The question is incomplete. The complete question is :
The volume of a sphere is increasing at a rate of 7 cm^3/sec. Find the rate of change of its surface area when its volume is 4 pi / 3 cm^3. (Do not round your answer.)
Solution :
Volume of the sphere, [tex]$V=\frac{4}{3} \pi r^3$[/tex]
Given that [tex]$\frac{dV}{dt}= 7 \ cm^3/s $[/tex]
V = [tex]$\frac{4 \pi}{3} = \frac{4 \pi r^3}{3}$[/tex]
∴ r = 1
[tex]$\frac{dV}{dt} =\frac{4}{3} \pi .3.r^2 \ \frac{dr}{dt}$[/tex]
[tex]$7 = \frac{4}{3} ( \pi )(3) (1)^2 \frac{dr}{dt}$[/tex]
[tex]$\frac{dr}{dt}=\frac{7}{4 \pi}$[/tex] cm/s
Surface area, [tex]$A = 4 \pi r^2$[/tex]
[tex]$\frac{dA}{dt} = 8 \pi r \ \frac{dr}{dt}$[/tex]
[tex]$\frac{dA}{dt} = 8 \pi \times \frac{7}{4 \pi} \times 1$[/tex]
[tex]$=14 \ cm^2/s $[/tex]
PRACTICE ANOTHER A random sample of 100 people was taken. Eighty-two of the people in the sample favored Candidate A. We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 79%. We know that the p-value is 0.2307. At the 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is
Answer:
0.2307 > 0.05, which means that we accept the null hypothesis, that is, that the population proportion in favor of candidate A is close to 0.79, that is, it is not significantly more than 0.79.
Step-by-step explanation:
We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 79%.
This means that the null hypothesis is:
[tex]H_{0}: p = 0.79[/tex]
And the alternate hypothesis is:
[tex]H_{a}: p > 0.79[/tex]
We know that the p-value is 0.2307. At the 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is?
0.2307 > 0.05, which means that we accept the null hypothesis, that is, that the population proportion in favor of candidate A is close to 0.79, that is, it is not significantly more than 0.79.
ANSWER !!
ILL GIVE 40 POINTS !!
DONT SKIP :((
PLUS BRAINLIEST !
Answer:
Step-by-step explanation:
Root of forty rational root of forty times negative one irrational, root of forty times negative one rational, root of forty plus negative one irrational.
I believe this is right because rational should be positive and ir should be negative.......
The area of a rectangular deck is 680 square feet. The deck's width is 17 feet. What is the length?
Answer:
40
Step-by-step explanation: im sorry i dont know how to explain but hope this helps!
Answer:
ik what ur doing
Step-by-step explanation:
thsdpgiojojotnhtofkghbtnkjwalhbwgjknhbwthjgl;n: it is A aka 40 ft
One side of a rectangle is parallel to the x-axis. One vertex of the rectangle is located at (5,2) and another vertex at (1,4). What are the coordinates of the other two vertices?
Answer:
(1,2) and (5,4)
Step-by-step explanation:
Hello There!
I had made a graph to make it easier to understand.
The points given to us are represented by the green points
The points that would make a rectangle with lines that are parallel with the x axis would be (1,2) and (5,4) (represented by the red points)
As you can see the points added had created a rectangle with sides that are parallel with the x axis
This meets all of the requirements therefore the other two vertices would have the points (1,2) and (5,4)
I need help. This is due in a few minutes.
Answer:
choose the 3rd one is the one
You are cutting pieces of fabric for a craft project. You need three pieces that measure 6 2/3 inches, 4 1/2inches, and 3 5/8inches.
What is the total length of fabric that you need ?
Answer:
You need 14 19/24 inches of fabric
Step-by-step explanation:
We'll need a common denominator between 2/3, 1/2, and 5/8. 24 is the least (lowest) common denominator.
3 x 8 = 24, so we multiply the numerator and denominator by 8 and 6 2/3 becomes 6 16/24ths
2 x 12 = 24, so we multiply the numerator and denominator by 12, and 4 1/2 becomes 4 12/24
8 x 3 = 24, so we multiply the numerator and denominator by 3, and 3 5/8 becomes 3 15/24.
Now we are adding 6 16/24 + 4 12/24 + 3 15/24
6 16/24 + 4 12/24 + 3 15/24 = 6 + 4 + 3 + 16/24 + 12/24 + 15/24
= 13 + 43/24 = 14 19/24
Please lmk if you have questions.
Please help I'll give brainliest
Answer:
m∠A = 130
Step-by-step explanation:
Here, In a given figure
m∠A = 2x - 30°
Now, we know that the sum of all angle is 180° on a straight line
So,
2x - 30° + 50° = 180°
2x + 20° = 180°
2x = 180° - 20°
2x = 160°
x = 160° ÷ 2
x = 80°
Here, we get the value of x is 80°
Now,
m∠A = 2x - 30°
m∠A = 2(80°) - 30°
m∠A = 160° - 30°
m∠A = 130
Thus, m∠A = 130
-TheUnknownScientist
Sarah is going to invest $280 and leave it in an account for 9 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Sarah to end up with $410?
Answer:
4.2%
Step-by-step explanation:
Help please will mark brainliest
Answer:
9.9
Step-by-step explanation:
4.8 x 2 = 9.6
29.5 - 9.6 = 19.9
19.9/2 = 9.95
round up
9.9
Answer:
10 I think
Step-by-step explanation:
The amount of revenue for a business can be modeled by the function
H(t) = 8400(3)2. Write an equivalent function of the form H(t) = ab'.
Answer:
Step-by-step explanation:
This solid was created by joining two right rectangular prisms.
7 cm
9 cm
5 cm
4
4 / 3cm
12 cm
Enter the volume of the solid in cubic centimeters.
Answer: 648
Step-by-step explanation:
I need help again haha
Answer:
15⁰
Step-by-step explanation:
a straight line is 180⁰. 180-165=15
Step-by-step explanation:
Since a line is 180°, we can add 165 to x equal to 180
[tex]165+x=180[/tex]
[tex]x=15[/tex]
Hope that helps :)
After painting 3/8 of a fence he finds that he has painted 15 feet
Answer:
whats the question? theres no context other than that little bit
Answer:
The fence is 40 feet long.
Step-by-step explanation:
I suppose the question is "What is the length of the entire fence?"
Formula
3/8 x = 15 Multiply both sides by 8
8*(3/8)x = 15*8 Cancel
3x = 120 Divide by 3
3x/3 = 120/3
x = 40
Imagine looking for a certain angle whose cosine is positive and whose sine is negative.
Part 1: Name the two quadrants in which cosine is positive.
Part 2: Name the quadrants in which sine is negative.
Part 3: Use the information in parts a and b to identify the quadrant in which cosine is positive and sine is negative.
Part 4: Write down one angle, in degrees, that has a negative sine and a positive cosine.
Part 5: Using your calculator, confirm your choice by writing the cosine of your angle and the sine of your angle below.
The two quadrants in which cosine is positive are the first quadrant (Q1) and the fourth quadrant (Q4).
How to explain the informationPart 2: The quadrants in which sine is negative are the third quadrant (Q3) and the fourth quadrant (Q4).
Part 3: Based on the information from parts 1 and 2, the quadrant in which cosine is positive and sine is negative is the fourth quadrant (Q4).
Part 4: One angle that has a negative sine and a positive cosine in the fourth quadrant is 135 degrees (or 3π/4 radians).
Part 5: Using a calculator, we can confirm the values of cosine and sine for 135 degrees:
Cosine of 135 degrees: cos(135°) ≈ -0.7071 (rounded to four decimal places)
Sine of 135 degrees: sin(135°) ≈ -0.7071 (rounded to four decimal places)
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Solve for u. -5u/8=-10
Answer:
u 16
Step-by-step explanation:
Find the GCF of 2m^5 and 28m4
a. 28m^4
b. m^4
c. 2m^4
d. 2m
9. Dawn has 338 peanuts and 13 boxes. If she wants to pack an equal number of peanuts in each box, how many peanuts will there be in each box?NO HACKERS AND I NEED ANSWERS QUICK
Answer:
26 in each box
Divide the total of 338 peanuts by 13 boxes (338÷13=26)
William says that 15years from now his age will be 3 times his age 5 years ago if x represents williams present age complete the following sentences
Answer:
Is the question complete
Use the elimination method to solve the system of equations.Choose the correct ordered pair. -x + y -2 , 2x -3y = 4
Answer:
To use the elimination method one coefficient of either x or y must be the same number with opposite signs, so the ordered pair is (-10, -8)
Step-by-step explanation:
2(-x+y=2) Make one of the coefficients equal, with opposite signs.
2x-3y=4 Combine equations.
-y=8 Solve, y=-8
Then find x, -x-8=2
-x=10, so x= -10
(-10, -8) is your answer.
Solve the equation. Find all real solutions.
9r3 - 144r = 0
Answer:
r=0
Step-by-step explanation:
9r x 3 - 144r = 0
27r-144r=0
-117r=0
r=0
Which of the following functions is graphed below?
15
10
5
o
5
-8
-6
-4
-20
N
4
6
od
.
5
(15, 10)-00=n4
substitute all the characters and then you will get (-4, 20)
Find the area of the square.
A =
m4
2
PLS HELP WILL GIVE BRAINLIEST IVE BEEN ASKING FOREVER :(((((
Answer:
__C) 0.36
Step-by-step explanation:
4÷11= 0.36363636363636
so it's 0.36 with a line over it indicating a repeating decimal
How many years will it take for your salary to be $105,000 per year?
Answer:
simple answer in edmentum
Step-by-step explanation:
help lol i can’t do math and everything is due at midnight
Here it is sry and thx!
Answer:
B
Step-by-step explanation:
hard to explain xD
Answer:
#2
Step-by-step explanation:
1x60+45=105
2x60+45=165
3x60+45=225
4x60+45=285
p=. RS. 200, R= 6%per six months. T= 3years
Answer:
36
Step-by-step explanation:
200×3×6/100 =36.is the ans
Mark stated that the slope of the line that passes through these two points (1, -19) and (-2, -7) is -¼. Is Mark correct? Explain. (show your work).
9514 1404 393
Answer:
no
Step-by-step explanation:
The slope formula is ...
m = (y2 -y1)/(x2 -x1)
We can use the values ...
(x1, y1) = (1, -19)
(x2, y2) = (-2, -7)
Putting these into the formula gives ...
m = (-7 -(-19))/(-2 -1) = 12/-3 = -4
The slope is -4, not -1/4. Mark is incorrect.
In the formulae below, make x the subject:
1. a) P = 2mx
Answer:
x = P/2m
Step-by-step explanation:
x is the subject of the formula, and we can express it as: x = P / (2m)
How make x the subjectTo make x the subject in the formula P = 2mx, we can rearrange the equation to isolate x on one side.
Starting with the equation:
P = 2mx
To solve for x, divide both sides of the equation by 2m:
P / (2m) = (2mx) / (2m)
This simplifies to:
P / (2m) = x
Therefore, x is the subject of the formula, and we can express it as:
x = P / (2m)
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In AJKL, j = 55 inches, k = 51 inches and L=38°. Find the area of AJKL, to the
nearest square inch.
Answer:
863
Step-by-step explanation:
From reference sheet.
Plug in values.
Area≈863.465≈863
Evaluate and round.