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iogann1982 [59]
3 years ago
15

Please solve both thank you!

Mathematics
2 answers:
Nina [5.8K]3 years ago
4 0

Answer:

First problem: 24 + 4x = 60

Second problem: 9

Step-by-step explanation:

24 + 4x = 60

4x = 36

x = 9

guapka [62]3 years ago
4 0
I’m pretty sure the x are 9 because it you do 9x4= 36 then you add 24 and it will equal to 60
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Calculus 2 master needed; stuck on evaluating the integral please show steps <img src="https://tex.z-dn.net/?f=%5Cint%20%7Bsec%2
kakasveta [241]

Answer:

\int \sec(\frac{x}{2})\tan^5({\frac{x}{2}})dx=\frac{2\sec^5(\frac{1}{2}x)}{5}-\frac{4\sec^3(\frac{1}{2}x)}{3}+2\sec(\frac{1}{2}x)+C

Step-by-step explanation:

So we have the integral:

\int \sec(\frac{x}{2})\tan^5({\frac{x}{2}})dx

First, let's use substitution to get rid of the x/2. I'm going to use the variable y. So, let y be x/2. Thus:

y=\frac{x}{2}\\dy=\frac{1}{2}dx\\2dy=dx

Therefore, the integral is:

=2\int \sec(y)\tan^5(y)dy

Now, as you had done, let's expand the tangent term. However, let's do it to the fourth. Thus:

=2\int \sec(y)\tan^4(y)\tan(y)dy

Now, we can use a variation of the trigonometric identity:

\tan^2(y)+1=\sec^2(y)

So:

\tan^2(y)=\sec^2(y)-1

Substitute this into the integral. Note that tan^4(x) is the same as (tan^2(x))^2. Thus:

=2\int \sec(y)(\tan^2(y))^2\tan(y)dy\\=2\int \sec(y)(\sec^2(y)-1)^2\tan(y)dy

Now, we can use substitution. We will use it for sec(x). Recall what the derivative of secant is. Thus:

u=\sec(y)\\du=\sec(y)\tan(y)dy

Substitute:

2\int (\sec^2(y)-1)^2(\sec(y)\tan(y))dy\\=2\int(u^2-1)^2 du

Expand the binomial:

=2\int u^4-2u^2+1du

Spilt the integral:

=2(\int u^4 du+\int-2u^2du+\int +1du)

Factor out the constant multiple:

=2(\int u^4du-2\int u^2du+\int(1)du)

Reverse Power Rule:

=2(\frac{u^{4+1}}{4+1}-2(\frac{u^{2+1}}{2+1})+(\frac{u^{0+1}}{0+1}}))

Simplify:

=2(\frac{u^5}{5}-\frac{2u^3}{3}+u)

Distribute the 2:

=\frac{2u^5}{5}-\frac{4u^3}{3}+2u

Substitute back secant for u:

=\frac{2\sec^5(y)}{5}-\frac{4\sec^3(y)}{3}+2\sec(y)

And substitute back 1/2x for y. Therefore:

=\frac{2\sec^5(\frac{1}{2}x)}{5}-\frac{4\sec^3(\frac{1}{2}x)}{3}+2\sec(\frac{1}{2}x)

And, finally, C:

=\frac{2\sec^5(\frac{1}{2}x)}{5}-\frac{4\sec^3(\frac{1}{2}x)}{3}+2\sec(\frac{1}{2}x)+C

And we're done!

7 0
3 years ago
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I need to get a answer for this problem I am stuck on it
kap26 [50]

Answer:

What problem

Step-by-step explanation:

there is no problem

7 0
3 years ago
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You randomly guess the answers to two questions on a multiple-choice test. Each question has three choices: A, B, and C.
kupik [55]

Answer:

Hello,

This question I've just been jotting down, so I won't explain much. If you want more, just comment!

:D

a. There is only one correct answer for both. Since each question has 3 outcomes, we will have 1 over 3(3). That's 1/9

Thus, a is 1/9.

(about 11.11%

b. If you eliminate one of the choices, then there will be two possible outcomes. We will have 1 over 2(2), so 1/4.

Thus, b is 1/4.

(a in options)

Hope this helps!

(I'm not sure if you just want these answered or the others.)

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3 years ago
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You earn $0.85 for every cup of hot chocolate you sell. Write and solve an equation to determine how many cups you need to sell
antoniya [11.8K]

Answer:

47 rounding to nearest 100th

Step-by-step explanation:

Divide 55.25 into 0.85 and get 46.96 then round to get 47 cups.

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Charlotte owns two entertainment websites. Here are some details about those websites for one entire month:
Simora [160]

Answer:

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Step-by-step explanation:

How's your day >?

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