What is the volume of the right rectangular prism?

Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by

elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)

3 0

2 years ago

Please help I will give you brainliest

mezya [45]

Answer:

Answer is 5 3/4

Step-by-step explanation:

Thanks Hope this helps

5 0

3 years ago

If the areas of the given pairs of shapes are equal, find the value of x.

den301095 [7]

Answer:

$x = 8cm$

Step-by-step explanation:

we are given a square and rectangle.we want to figure out x which is the width of the rectangle. we are also given a condition i.e

the area of the square equal to the area of the rectangle

therefore,

$\displaystyle \rm A _{square } = A _{rect}$

recall the formula of the area of square and rectangle so,

$\displaystyle {s}^{2} = lw$

now assign variables

$s \implies16cm$
$l \implies32cm$
$w \implies x$

thus substitute:

$\displaystyle 32cmx = {16cm}^{2}$

simplify square:

$\displaystyle 32cmx = 256cm^2$

divide both sides by 32:

$\displaystyle \boxed{x = 8cm}$

and we're done!

3 0

2 years ago

Read 2 more answers

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statisti

jeyben [28]

Answer:

We need a sample of size at least 13.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

90% confidence interval: (0.438, 0.642).

The proportion estimate is the halfway point of these two bounds. So

$\pi = \frac{0.438 + 0.642}{2} = 0.54$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

We need a sample of size at least n.

n is found when M = 0.08. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.08 = 1.96\sqrt{\frac{0.54*0.46}{n}}$

$0.08\sqrt{n} = 1.96\sqrt{0.54*0.46}$

$\sqrt{n} = \frac{1.96\sqrt{0.54*0.46}}{0.08}$

$(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.54*0.46}}{0.08})^{2}$

$n = 12.21$

Rounding up

We need a sample of size at least 13.

3 0

3 years ago

Below is a diagram of Hillcrest High School. The english and math buildings are congruent rectangles. The art building is a squa

rusak2 [61]

Answer/Step-by-step explanation:

1. Perimeter of the building = sum of all the length of the outer borders surrounding the building = 1,718 ft

Thus:

4x - 6 + 2x + 3x + 2(3x + 4) + 3x + 2x + x + x + x + 2x + 4x - 6 + 2(3x + 4) + 4x - 6 + 3x = 1,718

Open the Parentheses

4x - 6 + 2x + 3x + 6x + 8 + 3x + 2x + x + x + x + 2x + 4x - 6 + 6x + 8 + 4x - 6 + 3x = 1,718

Combine like terms

42x - 2 = 1,718

42x = 1,718 + 2

42x = 1,720

x ≈ 41

2. Missing perimeter of Building = 2x + 2x + 4x - 6

Simplify

= 8x - 6

Plug in the value of x

= 8(41) - 6

= 322 ft

3. Area of English Building = length * width

= (4x - 6 + 2x)(3x)

Simplify

= (6x - 6)(3x)

Plug in the value of x

= (6(41) - 6)(3(41))

= (246 - 6)(123)

= (240)(123)

= 29,520 ft²

5 0

3 years ago