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3 years ago

4. Nguyen is decorating the room for her sister's baby shower party. She is wrapping

Mathematics

1 answer:

Marianna [84]3 years ago

7 0

Answer:

Step-by-step explanation:

Given the information of the conical hat

diameter of 16 inches => Radius = 8 inches
height of 9 inches

=> the slant height of the hat is (use Pythagorean Theorem)

$s^{2}$ = $r^{2} + h^{2}$

<=> $s^{2}$ = $8^{2} + 9^{2}$

<=> s = $\sqrt{145}$

The area (without the base area) of tissue paper will she need to make one hat is:

SA = πrs in2

<=> SA = π*8* $\sqrt{145}$ in2

<=> SA =8 $\sqrt{145}$ π

=> the total tissue paper will she need for 21 hats is:

SA*21

= 8 $\sqrt{145}$ π*21

= 6352,18 in 2

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What type of exponential function is f(x)=0.6(2.4)^x ?

Vsevolod [243]

Answer:

<em>The function is of an exponential growth type</em>

<em>Rate of change is 240%</em>

Step-by-step explanation:

<u>Exponential Function</u>

The expression of an exponential function is

$f(x)=c.a^{bx}$

For a,b,c constants.

The function will be of an exponential growth type if, when x increases, f increases. That behavior comes from the combination of the three constants a,b,c. The best approach to find that out is by taking the first derivative

$f'(x)=b.c.lna.a^{bx}$

Since $a^{bx}$ is always positive, the product of b.c.lna must be positive to make f increasing. For example, if a>1 and both b and c are of the same sign, f increases for all x. If 0<a<1, then, since lna<0, the product b.c must be negative, i.e. both should have different signs

The function is expressed as

$f(x)=0.6\ 2.4^x$

we can see a>1, b and c are positive, so the function is of an exponential growth type.

Talking about rates change of real functions takes us to the derivative function. We have already seen the derivative is dependent on all three constants and also of the value of x, so it cannot be predicted as a fixed percentage.

Now, if we picture the function as the general term of a sequence, where x can only take natural values, we can say

$\displaystyle \frac{0.6(2.4)^{x+1}}{0.6(2.4)^{x}}=2.4$

Each term is obtained as the previous term by 2.4. It's accurate to say the rate of change is 240%

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3 years ago

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mars1129 [50]

We have to select all of the transformations that could change the location of the asymptotes of a cosecant of secant function.

So given function can be written as:

y=csc( sec(x))

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From attached graph we see that Asymptotes (Green lines) are vertical.

So Vertical shift or vertical stretch will not affect the location of asymptote because moving up or down the vertical line will not change the position of any vertical line.

only Left or right side movement will change the position of vertical asymptote. Which is possible in Phase shift and period change.

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3 years ago

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What type of 3D shape is this and how do you know?

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3 years ago

Use the ordinary division of polynomials to find the quotient and remainder when the first polynomial is divided by the second.

Vanyuwa [196]

The quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively

<h3>How to determine the quotient and remainder when the first polynomial is divided by the second?</h3>

The polynomials are given as:

-4w^3 + 5w^2 - 8, w - 3

Set the divisor to 0.

So, we have

w - 3 = 0

Add 3 to both sides

w = 3

Substitute w = 3 in -4w^3 + 5w^2 - 8 to determine the remainder

-4(3)^3 + 5(3)^2 - 8

Evaluate the expression

-71

This means that the remainder when -4w^3 + 5w^2 - 8 is divided by w - 3 is -71

The quotient (Q) is calculated as follows:

Q = [-4w^3 + 5w^2 - 8]/[w - 3]

The numerator can be expressed as follows:

Numerator = -4w^3 + 5w^2 - 8

Subtract the remainder.

So, we have:

Numerator = -4w^3 + 5w^2 - 8 + 71

This gives

Numerator = -4w^3 + 5w^2 + 61

So, the quotient becomes

Q = [-4w^3 + 5w^2 + 61]/[w - 3]

Expand

Q = [(w - 3)(-4w^2 - 7w - 21)]/[w - 3]

Evaluate

Q = -4w^2 - 7w - 21

Hence, the quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively