The surface area of the balloon is increasing at a rate of 5 square centimeters per second when the radius is 5 cm.
A) We know that the volume of a sphere is given by:
V = (4/3)πr^3
Taking the derivative of both sides with respect to time, we get:
dV/dt = 4πr^2 (dr/dt)
where dV/dt is the rate of change of volume (which is 10 cubic centimeters per second in this case), dr/dt is the rate of change of radius, and 4πr^2 is the surface area of the sphere.
Rearranging the equation, we get:
dr/dt = (1 / (4πr^2)) dV/dt
Substituting dV/dt = 10 cubic centimeters per second, we get:
dr/dt = (1 / (4πr^2)) (10) = (5 / (2πr^2)) cubic centimeters per second
Therefore, the expression for the rate at which the radius of the balloon is increasing is dr/dt = (5 / (2πr^2)) cubic centimeters per second.
B) When the diameter is 40 cm, the radius is 20 cm. We can use the expression we derived in part (A) to find the rate at which the radius is increasing:
dr/dt = (5 / (2πr^2)) cubic centimeters per second
Substituting r = 20 cm, we get:
dr/dt = (5 / (2π(20^2))) cubic centimeters per second
dr/dt ≈ 0.00198 cm/s (rounded to 5 decimal places)
Therefore, the radius of the balloon is increasing at a rate of approximately 0.00198 cm/s when the diameter is 40 cm.
C) When the radius is 5 cm, the surface area of the sphere is given by:
A = 4πr^2
Taking the derivative of both sides with respect to time, we get:
dA/dt = 8πr (dr/dt)
We can use the expression we derived in part (A) to find the rate at which the radius is increasing:
dr/dt = (5 / (2πr^2)) cubic centimeters per second
Substituting r = 5 cm and dr/dt = (5 / (2πr^2)) cubic centimeters per second, we get:
dA/dt = 8π(5) ((5 / (2π(5^2))))
dA/dt = 5 cubic centimeters per second
Therefore, the surface area of the balloon is increasing at a rate of 5 square centimeters per second when the radius is 5 cm.
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Rewrite the function by completing the square.
f(x) = x^2 + 14x + 64
Step-by-step explanation:
step 1. (x^2 + 14x + 49) + 15
step 2. (x + 7)^2 + 15.
I need help on number 7
Answer:
y=2x+2 and increasing
Step-by-step explanation:
we see there is a pint (0,2) so the y intercept is 2, we know the slope is 2 because the slope formula can be used on ay two points, for example (0,2) and (1,4) 4-2 is 2 and 1-0 is 1. 2/1 =2 so the slope is 2
Ronald bought 1.5 pounds of red apples and 0.75 pounds of yellow apples. He bought 1.6 times as many pounds of green apples as red apples and yellow apples combined.
How many pounds of green apples did Ronald buy?
Answer:
To find the number of green apples he bought, We do the following:
calculate the total mass of red and yellow apples bought 1.5+0.75=2.25 poundsSince the mass of green apples bought was 1.6 times the combined mass of yellow and red apples bought we get;2.25×1.6=3.6pounds He bought 3.6 pounds green applesA TV has a listed price of $578.98 before tax. If the sales tax rate is 8.25%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$626.75
Step-by-step explanation:
First, we must find how much tax will be added to the TV's price:
Step 1: Convert the percentage to a decimal:
To convert a percentage to a decimal, divide it by 100
8.25/100 = 0.0825
Step 2: Multiply the TV's price by that decimal:
578.98 * 0.0825 = 47.76585
So $47.76585 will be added to the price
Now, we can calculate the total price:
Step 3: Add the tax we jsut calculated to the TV's price to find total price:
578.98 + 47.76585
= 626.74585
Step 4: Round to the nearest cent (2 decimal places)
626.75
So the total price is $626.75
How many degrees
in 1/20 of a full turn?
Answer:
18 degerees
Step-by-step explanation: i am 100% sure have a nice day.
Is the point (3, 11) a solution for the linear equation 1/3x + y = 12? Explain.
Answer:
Yes, because when the values are substituted in, the equation becomes a true statement
Step-by-step explanation:
plug in the values for x and y and see if the equation makes sense
x=3
y=11
1/3(3)+11=12
1+11=12
12=12
Since the above equation is true, the point is a solution for the linear equation.
5. A jewelry supply shop buys silver chains from a manufacturer for $45.00. and then sells the
chains at a 57% markup. What is the retail price of a silver chain?
what is 26.02-5.348=??????
Answer:
20.672
Step-by-step explanation:
26.02 - 5.348= 20.672
that's what I got... hopefully I got what your looking for.. :D
Rashid can do a piece of work in 8 days, which Tipu can finish in 12 days. If they work on alternate days with Rashid Beginning, in how many days, the work will be finished?
Answer: 9.6 days
Step-by-step explanation:
Rashid can do a piece of work in 8 days. Rashid work rate will then be:
= 1/8 owe day.
Tipu can finish in 12 days. Tipu's work rate will be: = 1/12 owe day.
Their work rate together will then be:
= 1/8 + 1/12
= 3/24 + 2/24
= 5/24
From the calculation, together they will finish the work in:
= 1 ÷ 5/24
= 1 × 24/5
= 24/5 days
= 4.8 days
Busy since they are working on alternate days, then this will be multiplied by 2 which will be:
= 4.8 × 2
= 9.6 days
3/8÷5/2
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Answer:
3/20
Step-by-step explanation:
Answer this to be Donkey Kong's friend
36x + 324 - 28x + 196
combine like terms: 36x - 28x = 8x and 324 + 196 = 520
8x+520
2 Do the following calculations
a) 55,8965 + 12,443 x 3
b) (6 x 3) - 4 + 26 - 2
c) 44,65 = 3 x 11,11 + 68
d) 24 - 16 + 3 + 5 - 6 + 10 - 2
e) 15 = (2+2)
Answer:
a) 93,2255
b)38
c)false
d)18
e)false
why do the angles in a triangle add up to 180 degrees?
Answer:
Angles in a triangle add up to 180 degrees because triangles are have the measure and sizes of quadrilaterals, which have an angle measure of 360 degrees. If you divide 360 degrees by 2, you will get 180 degrees.
Step-by-step explanation:
Hope that helps!
Answer:
Let N equal the number of angles in the polygon
Use the formula:
(N x 180)-360 = the sum of all the angles in the polygon
A triangle has 3 angles so:
(3 x 180)-360=180 degrees
(this formula works for any polygon, regardless of the number of it's angles)
At midnight in Minnesota, the temperature was -59. Over the next three hours, the
temperature dropped 7. What was the temperature at 3:00 a.m.?
A-12
B-5°
C -2°
D 2
PLEASE HELP!!!
9514 1404 393
Answer:
A. -12°
Step-by-step explanation:
The final value is found by adding the change to the initial value.
final temp = initial temp + change in temp
final temp = -5° + (-7°) = (-5 -7)°
3 am temp = -12°
Answer:
A
Step-by-step explanation:
1. Write the equation: -5-7. We get that equation because we start at -5 and then it drops 7 degrees. "dropped" is the keyword that tells us to subtract.
2. Solve the equation: -12 degrees. You can solve it very easily by plugging it into a calculator or mentally.
P.S: You typed the question wrong, you said 56 degrees instead of 5. That really had me stumbled lol.
The graph shows your elevation during a run. Which statement is true about your run?
A- You were running uphill for the first 15 minutes.
B- You were running uphill between 10 and 20 minutes into the run.
C- You were running downhill for the last 10 minutea.
D- You were running downhill the first 15 minutes.
Answer:
Its D. You were running downhill the first 15 minutes.
Find the measure of arc BC
Answer:
The measure of the Arc BC is 80
z > 34. Which of the following statements is the best way to describe the value of z?
A. The value of z is less than 34.
B. The value of z is more than 34.
C. The value of z has a maximum of 34.
D. The value of z has a minimum of 34.
Answer:
B
Step-by-step explanation:
The open end is always going to be by the larger number.
Answer:
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
HAHAHA
Step-by-step explanation:
A recipe requires 4 cups of flour to make 28 dinner rolls. How many cups of flour is needed to make 112 rolls?
Answer:
16 cups
Step-by-step explanation:
You have the ratio 4 cups = 28 dinner rolls. 28 * 4 = 112, so you know that if you multiply both sides of that equation by 4 you will get the number of cups of flout to make 28 dinner rolls:
4 cups = 28 dinner rolls
becomes
16 cups = 112 dinner rolls
so the answer is 16 cups
Answer:
16 cups of flour are needed to make 112 dinner rolls.
Step-by-step explanation:
28 divided by 4 is 7 which is the number of rolls for one cups of flour. Divide 112 by 7 and thats the amount of flour needed for 112 dinner rolls. You can also multiply 28 4 times since 4 can go into 16 when multiplied.
What is the measure of arc BD?
Step-by-step explanation:
step 1. mBD = 63°. The arc angle measures the same from the center of a circle.
You are raising money by holding a bake sale at school. You have a budget of $100 to set up the bake sale. You provide volunteers with $40 of materials. Each table that you plan to rent costs a flat rate of $10. How many tables can you rent?
Answer:
6 Tables
Step-by-step explanation:
100 = 10x + 40
60 = 10x
6 = x
good luck, hope this helps :)
6 tables
100-40=60
each table = 10
60 divided by 10=6
Factor the expression below.
x2 - 81
O A. (X-9)(x - 9)
O B. (x + 27)(x-3)
O C. (x-27)(x - 3)
O D. (x + 9)(x-9)
mean median mode and range,4,8,6,4,4,1,1
Plllzzzzz help quick
Answer:
also click the first choice. It has 10 sides.
Step-by-step explanation:
1440=(N-180)-360
N-180=1080
n=10 sides
Answer: The answers would be A
Step-by-step explanation- The sum of all angles in a decagon will always equal 1440 degrees. That is all. Plz mark brainliest?
A shadow is cast by a pole. The angle of elevation from the end of the shadow to the top of
the pole is 35 degrees. If the distance from the base of the pole to the end of the shadow is 22
feet, how far is it from the end of the shadow to the top of the pole?
Answer:
13ft
Step-by-step explanation:
35-22=13
simplify this: (1/5^3)^4
Answer: The simplest form of (1/5^3)^4 is 1/244140625
Step-by-step explanation: Strange answer, huh?
How many gallons of gas would it take to drive 13,500 miles? (URGENT)
Answer:
24 gallons :)
Step-by-step explanation:
y=4x+6 2y=8x+12 what’s the solution is it one solution, no solution, or infinitely many solutions
Answer:
Infinitely many solutions.
Step-by-step explanation:
y=4x+6
2y=8x+12
------------
simplify 2y=8x+12 into y=4x+6
y=4x+6 matches the second equation.
Solve for w.
-4(w+1) = -24
Answer:
w=5
Step-by-step explanation:
what is the equation of a line that passes through points (0,7) and( 2,8)write your answer in slope intercept form
Answer:
(0,7) and (2,8)
slope =8-7=1
2-0=2
m=1/2 meaning slope
equation=y-7/x-o=1/2
2(y-7)=1(x-0)
2y-14=x -o
2y=1x +14
y =1/2 x +7
Step-by-step explanation:
to get the slope is y 2-y 1 divide by x 2-x 1 to get 1/2
you then take one point as (x,y) and one of the coordinates =the slope
then you divide by the 2 on both sides in order to get y=mx + c
Other option
D: 15.7
Answer:
I see a typo in the problem. When it says LR. This triangle isn't in the direction of L its the opposite direction. I think the answer might be C but im not completely sure.
Step-by-step explanation:
Big Brain