What is the volume of a circular mine passage that is 19.0 feet in diameter and 210.0 feet long?

Answers

Answer 1

Answer: $d = diameter : d =19 \ ft \n \nradius : r=(d)/(2)=(19)/(2)=9.5 \ ft \n\n length of object : \ h=210 \ ft \n\nCircle Area : \ A= \pi r^2\n \nCircular Volume = A*h = \pi r^2h \n \nCircular Volume = \pi\cdot 9,5^2*210 =90,25 \cdot 210\cdot \pi =18952.5 \ \pi \ ft^3$

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Look at the image of the table of values below. Over which interval of x is the average rate of change the largest?

Answers

Between 5 & 8.

$\displaystyle {21-15\over 8-5} = 6/3 = 2$ is the largest rate of change, differentiating from $5\over3$ and $11\over6$

Jillian is selling boxes of cookies to raise money for her basketball team. the 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. at the end of one week, she collected $97.50, selling a total of 24 boxes. the system of equations that models her sales is below.x y= 24

3.50x 5.00y = 97.50

solve the system of equations. how many 10 oz. boxes were sold?

6
9
12
15

Answers

Answer:

Step-by-step explanation:

If 10 oz. box costs $3.50 and a 16 oz. box costs $5.00 and she collected $97.50 we can represent an expression that relates for how many money Jillian made:

$3.5*x+5*y=97.50$ (1)

where x is the number of 10 oz. boxes and y is the number of 16 oz. boxes.

She sold 24 boxes therefore:

$x+y=24$ (2)

We can right equation in terms of y and substitute it into equation 1:

$y=24-x$ (2)

$3.5*x+5*(24-x)=97.50$

Solve for x:

$x=15$

Jillian sold 15 10oz. boxes

x + y = 24...y = 24 - x
3.50x + 5.00y = 97.50

3.50x + 5(24 - x) = 97.50
3.50x + 120 - 5x = 97.50
3.50x - 5x = 97.50 - 120
-1.5x = -22.50
x = -22.50/-1.5
x = 15....there were 15 ten oz boxes (x) sold

Charlie solved an equation, as shown below:Step 1: 5x = 30

Step 2: x = 30 - 5

Step 3: x = 25

Part B: How many solutions will this equation have?

Answers

well the equation should lead up to about four solutions byut my calculation might be wrong

A water pitcher weighs 1.72 kg when empty and 2.01 kg when filled with water. How much does the water weigh?

Answers

the water weigh:
2.01-1.72=0.29kg

Y=8 when x=20 find y when x= 30

Answers

Answer:

y=13

Step-by-step explanation:

if x=20 when y=8 (we can creat equation )

x=2y+4 (you can prove that the equation is correct by substitute )

so the question is if x=30 find the value of y

30=2y+4

30‒4=2y

26=2y

26/2=2y/2

13=y

i hope this helps you

Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000? A. 10 years. B. 6 years. C. 7 years. D. 4 years

Answers

You need to use the equation y=p(1+r)^t where p= the principle (initial amount), r= the rate of decay or growth, and t= the time. So y=5,000(1.03)^x is the equation you'd want to use. At 6 years you'd have $5,970.3 and at 7 $6,149.40, so the answer is C.

taking into consideration that the interest is compound (yearly)
the amount of money gather through the years can be calculated by

A = P (1+r)^(t)
6000 = 5000 (1.03)^t

t = ln(6000/5000)/ln(1.03) = 6.16 ≈ 7

c. 7 years

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