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3 years ago

How does the volume of a cone change when the radius is quadrupled and the height id reduced to 1/5 of the original size?

1 answer:

8 0

The volume (V) of the cone is one-third of the product of its height (h) and area (A).
V = A x h = πr²h
Now, if the radius is quadrupled and the height is reduced to 1/5, the equation will be,
V2 = π(4r)²(1/5 h) = π(3.2)r²h
Thus, the second volume would be 3.2 time the first volume.

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What is the common ratio in this sequence: 3, 12, 48, 192? A. 1/4 B. -4 C. 3 D. 4

frozen [14]

I believe c is correct!!!!

4 0

2 years ago

Read 2 more answers

Find number a and k so that x-2 is afactor<br>OF F(x)=x4-2ax tax-<br>X+k and F(-1)=3

Slav-nsk [51]

Question:

Find numbers a and k so that x-2 is a factor of

$f(x)=x^4-2ax^3+ax^2- x+k$

and

$f(-1)=3$

Answer:

$k = -2$ and $a=1$

Step-by-step explanation:

Given

$f(x)=x^4-2ax^3+ax^2- x+k$

$Factor:\ x - 4$

$f(-1)=3$

Required

Find a and k

For $f(-1)=3$

Substitute -1 for x

$f(x)=x^4-2ax^3+ax^2- x+k$

$f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k$

$f(-1) = 1 - 2a *-1 + a*1 +1 + k$

$f(-1) = 1 +2a + a +1 + k$

$f(-1) = 2 +3a + k$

Substitute 3 for f(-1)

$3 = 2 +3a + k$

Collect Like Terms

$3 - 2 = 3a + k$

$1 = 3a + k$

Also:

If $x - 2$ is a factor, then

$f(2) = 0$

Substitute 2 for x and 0 for f(x)

$f(x)=x^4-2ax^3+ax^2- x+k$

$0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k$

$0 = 16 - 2a * 8 + a * 4 - 2 + k$

$0 = 16 - 16a + 4a - 2 + k$

$0 = 16 - 12a - 2 + k$

Collect Like Terms

$2 - 16 = - 12a + k$

$-14 = k - 12a$

$k = 12a - 14$

Substitute 12a - 14 for k in $1 = 3a + k$

$1 = 3a + 12a - 14$

$1 = 15a - 14$

Collect Like Terms

$15a = 1 + 14$

$15a = 15$

Solve for a

$a = \frac{15}{15}$

$a=1$

Substitute 1 for a in $k = 12a - 14$

$k = 12 * 1 - 14$

$k = 12 - 14$

$k = -2$

3 0

2 years ago

Landon is building new bookshelves for his bookstores new mystery section. Each shelf can hold 34 books. There are 1,265 mystery

nignag [31]

1,265 divided by 34 is 37.20
You can't put a fraction of a book on a shelf so each shelf will have ABOUT 37 books

Make sure you include ABOUT in your answer

4 0

2 years ago

What is 1/144 as an expression using a negative exponent

MrRissso [65]

ANSWER

${12}^{ - 2}$

EXPLANATION

The given expression is

$\frac{1}{144}$

This is the same as:

$\frac{1}{12 \times 12}$

In index notation, we write this as

$\frac{1}{ {12}^{2} }$

To write this as a negative index, we use the property:

$\frac{1}{ {a}^{m} } = {a}^{- m}$

This implies that;

$\frac{1}{ {12}^{2} } = {12}^{ - 2}$

3 0

2 years ago

Given the relation {(1, 4), (3, 6), (5, 4), (1, 8)},

skelet666 [1.2K]

Answer:

The domain of relation is {1,3,5}

It is not a function.

Step-by-step explanation:

Given the relation {(1, 4), (3, 6), (5, 4), (1, 8)}

We need to find the domain and determine if the given relation is function or not.

The domain of relation is {1,3,5}

But the given relation is not function because we have x=1 twice in the relation and the for the relation to be function the values of domain can't be repeated.

So, It is not a function.

5 0

2 years ago