Volume of a sphere:
V = 4/3 π r ³
Differentiate V with respect to time t :
dV/dt = 4π r ² dr/dt
Surface area of a sphere:
A = 4π r ²
Differentiate A with respect to t :
dA/dt = 8π r dr/dt
You're given that the volume is increasing at a constant rate, dV/dt = 10 cm³/s, so
10 cm³/s = 4π r ² dr/dt
Solve for dr/dt (the rate of change of the sphere's radius):
dr/dt = 5/(2π r ²) cm³/s
Substitute this into the equation for dA/dt :
dA/dt = 8π r (5/(2π r ²) cm³/s)
dA/dt = 20/r cm³/s
At the moment the radius is r = 5 cm, the surface area is increasing at a rate of
dA/dt = 20/(5 cm) cm³/s = 4 cm²/s
When the surface area is increasing at a rate of dA/dt = 2 cm²/s, the radius r is such that
2 cm²/s = 20/r cm³/s
which happens when the radius is
r = 20/2 (cm³/s) / (cm²/s) = 10 cm
Given: AB=BC,AM=MC
BM IAC , EF I BC
EC
FC
Prove:
AB
MA
B
F
с
A
EM
Answer:
AB=BC,AM=MC
BM IAC , EF I BC
Step-by-step explanation:
AB
MA
B
F
с
A
plsss help meee in math :(((
Answer:
a = 30
2a = 60
3a = 90
Step-by-step explanation:
3a + 2a + a = 180 ( Sum of angles of a triangle is 180)
6a = 180
a = 180/6
a = 30
2a = 2 x 30 =60
3a = 3 x 30 = 90
Can someone help me? I’ll reward points + brainalist
Answer:
your answer is c
Step-by-step explanation:
PLEASE PLEASE HELP!!!
These tables of values represent continuous functions. In which table do the
values represent an exponential function?
find the errors and correct the following mathematical sentences:
Answer:
You are supposed to correct the equation here not solve it.
Darnell rented a moving truck, the weight of the truck was 7,860 pounds but the truck is empty, nothing is in there. When he puts the items of his own in the truck, it weighs 6 tons. What was the weight in pounds of the item that Darnell placed in the truck?
Answer:
The item weighed 4140 pounds.
Step-by-step explanation:
1 ton = 2000pounds, 6 tons=12000pounds.
12000-7860=4140pounds.
Finley's pumpkin had a mass of 6.5 kilograms (kg) before he carved it. After carving it, the pumpkin had a mass of 3.9 kg
Answer:
[tex]\%Change = -40\%[/tex]
Step-by-step explanation:
Given
[tex]Initial = 6.5kg[/tex]
[tex]Final = 3.9kg[/tex]
Required
Determine the percentage change --- Missing from the question
This is calculated as
[tex]\%Change = \frac{Final - Initial}{Initial} * 100\%[/tex]
[tex]\%Change = \frac{3.9kg - 6.5kg}{6.5kg} * 100\%[/tex]
[tex]\%Change = \frac{-2.6kg}{6.5kg} * 100\%[/tex]
[tex]\%Change = \frac{-260}{6.5}\%[/tex]
[tex]\%Change = -40\%[/tex]
what would it be?...
Answer:
19 Dollars
Step-by-step explanation:
Discount means that a certain percentage of the price is being deducted from the final price. So, it this case, we first have to find 5% of 20. 5% of 20 is 1 because 20 * .05 is one. Then, we just have to deduct 1 dollar from 20 dollars, making it 19 dollars.
Which of the following ratios is not equivalent to the other two? * 1 1/2, 1:2, or 2 to 1
Answer:
1 1/2
Step-by-step explanation:
Solve for x.
3
24
Will mark brainliest
Please find the area of of the shaded polygon
Answer:
i think it might be 15... im not sure, im not good at math but im good with finding the answers to these type of problems
Step-by-step explanation:
hope this helps
There are 3 blue marbles, 6 red marbles, 2 green marbles and 1 black marble in a bag. You choose a marble, REPLACE it, and choose another. Find each probability
PLEASE HELP IM STRUGGLING
7) P (green and black) __
8) P (green, red) __
9) P (red, red) __
Answer:
Step-by-step explanation:
prob blue = 3/12 = 1/4
since you are replacing ,
prob(blue, blue) = (1/4)(1/4) = 1/16
Pam bought 20 pieces of fruit for her class.
o Each piece of fruit was either an apple or an orange.
o She spent $1.25 on each apple.
o She spent $0.95 on each orange.
o Pam spent a total of $22.60.
Write a system of equations that can be used to find the number of apples Pam bought. Make sure to define your variables.
Choose the correct define variables and the correct system of equations
Answer:
Step-by-step explanation:
Let O=number of oranges and A=number of apples.
O+A=20
O=20-A
1.25A+0.95O=22.60, using O found above makes this become
1.25A+0.95(20-A)=22.60
1.25A+19-0.95A=22.60
0.3A+19=22.60
0.3A=3.6
A=12, since O=20-A
O=20-12
O=8
So she bought 8 oranges and 12 apples. The question really only asks for the number of apples bought.
12 apples were bought.
Answer:
1.25x+0.95y=22.60
x is apples y is oranges
Step-by-step explanation:
20 - 12 = 8
1.25(12) + 0.95(8) = 22.60
1.25 · 12 = $15
0.95 · 8 = $7.60
15.00 + 7.60 = $22.60
i hope that makes sense
A ranch hand herded his cattle to some grazing land. Then he began riding back to the ranch,
which is due west, at 7 miles per hour. Simultaneously, the cows began moving away from
him, too, headed due east at 3 miles per hour. How long did it take for the herd and the
ranch hand to be 2 miles apart? (Please help me !!)
Answer:
1/5 hr or 12 min
Step-by-step explanation:
We are going to use the formula D = RT
Let t = the time for them to be 2 mi. apart
Then 7t = the distance the ranch hand traveled
and 3t = the distance the cows traveled
Since they traveled in opposite directions, the sum of their distances will give us how far they are apart.
So, 7t + 3t = 2
10t = 2
t = 2/10 = 1/5 hr. = 12 min.
a school is having a competition to see who can read the most books in one month (30 days). In the first 5 days, Jake reads 4 books. Meanwhile, Amy reads 5 books over 6 days. If they continue at these rates, who will win? By how many books?
Answer:
Amy will winStep-by-step explanation:
Jake
4 books ⇔ 5 days
x books ⇔ 30 days
5x = 4*30x = 120/5x = 24 booksAmy
5 books ⇔ 6 days
x books ⇔ 30 days
6x = 5*30x = 150/6x = 25 booksAmy will win by 25 - 24 = 1 book
Find the equation of the line.
Use exact numbers,
Answer:
y = 3x + 3
Step-by-step explanation:
Rise: 3 Run: 1
slope (m) = 3/1 = 3
y intercept (b) = 3
y = mx + b = 3x + 3
what does the 50th term of this arithmetic sequence: 29,32,35,38
Answer:
176
Step-by-step explanation:
First term (a) = 29
Common difference (d) = 32 - 29 = 3
For calculating the 50th term , n = 50
Now
[tex]t_{50} = a + ( n - 1) d\\t_{50} = 29 + ( 50 - 1 ) *3\\ t_{50} = 29 + 147\\t_{50} = 176[/tex]
hope it will help :)
what is a correct name fo the angle shown. R S RTS SRT
Four points A, B, C, and d are on a number line, in some order, so that AB=1, BC=2, CD=3, and DA=4. Which two points are farthest away from each other?
Answer: B or C sorry if its wrong
Step-by-step explanation: have a nice day
Can someone please give me the answer I’m giving brilliant for correct answer
Answer:
the last one (1,2)
Step-by-step explanation:
.......................
Answer:
C (-1,-2)
Step-by-step explanation:
The fourth vertex should be on the same Y value as the 2nd vertex and the same X value as the 3rd vertex so it should be (-1,-2)
HELP ME PLEASE
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Explain why the absolute value function y = |x| is an example of a piecewise function
Pls help with math ASAP due tonight
Answer:
The equation of the line is y=-1/2x-3.5
Step-by-step explanation:
Given the two points on the line, (1, -4) and (3, -5), find the slope of the line with the equation [tex]m=\frac{y2-x2}{y1-x1}[/tex].
[tex]m=\frac{-5-(-4)}{3-1} =\frac{-5+4}{3-1} =\frac{-1}{2}[/tex]
After you find the slope of the line, substitute x and y with either point given to you. For me, I'll use point (1, -4) to solve for the y-intercept.
[tex]-4=\frac{-1}{2} (1)+b[/tex]
[tex]\frac{1}{2} -4=\frac{-1}{2} +\frac{1}{2} +b[/tex] add both sides by 1/2 so that b is alone
[tex]\frac{-7}{2} =b[/tex]
You can rewrite -7/2 as -3.5.
Custom drapes are being fitted for a large circular
window. It is difficult to get these measurements, but the
window has an 8 ft horizontal shelf with a 2 ft brace that
sits in the frame. If the brace is extended upward, it
would go through the center of the shelf and the circle.
What is the diameter of the window?
Diameter =
feet
Help please
The basketball coach spent $35 on 5 t shirts for his team last season. This season, he needs to purchase 7 t shirts. If he pays the same rate as last year, how much will the t shirts cost?
Answer:
5 dollars
Step-by-step explanation:
last year he got 5 they were 7 dollars because 7x5 is 35 so do the same thing to do other it also equals 35
A high school drama department sold 238 tickets for their performance.
o An adult ticket cost $6.75.
o A student ticket cost $3.50.
o The high school drama department collected $1,252.25 in ticket sales.
How many student tickets were sold?
Answer:
$6.75 + $3.50 = X
X ÷ $1,252.25
Step-by-step explanation:
$6.75 + $3.50 = $10.25
$10.25 ÷ $1,252.25 = 0.00818526652
Help quick please I’m timed
Answer:
Midpoint.
It is equidistant.
Contamination problems in semiconductor manufacturing can result in a functional defect, a minor defect, or no defect in the final product. Suppose that, 20, 50 and 30% of the contamination problems result functional, minor and no defects respectively. Assume that the effects of 10 contamination problems are independent. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that the 10 contamination problems result in two functional defects and five minor defects
Answer:
The answer is "[tex]8.5\times 10^{-9}[/tex]".
Step-by-step explanation:
Following are the calculation of the multinomial distribution probability:
[tex]\to (\frac{10!}{(2! \times 5! \times 3!)})\times(0.2)^2 \times(0.5)^5 \times (0.3)^3 \\\\ \to (\frac{10!}{(2! \times 5! \times 3!)})\times 0.04 \times 0.03125 \times 0.027\\\\ \to (\frac{10\times9\times8 \times7 \times6 \times5! }{(2! \times 5! \times 3!)})\times 3.37 \times 10^{-5}\\\\ \to (\frac{10\times9\times8 \times7 \times6 }{(2 \times 1 \times 3 \times 2 \times 1 )})\times 3.37 \times 10^{-5}\\\\[/tex]
[tex]\to (\frac{10\times9\times8 \times7 }{(2)})\times 3.37 \times 10^{-5}\\\\ \to (5 \times 9 \times 8 \times 7 )\times 3.37 \times 10^{-5}\\\\ \to 45 \times 56 \times 3.37 \times 10^{-5}\\\\ \to 45 \times 56 \times 3.37 \times 10^{-5}\\\\ \to 2520 \times 3.37 \times 10^{-5}\\\\\to 8492.4 \times 10^{-5}\\\\\to 8.4924\times 10^{-9}\\\\ \to 8.5\times 10^{-9}[/tex]
Solve for x
x^2+ 6x + 9 = 12
Answer:
x=−3+2√3 or x=−3−2√3
Step-by-step explanation:
pretty please help me!!! i’ll mark brainliest! i tried putting this at 13 points!
Answer:
m∠T = 54°
Step-by-step explanation:
The measure of a straight line is 180°. (Linear angles theorem)
So, m∠WMT + 117° = 180°
m∠WMT = 180 - 117 = 63°
The base angles in an isoceles triangle are equal in measure (base angle theorem)
So,
m∠MWT = m∠WMT
m∠MWT = 63°
The sum of angles in a triangle is 180°. (Sum of angles in a triangle theorem) So,
m∠MWT + m∠WTM + m∠WMT = 180°
Substitute the measures we already found.
63 + m∠WTM + 63 = 180
Simplify.
126 + m∠WTM = 180
m∠WTM = 54°
m∠T = 54°
I hope this helps! Feel free to ask any questions!
Answer:
54°
Step-by-step explanation:
First calculate Angle WMT as: 180° - 117° = 63°
And note that Angle WMT = Angle MWT = 63°
Therefore, Angle T = 180° - 63° - 63°
Angle T = 54°