hello , how to do 6(iii)?
Answer:
[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}[/tex]
Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:
[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]
Therefore:
[tex]\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]
Next, the surface area of a sphere S is given by:
[tex]\displaystyle S=4\pi r^2[/tex]
Therefore:
[tex]\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}[/tex]
We can divide both sides by 2:
[tex]\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}[/tex]
We can substitute this into dV/dt. Rewriting:
[tex]\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)[/tex]
So:
[tex]\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}[/tex]
Since dV/dt = 0.03 or 3/100:
[tex]\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}[/tex]
Therefore:
[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)[/tex]
Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
David wants to buy a bowling ball that has a price of $120. As a member of a bowling league, he is entitled to a 15% discount off the price of the bowling ball. He will also have to pay 6% sales tax on the discounted price of the bowling ball. What is the final price David pays for the bowling ball, after the sales tax and discount applied?
Answer:
$109.2
Step-by-step explanation:
Given data
Cost of bowling ball= $120
DIscount= 15%
Tax= 6%
let us calculate the discount and tax
=15/100*120
=0.15*120
=$18
=6/100*120
=0.06*120
=$7.2
In all the bill is 120-18+7.2
=102+7.2
=$109.2
Find the sum of 0.5 and -0.5.
Amswer
The answer is 0
What is the equation of the linear function represented by the table?
y=-X+9
y=-x+ 13
Y = X+ 13
Y = X+9
Answer:
Step-by-step explanation:
I am sorry but please give detailed question where is the table
Indicate whether the following question is a statistical question. Explain why or why not.
How much does Susan’s dog weigh?
A total of 150 tickets were sold for the annual concert. Student tickets were $4 and non-students $8. If the total revenue was $840, how many tickets of each type were sold ?
Answer:
x = 90
y = 60
Step-by-step explanation:
Let x = student
Let y = non-student
x + y = 150
4x + 8y = 840 <—— Use elimination/addition ethos for both equations
8 (x + y = 150)
-1 (4x + 8y = 840) <—— Let’s eliminate y
8x + 8y = 1200
+ -4x - 8y = -840
—————————————
4x = 360
x = 90
x + y = 150 <— substitute for x from above
90 + y = 150
- 90 = - 90 <— subtract from both sides
y = 60
What is the slope of (4,2) and (0,-1)
Step-by-step explanation:
The slope is m = -3 / -4 = 0.75
Find the value of x.
I need to show my work.
Thank you~~~~~~~~
Answer:
180-72-72=36
90-36=54
180-54-54=72
72=7x-12
84=7x
x=12
Step-by-step explanation:
A new bank customer with $3,500 wants to open a money market account. The bank is offering a
simple interest rate of 1.1%.
a. How much interest will the customer earn in 10 years?
b. What will the account balance be after 10 years?
Answer:
A. they will earn 385 dollars in interest in ten years
B. the accounts balance will be $3,885 after 10 years
Step-by-step explanation:
for part A, there are 2 possible answers, depending on what your looking for, if your looking for the percentage interest, then its 11%, but if your looking for how much they will make off of interest in 10 years, then the answer would be $385.
x /− 8 + 9 = 43 x = ?
Solve for x Round to the nearest 100th if needed.
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
n
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
O y=-x+9
y=-*x+5
y=-3x - 11y
y=-3x + 25
Answer:
Y=-3x-11y
Step-by-step explanation:
Not sure but I am pretty sure it is this
Help me please!!
What is the speed of a wave with a wavelength of 2.0 m and a frequency of 6.0 Hz?
6m/s
calculate the number of balloon that can be filled up.
Step-by-step explanation:
speed =wavelength ×Frequency
=6×2 =12m/d
Here is the sales tax on the same items in City 3.
What is the tax rate in this city? Show work on the
sketch. (Remember to round to the nearest penny.)
Sales tax percentage
Check
For the sales tax on the laundry soap, Kiran says it
should be $0.84. Lin says it should be $0.87. Do you
agree with either of them? Explain your reasoning.
I agree with Kiran
I agree with Lin
I don't agree with either of them
Explain your thinking.
cause your multiplying the numbers
Edit my response
Answer:
This needs more detail.
Step-by-step explanation:
please answer and make sure youre right i got a 50
Answer and Step-by-step explanation:
First, let's solve for z.
3z - 1 ≥ -7
We add 1 to both sides.
3z ≥ -6
Now we divide both sides by 3.
z ≥ -2
Since we got this as our answer, that means Answer choice D is the correct answer.
#teamtrees #WAP (Water And Plant)
solve the equation P=b+c+a solve for b
Answer:
b = P - c - a
Step-by-step explanation:
Adriana y Luisa fueron a la feria y decidieron subirse a la rueda de la fortuna. Si el diámetro de la rueda es de 8 metros, ¿Qué recorrido hicieron dando una vuelta completa? Considera Pi= 3.14
Answer:
Translation?
Step-by-step explanation:
Solve 0 = x2 + 6x + 13 by completing the square.
A. x = 5 and x = 1
B. x = 3 + i22−−√ and x = 3 − i22−−√
C. x = −1 and x = 1
D. x = −3 + 2i and x = −3 − 2i
Answer:
x = -3 - 2i and x = -3 + 2i
Step-by-step explanation:
I was too lazy to complete the square but solved it on WolframAlpha
What are the terms in x - 53 - 4x - w + 6x + 8
Answer:
3x, -45, -w
Step-by-step explanation:
We want to simplify this expression to find which terms there are.
x - 53 - 4x - w + 6x + 8
We can group the x's, w's and constants.
(x - 4x + 6x) + (-53 + 8) + (-w)
3x - 45 - w
The terms are, 3x, -45, -w
Answer is 3x-w-45 how did I get the answer.
1. steps: x- 53 - 4x - w + 6x + 8
2. Steps: Group like terms x - 4x + 6x - w -53 + 8
3. Steps: Addsimilar elements: x - 4x + 6x = 3x
= 3x - w - 53 + 8
4. Steps: Add/Subtract the numbers: - 53 + 8 = -45
= 3x - w -45
That is your answer for this problem.
jack paid 36.25 for 12 1/2 for his car what is the price per gallon
Answer:
66.89
Step-by-step explanation:
Simplify: ⅕y - ⅗y + 5 - ⅖y - 8
pls
Answer:
The answer is -(4/5)y - 3.
Step-by-step explanation:
The steps are :
[tex] \frac{1}{5} y - \frac{3}{5} y + 5 - \frac{2}{5} y - 8[/tex]
[tex] = ( \frac{1 - 3 - 2}{5} y) + (5 - 8)[/tex]
[tex] = - \frac{4}{5} y - 3[/tex]
Step-by-step explanation:
⅕y - ⅗y + 5 - ⅖y - 8
-0.8y-3
-4/5y-3
lena purchased a prepaid phone card for $20. long distance call cost 18 cents a minute using this card. Lena used her cared only once to make a libg distance call. if the remaining credit on her card is $13.34, how many minutes did her call last?
Answer:
37 minutes
Step-by-step explanation:
We start by finding the difference between the original amount and what is left
Mathematically, that will be;
20-13.34 = 6.66
To
cents that will be 6.66 * 100 = 666 cents
We now divide by the amount per minute
The amount per minute is 18 cents
Thus, the number of minutes will
be 666/18 = 37
Someone plz help me
Answer:
8.5 i think
Step-by-step explanation:
Answer:
the answer would be 8.5 inches
Step-by-step explanation:
its 8and a half not 0.85 so its placed wrong
4.-2+ (-8)
I was wondering what’s the answer
Answer:
-10
Step-by-step explanation:
Answer:
4.−10..?
Step-by-step explanation:
Use Cymath.com for your math equations so you don't have to waste points on here!
Equivalent factored form for 10x^2+15x-9=2x^2+x-14
You are offered a job that pays $41,000 during the first year, with an annual increase of 7% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.07 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.
Answer:
50227
Step-by-step explanation:
Help? Please? And make sure the answer is right plz!! :) and have a good day
Answer:
-7
Step-by-step explanation:
The amount of degrees would be the same in both those corner/angle/section are. and have a good day as well!
A ______________ is a relation that assigns exactly one output value to one input value
Answer:
A __function__ is a relation that assigns exactly one output value to one input value.
Step-by-step explanation:
Answer:
A function is a relation that assigns exactly one output value to one input value.
1.Give one real world example in which we use volume of rectangular prisms.
2.Give one real world example in which we use surface area of rectangular prisms.
Answer:
construction workers uses those measurements for buildings and architects
Surface area
BRAINIEST WILL BE GIVEN
Answer:
716
Step-by-step explanation:
Answer:
856
Step-by-step explanation:
Suppose that 8% of all cars produced at Plant A have a certain defect, and 5% of all cars produced at Plant B have this defect. A quality control manager takes separate random samples of 150 cars from each plant. The manager will then look at the difference (A-B) between the proportions of cars with the defect in each sample.
What will be the shape of the sampling distribution of the difference in sample proportions, and why?
Choose 1 answer:
A. Approximately normal, because we expect 12 defective and 138 defect-free cars from Plant A, and 15 and 135 from Plant B, and all of these counts are at least 10.
B. Approximately normal, because we expect 16 defective and 134 defect-free cars from Plant A, and 10 and 140 from Plant B, and all of these counts are at least 10.
C. Not normal, because we expect fewer than 10 defective cars in Plant A.
D. Not normal, because we expect fewer than 10 defective cars in Plant B.
Answer:
Not normal, because we expect fewer than 10 defective cars in plant B
Step-by-step explanation:
Answer: D
Not normal, because we expect fewer than 10 defective cars in Plant B. [tex].05*150=7.5[/tex]
Step-by-step explanation: Khan Answer