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harkovskaia [24]

2 years ago

15

What is the exact volume of the cone? 80π ft³ 4003π ft³ 400π ft³ 418710π ft³ Outline of cone with a dotted line rising from midd

le of base to the point. Line is labeled sixteen feet. A second dotted line extends horizontally from middle of base to its edge. Line is labeled five feet. HELP ASAP

2 answers:

rodikova [14]2 years ago

6 0

Volume of cone = 1/3 x pi x r^2 x h
where r = 5 ft and h = 16ft

Volume = 1/3 x pi x 5^2 x 16 = 400/3 π ft^3

ivolga24 [154]2 years ago

4 0

Answer: $\text{Volume of cone}=\frac{400}{3}\pi\ ft^3$

Step-by-step explanation:

Given: Outline of cone with a dotted line rising from middle of base to the point. h = 16 feet

A second dotted line extends horizontally from middle of base to its edge r= 5 feet

We know that the volume of cone is given by :-

$\text{Volume of cone}=\frac{1}{3}\pi r^2h\\\\\Rightarrow\ \text{Volume of cone}=\frac{1}{3}\pi(5)^2(16)\\\\\Rightarrow\ \text{Volume of cone}=\frac{1}{3}\pi(25)(16)\\\\\Rightarrow\ \text{Volume of cone}=\frac{400}{3}\pi\ ft^3$

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9966 [12]

Answer:

a) P-value = 0.0968

b) P-value = 0.2207

c) P-value = 0.0239

d) P-value = 0.0040

e) P-value = 0.5636

Step-by-step explanation:

As the hypothesis are defined with a ">" sign, instead of an "≠", the test is right-tailed.

For this type of test, the P-value is defined as:

$P-value=P(z>z^*)$

being z* the value for each test statistic.

The probability P is calculated from the standard normal distribution.

Then, we can calculate for each case:

(a) 1.30

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(b) 0.77

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(c) 1.98

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(d) 2.65

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7 0

2 years ago

Kim drove 627 miles in 9.5 hours. What is

Zarrin [17]

Answer:

Step-by-step explanation:

66 mile per hour .

4 0

2 years ago

119.31 is 82% of what number

madam [21]

To solve
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Hope this helps :)

5 0

1 year ago

Read 2 more answers

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the account after 24 years, to t

Amanda [17]

Answer:

A = $18,326.00

(assuming simple interest)

Step-by-step explanation:

Assuming simple interest, the following formula applies:

final amount = (principal amount) x [1 + (annual rate)(time elapsed) ]

or

A = P (1 + rt)

in our case,

P = $7,700

r = 5.75% = 0.0575

t = 24 years

hence,

A = 7700 [ 1 + (0.0575)(24)]

A = 7700 ( 1 + 1.38)

A = 7700 x 2.38

A = $18,326.00

4 0

2 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

1 year ago