solution is incorrect?
Answer:
Step 3 is wrong. If 3x+28=15, then 3x= 15-28
what operation appears to be "flipping" the sign?
Supplemental Activities - Ch 1
Steps to solve an inequality Active
Prompt
What are the steps in solving the below inequality?
2x - 3 > 15
x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6 or in interval notation [-9,6]
To find out what are the steps in solving the below inequality:
Given equation is 2x - 3 > 15
The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
−15≤2x-3≤15
First, subtract 3 from each segment of the system of equations to isolate the x term while keeping the system balanced:
−15−3≤2x-3−3≤15−3
−18≤2x-6≤12
−18≤2x-6≤12
Now, divide each segment of the system by 2 to solve for x while keeping the system balanced:
[tex]-\frac{18}{2}\leq \frac{2x}{2} \leq \frac{12}{2}[/tex]
-9 [tex]\leq[/tex] x [tex]\leq[/tex] 6
or
x [tex]\geq[/tex] -9; x [tex]\leq[/tex] 6
or in interval notation [-9,6]
on the horizontal axis.
The lines will be a solid line because the inequality operators contain "or equal to" clauses.
We will shade between the lines to show the interval:
Hence the steps to solve an inequality has been show
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On a map, 1 inch represents a distance of 100 miles. Two towns are 6 inches apart on the map. What is the distance between the two towns?
Answer:
600 miles
Step-by-step explanation:
1 Inch = 100 Miles
6 Inches = 600 Miles
What’s the answer to this ?
1. The measure of angle H is 79 degrees
2. The measure of angle G is 54 degrees
What is isosceles triangle?
An isosceles triangle is one that has two sides of equal length.
The angles opposite to equal sides are equal.
1. Given is isosceles triangle
∠H=∠O = x
sum of all interior angles of a triangle= 180 degrees
22+x+x=180
2x+22=180
2x=158
x=158/2=79
So, ∠H=79
2. Given is isosceles triangle
∠D=∠O = 63
Let ∠G=x
sum of all interior angles of a triangle= 180 degrees
63+63+x=180
x+126=180
x=180-126=54
So, ∠G=54
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There is one negative solution and two nonreal solutions to the equation x3 + 87 = 7x2 + x. What are the solutions?
3, 5 + 2i, 5 – 2i
3, –5 + 2i, –5 – 2i
–3, 5 + 2i, 5 – 2i
–3, –5 + 2i, –5 – 2i
The solution of the equation is -3, 5+2i, 5-2i
What is solution of equation?
The solution of an equation is the array of all values that, when replaced for unknowns, make an equation true. For equations requiring one unknown, raised to a power one, two basic algebra rules involving the additive property and the multiplicative property are used to decide its solutions.
given equation is [tex]x^3+87=7x^2+x[/tex]
we can write it as
[tex]x^3+7x^2+x+87=0[/tex]
solving this cubic equation, we get
(x+3)(x2-10x+29)=0
x = -3 is the first root of the equation.
x2-10x+29 = 0
x =(-b±√b2-4ac)/2
x =(10±√-16)/2
x =5±2i
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40. a sample of size 100,000 is selected from a population with p 5 .75. a. what is the expected value of p? b. what is the standard error of p? c. show the sampling distribution of p. d. what does the sampling distribution of p show?
Answer are
a) The Excepted value (p-hat) of p is 0.57
b) The Standard error of p is 0.05
c) Sampling distribution of p is Normal distribution
d) E(p-hat) = 0.57 , σ(p-hat) = 0.05
Excepted value or "p-hat" is defined as the ratio of number of succes in any sample or event to the total the size of sample . It is also known as sample proportion.
P-hat = X/ N
we have given that,
Sample size (N) = 100
Probability of an event occuring (p) or population proportion = 0.57
The Excepted value of sample proportion i.e p-hat is equal to population proportion i.e p
a) so, excepted value of p = 0.57
b) Standard error of p-hat is equal to square roots of product of p and (1-p) divided by sample size .
Standard error of p- hat = √p(1-p)/n
= √0.57 × 0.43/100= 0.05
c) Sampling distribution of sample mean is normal distribution using central limit theorem.
d) Sampling distribution of p shows
E(p-hat) = 0.57
σ(p-hat) = 0.05
Hence, we get all the required values of excepted value of p , standard error of p , distribution of p.
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PLEASE HELP!!!
find the missing length indicated for each
Using the triangle proportionality theorem, the missing lengths that are indicated are:
1. 35
2. 14
3. 28
4. 18
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that when a line is drawn to be parallel to any side of a triangle that it intersects two of the side of the triangle at two different points, then the two sides are divided proportionally or in the same ratio.
Apply the triangle proportionality theorem to find all the missing length that are indicated. Let the missing side be represented as x.
Problem 1:
x/28 = 15/12
x = (28)(15)/12
x = 35
Problem 2:
x/28 = 6/(18 - 6)
x/28 = 6/12
x/28 = 1/2
x = 28/2
x = 14
Problem 3:
x/35 = 12/(12 + 3)
x/35 = 12/15
x/35 = 4/5
x = (35)(4)/5
x = 28
Problem 4:
x/54 = 8/24
x/54 = 1/3
x = 54/3
x = 18
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Select the correct answer from each drop-down menu. A transversal t intersects two parallel lines a and b, forms two groups of angles. On top line a, starting from the top left, clockwise, angles are 1, 2, 3, and 4. On below line b, starting from the top left, clockwise, angles are 5, 6, 7, and 8. In the figure, , and both lines are intersected by transversal t. Complete the statements to prove that m∠1 = m∠5. (given) m∠1 + m∠3 = 180° (Linear Pair Theorem) m∠5 + m∠6 = 180° (Linear Pair Theorem) m∠1 + m∠3 = ∠5 + ∠6 ( ) m∠3 = m∠6 ( ) m∠1 = m∠5 (Subtraction Property of Equality)
The angles formed between the parallel lines a and b and their common transversal are; on line a; 1,2,3,4. On line b; 5,6,7,8,
A two column table can be used to prove m∠1 = m∠5 with the correct options underlined as follows;
Statements [tex]{}[/tex] Reasons
1. a ║ b [tex]{}[/tex] 1. Given
2. m∠1 + m∠3 = 180° [tex]{}[/tex] 2. (Linear pair Theorem)
3. m∠5 + m∠6 = 180° [tex]{}[/tex] 3. (Linear pair Theorem)
4. m∠1 + m∠3 = m∠5 + m∠6 [tex]{}[/tex]4. (Substitution property of equality)
5. m∠3 = m∠6 [tex]{}[/tex] 5. (Alternate interior angles)
6. m∠1 = m∠5 [tex]{}[/tex] 6. (Subtraction Property of Equality)
What are parallel lines?Parallel lines are lines on the same plane that do not intersect or have a common point as they extend indefinitely in both directions.
The theorems and properties used to prove that the angles m∠1 = m∠5 are as follows
Linear pair theorem;
The linear pair theorem states that two angles that together form a linear pair are supplementary angles (Add up to 180°)
Substitution property of equality;
The substitution property of equality states that if two variables have the same value, then one variable can replace the other variable in equations and expressions without changing their value.
Subtraction property of equality
The subtraction property of equality states that when the same quantity is subtracted from two equal expressions, the values of the new expressions will also remain equivalent
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please help
One side of a triangle is 1 inch longer than the shortest side and is 1 inch shorter than the longest side. The perimeter is 17 inches. Find the dimensions of the triangle.
Answer: [tex]4\frac{2}{3} in;[/tex] [tex]5\frac{2}{3} in;[/tex] [tex]6\frac{2}{3} in[/tex]
Use mental math to solve the equation.
4.
Z
= _5 (1 point)
-12
07
O-60
O-17
O 60
Using cross multiplication method we find out that the value of z is equals to 60. Therefore, the last option is correct.
The given equation is -
[tex]\frac{z}{-12}=-5[/tex]
We have to solve this equation.
Now,
[tex]\frac{z}{-12}=-5\\[/tex]
We have to use cross multiplication method to solve the given equation.
[tex]\frac{z}{-12}=-5\\\\= > z= (-5) (-12)\\= > z = 60[/tex]
Thus, by solving through cross multiplication method we find out that the value of z is equals to 60. Therefore, the last option is correct.
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In math class ,60 percent of the student are male.There are 30 students in the class.How many students are males?
i need help, which one is it???
Answer
the one on the bottom left
Step-by-step explanation:
find the annual salary of a person who is $835.50 per week and show working for the answer for this question
Answer:
43446
Step-by-step explanation:
52 weeks in an year
835.5*52
= 43446
Select the correct answer.
What are the attributes of the boundary line of this inequality?
-3x − 2y < 6
A.
The line is solid with a y-intercept at (0,-2) and slope of
B.
The line is solid with a y-intercept at (0,-3) and slope of -
C.
The line is dashed with a y-intercept at (0,-2) and slope of
D.
The line is dashed with a y-intercept at (0,-3) and slope of -
The line is dashed with a y-intercept at (0,-2) and slope of -3/2 which is a correct option(C)
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
-3x - 2y <6
Let's consider an equation of a line,
-3x-2y = 6
-2y = 3x + 6
y = -3/2x - 3
So, slope = -3/2
Substitute y =0 in the equation of a line
So, y-intercept at (0,-2)
Due to Inequality, the graphical representation of the line is a dashed line.
Hence, the line is dashed with a y-intercept at (0,-2) and a slope of -3/2
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Caho needed to get her computer fixed. She took it to the repair tore. The
technician at the tore worked on the computer for 5 hour and charged her
$102 for part. The total wa $627. Write and olve an equation which can be
ued to determine 2, the cot of the labor per hour.
Answer:
105
Step-by-step explanation:
627-102=525
525 divided by 5 is 105
The population of white-tailed deer i growing rapidly in the united tate. In 1905 the population wa approximately 5x10^5 and in 2000 the population wa approximately 2x10^7 how many time larger wa the population of white tailed deer in 2000 than it wa in 1905
The population of white tailed deer was increased by 40 times .
What are white tailed deer?
The medium-sized white-tailed deer is a native of North America, Central America, and South America as far south as Peru and Bolivia. It is often referred to as the white tail or Virginia deer.
Main body:
population of white tailed deer in 1905 = 5*10^5
population of white tailed deer in 2000 = 2*10^7
Population increase can be calculated by using simple division ,
calculating :
⇒ 2*10⁷/5*10⁵
⇒ 2*10⁽⁷⁻⁵⁾/ 5
⇒ 2*10²/ 5
⇒ 200/5
⇒ 40
Hence population increased by 40 times from 1905 to 2000 for white tailed deer.
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Gabrielle picked 5 5/6 pounds of berries. She divided them evenly among 7 containers. How many pounds of berries did Gabrielle put in each container?
The pounds of berries that Gabrielle put in each container, given the pounds of berries she picked, are 5/6 pounds
How to find the pounds of berries?Gabrielle was able to pick 5 ⁵/₆ pounds of berries. First convert this to an improper fraction for easier calculations:
= 5 ⁵/₆
= ((6 x 5) + 5) / 6
= 35 / 6
The pounds of berries that went into each container is:
= Pounds of berries / Number of containers
= 35 / 6 ÷ 7
= 35 /6 x 1/7
= 35/42
= 5/6 pounds
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Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answer:
<3, < 6, <7 are all 102,
<1, <4, <5 and <8 are all 78
Step-by-step explanation:
If you slide angles 1, 102, 3 qnd 4 down along p, they will fit perfectly over 5,6,7 and 8. So if you find the top four angles, you have found the bottom 4 angles.
<3 is a vertical angle to 102 and vertical angles always have the same measurement.
Angles 1 and 4 are supplemental to 102. That means that the two angles will add to 180. 180 - 102 = 78
Find the two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex]
The two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).
In the given question we have to find the two x intercept of the equation.
The give equation is [tex]y=\frac{1}{2}(x+2)^2-4[/tex].
We can find the x intercept by putting y=0. Then solving the equation for x.
Now putting y=0 in the given equation.
0= [tex]\frac{1}{2}(x+2)^2-4[/tex]
Add 4 on both side, we get
[tex]\frac{1}{2}(x+2)^2[/tex] = 4
Multiply by 2 on both side, we get
[tex](x+2)^2[/tex] = 8
Taking square root on both side, we get
x+2 = √8
x+2 = ±2√2
Subtract 2 on both side we get
x=±2√2-2
Taking 2 common
x=2(±√2-1)
Now the values of x
x={2(-√2-1), 2(√2-1)}
x={-2(√2+1), 2(√2-1)}
Hence, the two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).
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Which equation is a point slope form equation for line AB?
A. y−2=2(x+2)
B. y−2=−2(x+6)
C. y−6=−2(x+2)
D. y−2=−2(x+2)
The equation of the line in point slope form is (c) y - 6 = -2(x + 2)
How to determine the line equation?The graph represents the given parameter
On the graph, we have the following points
(x, y) = (2, -2) and (-2, 6)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (2, -2) and (-2, 6)
Substitute the known values in the above equation
So, we have the following equation
m = (6 + 2)/(-2 - 2)
Evaluate
m = -2
The equation of a line can be represented as
y - Y = m(x - X)
Where
Slope = m = -2
(X, Y) = (-2, 6)
So, we have
y - 6 = -2(x + 2)
Hence, the line has an equation of y - 6 = -2(x + 2)
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Solve four-sixths minus three-fifths equals
Answer:
D 1/15 or 2/30
Step-by-step explanation:
Just make sure your subtracting and making sure that the answer choices don't throw you off, reduce all of the answers
Answer:
2/30
Step-by-step explanation:
4/6-3/5
We have to find common denominator
30 is a common factor so we change both fractions to have a denominator of 30
4x5/6x5-3x6/5x6
20/30-18/30
Now we subtract numerators and keep denominators the same
2/30
Hopes this helps please mark brainliest
25 PTS!!! NEED ANSWER WITHIN 5 MINS!!!!!!
Select the correct answer.
Which line has a y-intercept of 2 and an x-intercept of -3?
Answer:
W
Step-by-step explanation:
It intercepts the y at 2 and x at -3
Answer:
W.
Step-by-step explanation:
The y-intercept of 2 can be found on the vertical line ( up and down ) and the x-intercept of -3 can be found on the horizontal line ( left to right )
Therefore the answer would be graph W.
Find both unit rates.
They paid $96.88 for 8 pizzas.
Question 1 options:
$12.11/pizza and about 0.08 pizza/dollar
A: $12.11 pizza/dollar and about $0.08/pizza
B: $96.88/pizza and about 8 pizzas/dollar
C: 8 pizzas/dollar and about $96.88/pizza
Answer:
A
Step-by-step explanation:
what is the goal of a confidence interval? select one: a. to create a larger sample b. to provide a range of values that are reasonable for the parameter of interest c. to determine if the data can refute an assumption about a parameter or population d. to give a strong statement about a statistic
The goal of a confidence interval is to provide a range of values that are reasonable for the parameter of interest. So the correct option is (A).
The goal of a confidence interval is to provide a range of values that is reasonable for the parameter of interest. The confidence interval is based on the sample data and the level of confidence. The level of confidence is the probability that the confidence interval contains the true value of the parameter.
The confidence interval is calculated using the sample mean, the sample standard deviation, and the level of confidence. The confidence interval is calculated by adding and subtracting the margin of error from the sample mean. The margin of error is the product of the critical value and the standard error. The critical value is based on the level of confidence. The standard error is the standard deviation of the sampling distribution.
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Write the equation of a sine or cosine function to describe the graph.
Answer:
Step-by-step explanation:
first of all the graph is shifted up by 1 then we should add 1 to the function we have.
after that its obvious that the function is sine because if we remove the 1 we add it then it will be 0 when the angle is 0.
the function we have now is y = 1 + sin(ax).
to know the value of a we choose an angle we already know its sine for example:
2 = 1 + sin(a * 1/8)
1 = sin(a * 1/8)
sin-1(1) = PI/2 = a*1/8 => PI = 180
a = 4 * PI
at the end we will have => y = 1 + sin(4PI * x).
Amy made $154 for 11 hours of work
At the same rate, how many hours would she have to work to make $126?
Answer: 9 hours
Step-by-step explanation:
Amount of money/ amount of hours worked
154/11 = 14
$14 made per hour, so $126 divide by 14 would equal to how many hours worked to have a same rate of $14 per hour.
126/14 = 9
QUESTION 6/10 HELP ASAPP
Answer:
Bottom left option is correct.
Step-by-step explanation:
Now we have to find,
→ the table represents y as function of x.
Then the table will be,
→ | x || y |
| -1 || -1 |
| 0 || -1 |
| 2 || 0 |
| 3 || 2 |
(Because the values of x is not repeated)
Hence, bottom left option is correct.
Table number three represents y as a function of x.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.
The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
The data in table number 3,
x y
-1 -1
0 -1
2 0
3 2
The above table has different values of input and the other tables have different values of output at the same value as the input which is not possible.
Therefore, table number three represents y as a function of x.
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