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3 years ago

Simplify (1/4 ad^3)^2

1 answer:

7 0

That "ad^3" bothers me; I'm not sure what you mean here.

I'm going to assume that you have (1/4*a*d^3)^2.

If that's the case, then you have (1/4)^2 * a^2 * d^6 = (1/16)*a^2*d^6.

If this is not what you were hoping for, double check to ensure that you have copied down this problem exactly as it was presented.

You might be interested in

-9/14 + 2/7 4 + (- 1 2/3) 15/4 + (-4 1/3)

vladimir2022 [97]

Answer:

it is b

Step-by-step explanation:

u welcome if im correct

4 0

3 years ago

Read 2 more answers

A 15-ft ladder leans against a wall. The lower end of the ladder is being pulled away from the wall at the rate of 1.5 ft/sec. L

Aleks [24]

Answer:

The top of the ladder is sliding down at a rate of 2 feet per second.

Step-by-step explanation:

Refer the image for the diagram. Consider $\Delta ABC$ as right angle triangle. Values of length of one side and hypotenuse is given. Value of another side is not known. So applying Pythagoras theorem,

$\left ( AB \right )^{2}+\left ( BC \right )^{2}=\left ( AC \right )^{2}$

From the given data, $L=15\:ft=AC$ , $y=9\:ft=AB$ and $x=BC$

Substituting the values,

$\therefore \left ( 9 \right )^{2}+\left ( x \right )^{2}=\left ( 15 \right )^{2}$

$\therefore 81+x^{2}=225$

$\therefore x^{2}=225-81$

$\therefore x^{2}=144$

$\therefore \sqrt{x^{2}}=\sqrt{144}$

$\therefore x=\pm 12$

Since length can never be negative, so $x= 12$ .

Now to calculate $\dfrac{dy}{dt}$ again consider following equation,

$\left ( y \right )^{2}+\left ( x \right )^{2}=\left ( l \right )^{2}$

Differentiate both sides of the equation with respect to t,

$\dfrac{d}{dt}\left(y^2+x^2\right)=\dfrac{d}{dt}\left(l^2\right)$

Applying sum rule of derivative,

$\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(l^2\right)$

$\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(225\right)$

Applying power rule of derivative,

$2y\dfrac{dy}{dt}+2x\dfrac{dx}{dt}=0$

Simplifying,

$y\dfrac{dy}{dt}+x\dfrac{dx}{dt}=0$

Substituting the values,

$9\dfrac{dy}{dt}+12\times1.5=0$

$9\dfrac{dy}{dt}+18=0$

Subtracting both sides by 18,

$9\dfrac{dy}{dt}=-18$

Dividing both sides by 9,

$\dfrac{dy}{dt}= - 2$

Here, negative indicates that the ladder is sliding in downward direction.

$\therefore \dfrac{dy}{dt}= 2\:\dfrac{ft}{sec}$

7 0

3 years ago

Shay works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with

Masja [62]

Answer:

Function: $p(x)=20(1.04)^x$

Range: option D. 20 ≤ x ≤ 27.37

Explanation:

The function must meet the rule that the pay starts at $20 and it increases each hour by 4%.

A table will help you to visualize the rule or pattern that defines the function:

x (# hours) pay ($) = p(x)

0 20 . . . . . . . . [starting pay]

1 20 × 1.04 . . . [ increase of 4%]

2 20 × 1.04² . . . [increase of 4% over the previous pay]

x 20 × 1.04ˣ

Hence, the function is: $p(x)=20(1.04)^x$

The range is the set of possible outputs of the function. To find the range, take into account that this is a growing exponential function, meaning that the least output is the starting point, and from there the output will incrase.

The choices name x this output. Hence, the starting point is x = 20 and the upper bound is when the number of hours is 8: 20(1.04)⁸ = 27.37.

Then the range is from 20 to 27.37 (dollars), which is represented by 20 ≤ x ≤ 27.37 (option D from the choices).

5 0

3 years ago

Read 2 more answers

Students were asked to write 6x^5 + 8x-3x^3+7x^7 in standard form

Klio2033 [76]

The standard form is $7x^7 + 6x^5 -3x^3 + 8x$

Solution:

Given that we have to write the given equation in standard form,

$6x^5 + 8x - 3x^3 + 7x^7$

In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write

The terms are ordered from biggest exponent to lowest exponent

In the given equation,

$6x^5 + 8x - 3x^3 + 7x^7$

7 is the highest exponent. So we write the standard form as,

$7x^7 + 6x^5 -3x^3 + 8x$

Thus the terms are arranged from highest exponent to lowest exponent

5 0

3 years ago

What is the simplified expression for

Romashka-Z-Leto [24]

Use FOIL.

-3(2x - y) + 2y + 2(2x - y)
-6x + 3y + 2y + 4x - 2y
Simplify.
-6x + 5y + 4x - 2y
-2x + 5y - 2y
-2x + 3y <-------------Answer

4 0

3 years ago