Water is flowing into a large spherical tank at a constant rate. Let V(t) be the volume of water in the tank and H(t) be the height of the water level at time t.
a) Give a physical interpretation of dV/dt and dH/dt.
b) Is dV/dt positive, negative, or zero when the tank is one-fourth full? Justify your answer.
c) Is dH/dt positive, negative, or zero when the tank is one-fourth full? Justify your answer.

Answers

Answer 1

Answer:

A) dV/dt = the rate of change of the given volume of water in the tank with respect to the time, t.

dH/dt = the rate of change of the height of the water in the tank with respect to the time

B) dV/dt is positive

C) dH/dt is positive

Step-by-step explanation:

We are given that;

V(t) is the volume of water in the tank and H(t) is the height of the water level at time t. Thus;

A) dV/dt = the rate of change of the given volume of water in the tank with respect to the time, t.

dH/dt = the rate of change of the height of the water in the tank with respect to the time

B) When the tank is one-fourth full, dV/dt is positive because the volume water in the tank is increasing with time.

C) when the tank is one-fourth full, dH/dt is positive because the height has increased from zero level to 0.25 times the height of the tank. Thus the height is increasing with time.


Related Questions

(a) Complete the table of values for the graph x + y = 6

Please help ❤️ complete the table leave the graph bit as I know how to do it

Answers

Answer:

(0,6)

(1,5)

(2,4)

(3,3)

(4,2)

Step-by-step explanation:

To solve this table first convert the equation to slope-intercept form (y=mx+b), to do this solve for y in the equation. The slope-intercept form is y=-x+6, where -1 is the slope and 6 is the y-intercept. Then from that, you can get your first point, because you know the y-intercept is 6, therefore when x equals 0 y must be 6. Next, because the slope is -1 that means the y-value decreases by 1 every time the x-value increases by 1. So to find the rest of the y-values simply subtract 1 from the previous y-value.

Help please!!!!!!!!!!!!!!!!

Answers

All you would have to do is substitute!
Answer:

First one will be 2
Second one will be 10
Third one will be undefined

Explanation:
So for the first one you are substituting x for -3 so then the equation would look like this: -3^2+9/-3^2, this will equal to 9+9/9 which your answer would be 2 since 18/9 is 2. For the second one it will look like this -1^2+9/-1^2 which would be 1+9/1, this would equal to 10. For the last one it will look like this 0^2+9/0^2 which would just be 0+9/0 9/0 would be undefined.

#4 . Simplify the expression 2(x − 8) + 2(12). *

Answers

Answer:

x = -4

Step-by-step explanation:

2x-16+24 = 2x+8

2x = -8

x = -4

Hey there!

2(x - 8) + 2(12)

DISTRIBUTE 2 WITHIN PARENTHESES

= 2(x) + 2(-8) + 2(12)

= 2x - 16 + 24

COMBINE the LIKE TERMS

= 2x + (-16 + 24)

= 2x + 8


Therefore, your answer is: 2x + 8


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Noah earned $232.70 at his job for 13 hours . How much money did he earned each hour

Answers

Answer: $20.82 per hour

Step-by-step explanation:

Answer:

$17.90 per hour

Step-by-step explanation:

Take $ 232.70 and divide it by 13 hours. Noah earned $17.90 every hour he worked.

need the answer please thank you!

Answers

Answer:

Step-by-step explanation:

Givens

a1 = -70

d = -10

an = - 100

Formula

an = a1 + (n - 1)*d

Solution

-100 = -70 + (n - 1)*-10               Remove the brackets.

-100 = - 70 + -10n + 10              Combine

-100 = -60 - 10n                        Add 60 to both sides

-100+60 = -60+60 - 10n           Combine

-40 = - 10n                                 Divide by - 10

-40/-10 = n

n = 4

ILL GIVE U A BRAINLIST
PLEASE I NEED HELP WITH THIS MATH HOMEWORK
I NEED EXPLANATION TOO!
Question: find the value of the varible

Answers

Answer:

2x+x+90=180 <-----Sum of angles in a triangle

3x+90=180<-------- Solve

3x=90

x=30

Step-by-step explanation:

C. What temperature is halfway between 3 degrees and -11degrees? And what is the mid point between -6 degrees and -10? And what is the midpoint between -60 degrees and 8 degrees?

Answers

Answer:

-4 is in between 3 and -11 is

-8 is in between -6 and -10

-26 is in between -60 and 8

Which is the best estimate for 19% of 205?


A- 40
B- 50
C- 100
D- 400

Answers

A. 40 is the correct answer

The best estimate for expression of 19% of 205 is 40.

Option A is the correct answer.

What is a percentage?

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying by 100.

The percentage change is also calculated using the same method.

In percentage change we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

To find a percentage of a number, we can convert the percentage to a decimal by dividing it by 100.

In this case, we want to find 19% of 205.

To do this, we first convert 19% to a decimal by dividing it by 100:

19 ÷ 100 = 0.19

This tells us that 19% is equivalent to 0.19 as a decimal.

Next, we multiply the decimal by the given number, which in this case is 205:

205 x 0.19 = 38.95

Therefore,

The best estimate for 19% of 205 is 40.

Learn more about percentages here:

https://brainly.com/question/11403063

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15. Express 2/5 as a percentage​

Answers

Answer:

[tex]40\%[/tex]

Step-by-step explanation:

[tex] \frac{2}{5} \times 100 = 40\%[/tex]

Divide 2 by 5 to get a decimal, then multiply the decimal by 100 to get a percent.

2/5 = 0.4

0.4x100 = 40

2/5 = 40%

37.
A bag contains 7 raspberry candies, 13 caramel candies, and 5
coffee candies. You are going to reach into the bag and pull out
some candies without looking. What is the least number of
candies that you must pull out to be sure that you have
removed at least three coffee candies?
if August 3rd wos four days after one

Answers

Answer:

15

Step-by-step explanation:

There are total cadies in the bag:

7 + 13 + 5 = 25

Probability of pulling a coffee candy is:

5/25 = 1/5

So each 5th candy should be coffee candy

Then you need to pull at least:

5*3 = 15 candies

Note:

To ensure 3 coffee candies you would need to pull 25 - 2 = 23 candies

Melissa wants to buy a new boat but needs money for the down payment. Her parents agree to lend her money at an annual rate of 4%, charged as simple interest. They lend her $3,000 for 3 years. She makes no payments except the one at the end of that time.

Answers

Answer:

never give her money again

What is 5 minus 3 2/7?

Answers

Answer:

1 5/7

abcdefghijklmnopqrstuvwxyz

Answer:

1 and 5/7?

Step-by-step explanation:

if i read that correctly that would read as 5 - 3 and 2/7. therefore when i subtract the whole number first i get 2. Then i proceed to subtract the fraction. which would leave me with 1 and 5/7.

A radio rs 3200 without VAT and rs 3600 including VAT. find the VAT amount and the VAT percentage.​

Answers

Answer:

amount: rs 400

percentage: 12.5%

Step-by-step explanation:

Before VAT: rs 3200

After VAT: rs 3600

VAT = 3600 - 3200 = 400

VAT = rs 400

percent = part/whole * 100%

percent = 400/3200 * 100%

percent = 12.5%

11. Find the missing number 1:2 = 3:
O A. 2
OB. 1
OC.3
OD. 6

Answers

Yh I think the missing number will be 6 because they are equivalent to 1:2

Answer:

c. hhhhhhhhhhhhuhuuuuuuuuuuuuuuuuuuuuu

For the equation, x-7=24, can a value be substituted for x to make that a true number sentence? How many values could be substituted for x and have a true number sentence?

Answers

we add 7 to both sides, making x=31. we can substitute 31 and make the true number sentence.
only 31 can be substituted, as it is only one x value, holding only one true value, which we found out is 31.
hope this helped!! xx

Answer:

1 variable or 31

Step-by-step explanation:

7+24=31 giving you the only variable

For a left-tailed test, the critical value of z so that a hypothesis test would __________ the null hypothesis at 5% significance level would be __________

Answers

Answer:

A) Reject

B) [tex]-Z_0_._0_5=-1.64485363[/tex]

Step-by-step explanation:

From the question above

Significance level =5%=0.05

a)Generally the first dash is Reject to aid the alternative hypothesis without which the is no need to test

b)Generally we solve mathematically for a critical value

critical value [tex]= -Z_\alpha[/tex]

From normal table

[tex]-Z_0_._0_5=-1.64485363[/tex]

Answer:

1.65

Step-by-step explanation:

gang gang

Calculate the average rate of change for the given function, from x = −3 to x = 7.

Answers

Answer:

The average rate of change for the given function, from x = −3 to x = 7 will be:

Average rate = -5

Step-by-step explanation:

Given the table

x                      f(x)

-3                     50

3                      10

7                       0

As the interval is from x = -3 to x = 7.

so

at x₁ = -3, f(x₁) = 50

at x₂ = 7,  f(x₂) = 0

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]

                       = [0 - 50] / [7-(-3)]

                      = [-50] / [7+3]

                      = -50 / 10

                      = -5

Therefore, the average rate of change for the given function, from x = −3 to x = 7 will be:

Average rate = -5

What is the answer for number 8 and 9 do not worry about 10

Answers

Answer:

8. 2

9. C

Hope this helps :)

Help plssssssssssssssssss

Answers

Answer:

It would be C.

Step-by-step explanation:

This is because they allow it to be 50 dollars and less, making it C.

A bag contains colored tiles.

* 7 tiles are red

* 6 tiles are green

* 7 tiles are blue

A tile will be randomly selected from the bag. What is the probability in decimal form that the tile selected will be green?

Answers

Answer:

0.35

Step-by-step explanation:

· The list price of an article is 25% above the selling price and the cost
price is 40% below the list price. Find the rate of discount and profit?

Answers

Answer:

p=25%

discount=25%

Step-by-step explanation:

Cost Price = 1.25 x - .4(1.25x)= 1.25x- .5x

Cost Price = .75x

S P = C+P

Profit = Selling price - Cost price

= x - 0.75x

=0.25x

the Profit is 25 %

Discount is 25 %

Millie has 2 apples, If millie picks 158 more, How many apples does millie have in all.

Answers

Answer:

160 APPLES

Step-by-step explanation: I WISH U ALL THE BEST IN EVERY OF YOURS

PLS MARK AS BRAINLIEST.

Answer:

160 apples

Step-by-step explanation:

You deposit $300 in a savings account that pays 6% interest compounded semiannually. How much will you have at the middle of the first year? How much at the end of one year?

Answers

Answer:

Please check the explanation.

Step-by-step explanation:

a)  How much will you have at the middle of the first year?

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 0.5 years

Total amount = A = ?

Using the formula

[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]

substituting the values

[tex]A=300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(0.5\right)}[/tex]

[tex]A=300\cdot \frac{2.06}{2}[/tex]

[tex]A=\frac{618}{2}[/tex]

[tex]A=309[/tex] $

Therefore, the total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 300.00 at a rate of 6% per year  compounded 2 times per year  over 0.5 years is $ 309.00.

Part b) How much at the end of one year?

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 1 years

Total amount = A = ?

Using the formula

[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]

so substituting the values

[tex]A\:=\:300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(1\right)}[/tex]

[tex]A=300\cdot \frac{2.06^2}{2^2}[/tex]

[tex]A=318.27[/tex] $

Therefore, the total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 300.00 at a rate of 6% per year  compounded 2 times per year  over 1 year is $ 318.27.

The difference of five times a number and 6 totals 29

Answers

Step-by-step explanation:

Let x represent the number.

We have 5x - 6 = 29 or 6 - 5x = 29.

=> 5x = 35 or 5x = -23

=> x = 7 or x = -4.6.

The number can be 7 or -4.6.

We have 5x - 6 = 29 or 6 - 5x = 29.

=> 5x = 35 or 5x = -23

=> x = 7 or x = -4.6.

The number can be 7 or -4.6.

PLEASE HELP !!
ILL GIVE BRAINLIEST
MATH PROBLEM!!
Find scale factor

Answers

Answer:

I think the scale factor is 2.5

Step-by-step explanation:

because 20 divided by 8 is 2.5

Define the type of sequence 7,14,28,56,112

Answers

Step-by-step explanation:

7 * 2 = 14

14 * 2 = 28

28 * 2 = 56

56 * 2 = 112

Every term is 2x the preceding term.

Hence the sequence is a geometric progression. (GP)

What is the value of point a on the number line?

I need help ASAP

Answers

Answer:

The answer is 7/6

George is given two circles, circle O and circle X, as shown. If he wants to
prove that the two circles are similar, what would be the correct second step
in his proof?
Given: The radius of circle O is r, and the radius of circle Xis t.
Prove: Circle Ois similar to circle X.
1.c - 2sr and C'- 2rr' by the definition of circumference.
2.
3. d= 2rand d = 2 by the definition of diameter.
4. d 2r and d ;by the division property of equality.
5.2 and by the substitution property.
d'-2r
6. Circle Ois similar to circle Xbecause all the linear dimensions are in the
same proportion.
(

Answers

Answer:

B the division one

Step-by-step explanation:

The solution is, : B.) The correct second step for the given proof is;

C/C' = 2πr/2πr' and, C/C' = r/r'

by the division property of equality.

What is division?

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

Explanation:

We want to find the correct second step for the given proof.

Recall that from division property of equality, when we have;

a=b and c=d, dividing the equations by each other, the equation will still be equal;

a/c = b/ d

For the given Prove;

statement 1 states that the circumference circle 1 and 2 can be expressed as;

C = 2πr and, C' = 2πr'  

So, for step 2;

Applying the division property of equality, we have;

C/C' = 2πr/2πr'

which then equals,

C/C' = r/r'

Therefore, the correct second step for the given proof is;

C/C' = 2πr/2πr' and, C/C' = r/r'

by the division property of equality.

To learn more on division click:

brainly.com/question/21416852

#SPJ7

Please help me I need to turn in tomorrow

Answers

Answer:

D. 0.5

Step-by-step explanation:

There are 4 groups

1. Alto

2. Bass

3. Tenor

4. Soprano

The question says "what is the probability that this member comes from the alto section"

Since there are 4 groups, I did 4/8 (since there are 8 people in Alto) and I got 0.5.

Hope I got it right and it helped you

*Note* I most likely got it right I just doubt myself too much lol

But just in case, I hope I got it right.

Answer:

there are 4 parts in that choir and the alto members are 8 in number so we say those in alto divided by the number of parts, we get→ 4÷8 =0.5, that's the ans.

what is 33.7 divided by 9.5 equals ?

Answers

Answer:The answer is 3.5273684211

Step-by-step explanation:

I your round it up then it would be 3.5

Answer:

33.7/9.5 = 3.547368421...

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