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julia-pushkina [17]

3 years ago

12

If these two trapezoids are similar, what is the measure of the missing angle?

1 answer:

Leokris [45]3 years ago

8 0

Answer:

90

Step-by-step explanation:

The angle has no tilt, only a turn, and i used a ruler, and the rulers meet as an L, making it a 90

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Help me with differentation and integration please!!

Marina86 [1]

Answer:

See below

Step-by-step explanation:

$\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x$

Recall

$\dfrac{d}{dx}\tan x=\sec^2$

Using the chain rule

$\dfrac{dy}{dx}= \dfrac{dy}{du} \dfrac{du}{dx}$

such that $u = \tan x$

we can get a general formulation for

$y = \tan^n x$

Considering the power rule

$\boxed{\dfrac{d}{dx} x^n = nx^{n-1}}$

we have

$\dfrac{dy}{dx} =n u^{n-1} \sec^2 x \implies \dfrac{dy}{dx} =n \tan^{n-1} \sec^2 x$

therefore,

$\dfrac{d}{dx}\tan^3 x=3\tan^2x \sec^2x$

Now, once

$\sec^2 x - 1= \tan^2x$

we have

$3\tan^2x \sec^2x = 3(\sec^2 x - 1) \sec^2x = 3\sec^4x-3\sec^2x$

Hence, we showed

$\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x$

================================================

For the integration,

$\int \sec^4 x\, dx$

considering the previous part, we will use the identity

$\boxed{\sec^2 x - 1= \tan^2x}$

thus

$\int\sec^4x\,dx=\int \sec^2 x(\tan^2x+1)\,dx = \int \sec^2 x \tan^2x+\sec^2 x\,dx$

and

$\int \sec^2 x \tan^2x+\sec^2 x\,dx = \int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx$

Considering $u = \tan x$

and then $du=\sec^2x\ dx$

we have

$\int u^2 \, du = \dfrac{u^3}{3}+C$

Therefore,

$\int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx = \dfrac{\tan^3 x}{3}+\tan x + C$

$\boxed{\int \sec^4 x\, dx = \dfrac{\tan^3 x}{3}+\tan x + C }$

6 0

3 years ago

WILL BRAINLIEST CORECT ANSWER

DanielleElmas [232]

Ok. So she wants to advertise that there are 100 different dolls available. If she adds another category, then at most she already had 99 different types. If I'm right (don't take my word for it) but the minimum she would have to have is one. <span />

3 0

3 years ago

A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the z-score corresponding to the given

Mariulka [41]

Answer:

A. -1.6; not significant

Step-by-step explanation:

The z-score of a data set that is normally distributed with a mean of $\bar x$ and a standard deviation of $\sigma$ , is given by:

$z=\frac{x-\bar x}{\sigma}$ .

From the question, the test score is: $x=48.4$ , the mean is $\bar x=66$ , and the standard deviation is $\sigma =11$ .

We just have to plug these values into the above formula to obtain:

$z=\frac{48.4-66}{11}$ .

This simplifies to: $z=\frac{-17.6}{11}$ .

$z=-1.6$ .

We can see that the z-score falls within two standard deviations of the mean.

Since $-2\le-1.6\le2$ the value is not significant.

The correct answer is A. -1.6; not significant

3 0

3 years ago

*PLEASE FIND THE ANSWER QUICK!!!!!* Find the SA of this solid. please show the unit measure in your answer

omeli [17]

Answer:

The SA of the rectangle is 270. The SA of both the triangles is 24

3 0

3 years ago

How do you turn 0.65 decimal into a fraction or mixed number into simplest form

Yakvenalex [24]

Put 65 over 100 so it's a fraction and simplify from there i think

5 0

4 years ago

Read 2 more answers