Can someone help me solve this Algebraic Equation please?
x^1/2 + 3x^-1/2 = 10x^-3/2
Answers
Answer:
x=2
Step-by-step explanation:
Related Questions
Which statement is not always true when
△ABC ≅ △ XYZ
1. BC ≅ YZ
2. CA ≅ XY
3. ∠CAB ≅ ∠ZXY
4. ∠BCA ≅ ∠YZX
Answers
If two triangles are congruent, it means that all corresponding sides and angles are equal. Therefore, all of the statements are always true when △ABC ≅ △ XYZ.
When we say that two triangles, △ABC and △XYZ, are congruent, we mean that they have exactly the same size and shape. This implies that all corresponding sides and angles of the two triangles are equal.
For example, if we say that △ABC ≅ △XYZ, then we know that side AB is equal in length to side XY, side AC is equal in length to side XZ, and side BC is equal in length to side YZ. Additionally, we know that angle A is equal in measure to angle X, angle B is equal in measure to angle Y, and angle C is equal in measure to angle Z.
Therefore, all of the statements in the original question are always true when △ABC ≅ △XYZ because congruence means that all corresponding sides and angles of the two triangles are equal.
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"why is simple linear regression called ordinary least-squares regression? what is ordinary about it?"
Answers
OLS regression is called ordinary because the regression is very first to be given and the variables have the similar values which reduces the complexity.
A regression model called simple linear regression uses a straight line to calculate the association between one independent variable and one dependent variable.
Both variables ought to have numerical values.
Many regression analysis differs from conventional least-squares regression analysis in that multiple explanatory variables are incorporated in the statistical procedure known as multiple linear regression (MLR), also known as multiple regression. Multiple regression, an extension of linear (OLS) regression, only makes use of one explanatory variable.
Therefore, OLS or Ordinary Least Square is the type of regression is called so ordinary because the regression is very first to be given and the variables have the similar values which reduces the complexity.
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continuation of previous question :)
Answers
Answer:
Below
Step-by-step explanation:
First let's determine the slope if thus function
Let m be the slope of this function
m = [0-(-4)]/ 2-0 = 4/2 =2
So our equation is:
y = 3x +b
b is the y-intercept wich is given by the image of 0
Here it's -4
So the equation is:
y = 2x-4 wich is also y = x-2 after simplifying
●●●●●●●●●●●●●●●●●●●●●●●●
A line that is parallel to this one will have the same slope.
Examples:
● y= 2x+3
● y = 2x-7
■■■■■■■■■■■■■■■■■■■■■■■■■■
A line that is perpendicular to this one and has a slope m' satisfy this condition:
m*m'= -1
m'= -1/m
m' = -1/2
So this line should have a slope that is equal to -1/2
Answers from the choices:
y = -1/2 x +1/2
y+1= -1/2 (x-3)
in a local election, votes were cast for mr. dyer, ms. frau, and mr. borak in the ratio of 4:3:2. if there were no other candidates and none of the 2,700 voters cast more than one vote, how many votes did mr. dyer receive?
Answers
To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Mr. Dyer received 1,080 votes.
Ratio of votes = 4:3:2
Total votes = 4 + 3 + 2 = 9
Total votes cast = 2,700
Mr. Dyer's votes = (4/9) x 2,700 = 1,080 votes
The ratio of votes cast for Mr. Dyer, Ms. Frau and Mr. Borak was 4:3:2 respectively. This means that for every 9 votes cast, 4 votes were for Mr. Dyer, 3 votes were for Ms. Frau and 2 votes were for Mr. Borak. Since none of the 2,700 voters cast more than one vote, the total votes cast for each candidate would be 2,700. To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Therefore, Mr. Dyer received 1,080 votes (4/9 x 2,700).
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Show one way that five children share
two pizzas equally
Answers
if there is 2 pizza and 5 children then 1/5 (fraction) of a pizza, or two slices, must be given to each child.
Start with two pizzas of equal size. Cut each pizza into 5 equal slices, so you have a total of 10 slices. Give each child 2 slices of pizza. Each child receives 2 slices of pizza, which is:
2/10 = 1/5 of a pizza
Each child now has 1/5 of a pizza.
Since there are 5 children, the total amount of pizza shared is:
5 × (1/5) = 1 pizza
Therefore, each child has 1/5 of a pizza, or 0.2 of a pizza.
To get the total amount of pizza that was shared, we can add up the amount of pizza each child received:
5 × (2/10) = 1 pizza
So, each child receives 2 slices of pizza, which is 1/5 of a pizza, and the total amount of pizza shared is 2 pizzas, or 1 whole pizza per 2 children.
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Find the slope of the line passing through the points (-6, -5) and (4,4).
Answers
Answer:
9/10 or 0.9
Step-by-step explanation:
Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run
where
rise = y2 - y1
run = x2 - x1
Given points (- 6, - 5) and (4, 4),
rise = 4 - (-5) = 4 + 5 = 9
run = 4 - ( - 6) = 4 + 6 = 10
Slope = rise/run = 9/10 or 0.9
A tidal wave caused by an earthquake off the Alaskan coast begins running toward Carmel, California. The water first goes down from its normal level, and then rises an equal distance above its normal level; the water then returns to normal. Assume that the depth of the water varies sinusoidally with time as the wave passes. Suppose the wave, with a period of 20 minutes and an amplitude of 12 meters, approaches a dock in Carmel where the normal depth is 8 meters.
Answers
y = 6 sin [(π/10)t] + 8; equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
Define the sinusoidal function?A sinusoidal function is a mathematical function that oscillates or fluctuates in a periodic manner, following a sine or cosine curve.
If the wave approaches a dock in Carmel where the normal depth is 8 meters and varies sinusoidal with time, then we can use the equation for a sinusoidal function:
y = A sin (ωt + φ) + C
where: A is the amplitude of the wave, which is given as 12 meters
ω is the angular frequency, which can be calculated as 2π / T, where T is the period of the wave (20 minutes in this case)
t is the time elapsed since the wave started passing the dock
φ is the phase angle, which we can assume to be 0 since we are not given any information about it
C is the vertical displacement of the wave from the normal depth, which is 8 meters in this case
putting the given values into the equation,
y = 12 sin [(2π/20)t] + 8
Simplifying this equation,
y = 6 sin [(π/10)t] + 8
This equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
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If f(x) = -3, then x = _____ .
Answers
Answer:
x = -5
Step-by-step explanation:
f(x) is the same thing as y. so when y=-3, find that point and the x is -5
The answer to the given problem can be stated as, "If f(x) = -3, then x = -5.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).In order to find the different values of f(x) for different x on a graph, draw perpendicular lines to both the axis.
The graph given in the problem shows different points lying on it.
In order to find the value of x at f(x) = -3, draw a perpendicular line from the graph at which the value of f(x) is -3.
The x coordinate obtained is given as x = -5.
Hence, the required value of x at f(x) = -3 is -5.
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Identify the characters of series below. nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n A) I Convergent, II Divergent, III Convergent B) I Convergent, Il Convergent, III Divergent C) I Convergent, II Convergent, III Convergent D) I Divergent, Il Divergent, III Divergent E) I Divergent, II Divergent, III Convergent
Answers
Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.
The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.
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The time t, in seconds, that it takes a car to accelerate to x mph can be described by t = 0.001(0.732x2 + 15.417x + 605.738). how fast, in mph, is the car going after 8.91 seconds? give your answer to the nearest tenth.
Answers
After substituting the given time of 8.91 seconds into the equation, we found that the car is going approximately 30.8 mph to the nearest tenth.
To find the speed of the car after 8.91 seconds, we need to substitute the value of t into the equation t = \(0.001(0.732x^2 + 15.417x + 605.738).\)
\(t = 8.91\) seconds
Plugging this value into the equation, we get:
\(8.91 = 0.001(0.732x^2 + 15.417x + 605.738)\)
Now, we can solve for x by isolating it:
\(0.732x^2 + 15.417x + 605.738 = 8.91 / 0.001\)
\(0.732x^2 + 15.417x + 605.738 = 8910\)
Next, we can rearrange the equation to a quadratic form:
\(0.732x^2 + 15.417x + 605.738 - 8910 = 0\)
\(0.732x^2 + 15.417x - 8304.262 = 0\)
To solve the quadratic equation,
we can use the quadratic formula:
\(x = (-b ± √(b^2 - 4ac)) / (2a)\)
In this case,
\(a = 0.732,\)
\(b = 15.417,\)
and\(c = -8304.262.\)
Plugging these values into the formula, we get:
\(x = (-15.417 ± √(15.417^2 - 4 * 0.732 * -8304.262)) / (2 * 0.732)\)
Simplifying the equation gives us two possible solutions for x.
However, only one of them is relevant in this case since we are looking for the speed of the car:
\(x ≈ 53.1\)
the car is going approximately 53.1 mph after 8.91 seconds.
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Let n be a positive integer that is not divisible by 3 and let G
be a group of order 3n. Prove that if x, y ∈ G are elements of
order 3, then y is conjugate to either x or x^(-1).
Answers
In a group G of order 3n, where n is a positive integer not divisible by 3, if x and y are elements of order 3, it can be proven that y is conjugate to either x or x⁻¹. This result highlights the relationship between elements of order 3 in such groups.
To prove that y is conjugate to either x or x⁻¹, we need to consider the properties of groups of order 3n and elements of order 3.
First, since the order of G is 3n, by Lagrange's theorem, the order of any element in G must divide the order of the group. Therefore, the orders of x and y must be divisors of 3.
Since x has an order of 3, it means that x generates a cyclic subgroup of order 3. Similarly, y also has an order of 3 and generates another cyclic subgroup of order 3 in G.
Now, if x and y are elements of the same cyclic subgroup, then they are conjugate to each other. This is because within a cyclic subgroup, every element is conjugate to any other element. Therefore, if x and y are in the same cyclic subgroup, y is conjugate to x.
On the other hand, if x and y are in different cyclic subgroups, we can consider the cosets formed by these subgroups. Since the order of G is 3n and each subgroup has an order of 3, there are exactly n cosets. This means that each element in one subgroup is conjugate to exactly one element in the other subgroup. Therefore, if x and y are in different cyclic subgroups, y is conjugate to x⁻¹.
Hence, we have shown that in a group G of order 3n, if x and y are elements of order 3, y is conjugate to either x or x⁻¹.
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The store has 6 blue notebooks, 11 red notebooks, 7 purple notebooks, 5 black notebooks, and 3 green notebooks. What is the percent chance that Melissa will buy a purple notebook?
22%
68%
25%
28%
Answers
Answer:
28%
Step-by-step explanation:
is your answer :)
Answer:
22% is the right
Step-by-step explanation:
A man bought a calf for $200 and sold it for
$250. What was his gain as a percentage of the
cost price?
Answers
Answer:
Step-by-step explanation:
250 is 125% of 200
So,
He gained 25% in profit
Based on the information given his gain as a percentage of the cost price is 25%.
Using this formula
Cost price percentage=Selling price-Cost price/Cost price
Where:
Selling price=$250
Cost price=$200
Let plug in the formula
Cost price percentage=$250-$200/$200
Cost price percentage=$50/200
Cost price percentage=0.25×100
Cost price percentage=25%
Inconclusion his gain as a percentage of the cost price is 25%.
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Which FAR Part 77 imaginary surface has slopes that may range from 20:1 to 50:1?
The primary surface
The horizontal surface
The approach surface
The conical surface
Answers
The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.
The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.
Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.
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The car and scooter are moving at constants speeds. The time, ‘t’ , when they will be in the same position is represented by ‘21t=19t+7’
Answers
After 3.5 minutes time the car and scooter be in the same position.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The car and scooter are moving at constants speeds.
And, The time, ‘t’ , when they will be in the same position is represented by,
⇒ 21t = 19t + 7
Now, We can solve the expression for time t as;
⇒ 21t = 19t + 7
Subtract 19t both side,
⇒ 21t - 19t = 19t + 7 - 19t
⇒ 2t = 7
⇒ t = 3.5
Therefore, After 3.5 minutes time the car and scooter be in the same position.
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a recipe uses 1 1/4 cups of milk to make 10 servings. if the same amount of milk is used for each serving how mant servings can be made using one gallon.
Answers
Answer:
I believe its 36
Step-by-step explanation:
so what i id is a took apart the answer, if 1 1/4 if 10 cups the 1/4 1/4 1/4 1/4 1/4 would also be 10 cups, so now i know that 1/4 = 2 servings
eso i took 3. 1/4 and that gave me 6 and now add the previous which is 10 so its 16 and i have 2 cups left
from here i knew 1 cup and 1/4 is 10 so subtract 1/4 which is -2 servings and you have 8 and 8+8 is 16 so
then i added
16+16= 36
which leads to my final answer of 36
Im so sorry if im wronge but if its right please give brainlest
What is the value of the expression below?
(-8)^2/3
Answers
Simplify the expression
Cancel the common factor of 3
Raise -2 to the power of 2
The value of the given expression i.e. \((-8)^2/3\) should be considered as the 4.
Calculation of the value of expression:Since the expression is \((-8)^{2/3\)
\(= (-2)^{4^{2/3}\)
Here the common factor should be cancelled out and then we have to riase -2 to the power of 2
So after solving it the value should be 4.
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answer choices
A. -4
B. 5.8
C.4
D.8
Answers
Answer:
the answer is C (4)
Work out the circumference of this circle.
Take a to be 3.142 and give your answer to 1 decimal place.
9m
Answers
Answer:
28.3 (explaination below)! :)
Step-by-step explanation:
Use the formula for cicrumfrence: C=2πr
Radius can be found by splitting the given number in half, (unless you were given the radius already, then you'd just multiply by 2).
Plug in our numbers. C= 2π4.5
Then, multiply.
You'd get 28.27433388230814.
Rounding to the first decimal place, you'd have a final answer of 28.3.
Hope this helps!
how to interpret histogram with normal curve
Answers
when interpreting a histogram with a normal curve, it is important to look at the shape of the histogram and compare it to the shape of the normal curve. This can help us determine if the data is normally distributed, identify outliers, and determine the goodness of fit of the data to a normal distribution.
Histograms and normal curves are two commonly used graphical representations of data. A histogram is a bar graph that represents the frequency distribution of a set of continuous data. A normal curve, also known as a Gaussian distribution or Bell curve, is a symmetrical and bell-shaped curve that represents the probability density function of a normally distributed set of data.
When a histogram is superimposed with a normal curve, it allows us to visually compare the distribution of the data with a normal distribution. In this article, we will discuss how to interpret a histogram with a normal curve.
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pls help with this one -4 divided by - 2/3
Answers
Answer:
6
Step-by-step explanation:
what you do is because you are dividing -4 by -2/3 you have to flip -2/3 to make it -3/2..
so ...
-4/ -2/3 = -4 x -3/2 ( so here you take -2/3 and flip it and multiply by -4)
now all you do is multiply
12/2 you get 6 ! HOPE this helped out alittle
Figure BCDE was transformed using the composition rx-axis ◦ T2,2. If point B on the pre-image lies at (3, 4), what are the coordinates of B'' on the final image?
(5, 6)
(5, –6)
(1, 2)
(1, –2)
Answers
The transformation can be defined as the introduction of a new set of mathematical coordinates. The correct option is B.
What is transformation?The transformation can be defined as the introduction of a new set of mathematical coordinates that are declared to be different functions of the original coordinates.
Given Figure BCDE, which is transformed using the composition rx-axis ◦ T2,2. Also, the coordinates of point B on the pre-image lies at (3, 4). Therefore, the coordinates of B'' on the final image will be,
rx-axis ◦ T2,2 (3,4)
= rx-axis ( T2,2 (3,4) )
= rx-axis ( 5,6 )
= (5, -6)
Hence, the correct option is B.
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ANSWER FAST PLEASE
10.
The first four numbers in a quadratic sequence are
shown below.
2, 3, 6, 11,...
What is the next number in the sequence?
A.
16
B.
18
C. 22
D. 27
Answers
Answer:
B.18
Step-by-step explanation:
2+1+3
3+3=6
6+5=11
11+7=18
6 - 3 = 3
3 - 2 = 1
Notice how all the differences is an odd number. The number after 11 needs have a difference of 7 when subtracted so it would be B. This sequence is an arithmetic sequence.
Answer: 18
Hope you learned something new! :D
find the equation of the line shown
Thanks
Answers
The linear equation in the graph can be written in the slope-intercept form as:
y= -x + 9
How to find the equation of the line in the graph?Remember that a general linear equation is written as:
y = ax + b
Where a is the slope and b is the y-intercept.
Here we can see that the y-intercept is at y = 9, then we can replace that value to get:
y = ax + 9
Now we can see that the line also passes through the point (9, 0), replacing these values in the equation for the line we will get:
0 = 9a + 9
-9 = 9a
-9/9 = a
-1 = a
Then the linear equation is:
y= -x + 9
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BC has endpoints at B(3, 8) and C(7,6). Find the midpoint M of BC.
Write the coordinates as decimals or integers.
Submit
Answers
Answer: (5, 7)
Step-by-step explanation: Midpoint formula is ((x1 + x2)/2, (y1+y2)/2) where (x1, y1) and (x2, y2) are points on a line. Thus
(3+7/2, 8+6/2) = (5, 7)
Oscar made 28 out of 35 field goals during football practice. Which proportion shows how to find the percent of field goals made?
Answers
Answer:
80 %
Step-by-step explanation:
Step one:
Given data
We are told that Oscar made 28 out of 35 field goals during football practice.
Required
The percentage accuracy
Step two:
% Accurracy= number of goals/number of practice*100
% Accurracy= 28/35*100
% Accurracy=0.8*100
% Accurracy= 80%
Hence the percentage that he made is 80 %
Answer:
It's 80
Step-by-step explanation:
a. What is the solution of the system?
Use substitution.
x-2y+z = -4
-4x+y-2z = 1
2x+2y- z = 10
Answers
By substitution, the solution of the system of equations, x - 2y + z = -4, -4x + y -2z = 1 and 2x + 2y - z = 10, is (x , y , z) = (2 , 1 , -4).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given three equations in x, y, and z,
x - 2y + z = -4 (equation 1)
-4x + y -2z = 1 (equation 2)
2x + 2y - z = 10 (equation 3)
Using the equation 1, find the value of one variable, lets say x, in terms of the other variables.
x - 2y + z = -4 (equation 1)
x = 2y - z - 4 (equation 4)
Substitute the equation 4 to equation 2 and 3 and find the value of another variable, lets say y, in terms of the other variable.
-4x + y -2z = 1 (equation 2)
-4(2y - z - 4) + y -2z = 1
-8y + 4z + 16 + y -2z = 1
-8y + y = 2z - 4z + 1 - 16
-7y = -2z - 15
y = -(2z + 15)/-7
y = (2z + 15)/7 (equation 5)
2x + 2y - z = 10 (equation 3)
2(2y - z - 4) + 2y - z = 10
4y - 2z - 8 + 2y - z = 10
4y + 2y = 2z + z + 10 + 8
6y = 3z + 18
y = (1/2)z + 3 (equation 6)
Substitute the value of y from equation 5 to equation 6 and solve for z.
y = (1/2)z + 3 (equation 6)
(2z + 15)/7 = (1/2)z + 3
2z + 15 = 7[(1/2)z + 3]
2z + 15 = (7/2)z + 21
2z - (7/2)z = 21 - 15
(-3/2)z = 6
z = -4
Substitute the value of z in either equation 5 or 6.
y = (1/2)z + 3 (equation 6)
y = (1/2)(-4) + 3
y = -2 + 3
y = 1
Finally, substitute the value of y and z to equation 4 and solve for x.
x = 2y - z - 4 (equation 4)
x = 2(1) - (-4) - 4
x = 2 + 4 -4
x = 2
Hence, the solution of the given system of equations is (x , y , z) = (2 , 1 , -4).
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- 3x + 3y = 6
x + 3y = 18
solve using substitution
find x and y
Answers
Answer:x = 3 and y = 5
Step-by-step explanation:
We have two equations:
-3x + 3y = 6 ........(1)
x + 3y = 18 ........(2)
We can use the second equation to solve for y in terms of x:
-4x = -12
x = 4
Now we substitute this expression for y into the second equation:
3 + 3y = 18
3y = 15
y = 5
Therefore, the solution to the system of equations is x = 3 and y = 5.
equation 1: - 3x + 3y = 6
equation 2: x + 3y = 18
start with equation 2:
x + 3y = 18
subtract 3y from both sides:
x = 18 - 3y
plug the new equation into equation 1:
- 3x + 3y = 6
- 3 (18 - 3y) + 3y = 6
multiply:
-54 + 9y + 3y = 6
collect like terms:
-54 + 12y = 6
add 54 to both sides, then divide the whole equation by 12:
12y = 60
y = 5
plug the y value into either equation to solve for x. for example, here is equation 2:
x + 3y = 18
x + 3(5) = 18
x + 15 = 18
x = 3
check answer:
x + 3y = 18
3 + 3(5) = 18
3 + 15 = 18
18 = 18 is true
Which event is important enough to include in a summary of this
story? Add the event to the chart.
D Event
Event
Event
Hester gives Ms.
Walker the letter
explaining her idea.
Ms. Walker agrees
to consider
Hester's idea.
?
Hester repeats a
*) phrase in her mind
over and over.
D
Hester packs up
her things when
the bell rings.
D
Hester returns to
her desk to read
her book.
Hester learns
about another way
to boost her grade.
Answers
When making a summary, it is important to read and understand the text which you are writing.
What is a Summary?This refers to the concise representation of the main points of a literary text without the use of bias.
Hence,w we can see that because the question is incomplete, you would need a general overview to understand it, so it would be best if you:
Read the given textUnderstand the plot and characterizationFollow the Rising Action, Climax, and Falling ActionList out the main pointsThen, join them in order of occurrence.Read more about summary here:
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Air is being pumped into a spherical balloon at the rate of 7 cm³/sec. What is the rate of change of the radius at the instant the volume equals 36n cm³ ? The volume of the sphere 47 [7] of radius r is ³.
Answers
the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.
The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.
We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)
7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³
36 = (4/3)r³
27 = r³
r = 3 Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)
(dr/dt) = 7 / (4π(9))
(dr/dt) = 7 / (36π)
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