Need help with this geometric question ASAP, Thank you

Replace x with π/2 - x to get the equivalent integral

[tex]\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

but the integrand is even, so this is really just

[tex]\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

Substitute x = 1/2 arccot(u/2), which transforms the integral to

[tex]\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du[/tex]

There are lots of ways to compute this. What I did was to consider the complex contour integral

[tex]\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz[/tex]

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

[tex]\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}[/tex]

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

[tex]\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}[/tex]

and it follows that

[tex]\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}[/tex]

Answer:

Step-by-step explanation:

Prove by multiplication

Similarly

So the expression is 5873/8

Now

We can prove the given statement to multiplication

Multiply with 8

And

Yes

We see 5873 lies between 5600 and 6400 hence the quotient is greater than 700 but less than 800

Answer:

so first you want to mulitply the 5,5,5.8, and 8 together to get 1160 then take away 464 from 1160 to get 696. then you add all of the numbers up to get 719.8 ten subtract .75 from that and you get 719.05. then take the cubic feet and get 200 then taky away 200 from 719.05 and get 519.05 then do that again

Step-by-step explanation:

219.05

The surface area of the image after the dilation is 219 3/8 m²

Area is the amount of space occupied by a two dimensional shape or object.

The surface area of the prism = 2(0.5 * 5 * 12) + (5 * 11) + (11 * 12) + (13 * 11) = 390 m²

The surface area of the image after the dilation = scale factor² *  390 m² = (3/4)² * 390 m² = 219 3/8 m²

The surface area of the image after the dilation is 219 3/8 m²

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The expression for the simplified total gas used is 1.43x.

let the gas used on the way to camp "x"

Then the gas used on the way back can be calculated as follows:

360 / 420 × 0.5 × x

To calculate the total fuel used, We need to add this to the 'x' used on the way.

Therefore,

total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x

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Step-by-step explanation:

this is the answer for you

Answer:

Just give me the questions and ill do it

Step-by-step explanation:

Answer:

C) 11.1

Step-by-step explanation:

7.4 -(-3.7)

- and - make +

7.4 + 3.7 = 11.1

Answer:

tkm

Step-by-step explanation:

First T the middle k and at last m

Answer:

Parallelogram

Step-by-step explanation:

Instead of one pair of parallel sides like in a trapezoid, a parallelogram has two pairs of opposite sides (for example a rectangle)

Answer:

(- 3, 1 )

Step-by-step explanation:

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

adding the 2 equations term by term will eliminate y

3x + 0 = - 9

3x = - 9 ( divide both sides by 3 )

x = - 3

substitute x = - 3 into either of the 2 equations and solve for y

substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (- 3, 1 )

Answer:

(–3, 1)

Step-by-step explanation:

Step 1: Solve for x

2x – 2y = –8 -----------(1)

x + 2y = –1. -------------(2)

⇒2x + x| -2y + 2y |= -8 -1

⇒3x = -9

⇒3x/3 = -9/3

⇒x = -3

Step 2; Solve for y

x + 2y = –1

(-3) + 2y = -1

-3 + 2y + 3 = -1 + 3

2y = 2

2y/2 = 2/2

y = 1

So, ( x,y) ⇒(-3,1)

Step-by-step explanation:

Answer: 78 /5 = 15.6 = 16 taxis. Step-by-step explanation: I HOPE THIS WILL HELP YOU AND MARK IT AS BRAINLIEST ANSWER PLEASE.

Answer:

6.46 seconds

Step-by-step explanation:

[tex] - 16 {t}^{2} + 65t + 248 = 0[/tex]

[tex]t = 6.46[/tex]

Answer:

Step-by-step explanation:

The angle containing y and 63 are vertically opposite. They are equal.

y + 23 = 63                   Subtract 23 from both sides

y +23-23 = 63 - 23

Answer y = 40

Please attach some form of question first, thank you!

Answer:

Step-by-step explanation:

c I think I did the math that’s what it leads to so yeah

Answer:

Step-by-step explanation:

top = 120sq m

middle = 17sq cm

bottom = 102 sq feet

Answer:

  7/3

Step-by-step explanation:

To write the ratio with no units. we need to have both parts of the ratio in the same units. That way the units cancel.

__

  6 weeks : 18 days = (6×7) days : (6×3) days = 7 : 3

The ratio as a fraction is ...

  (6 weeks)/(18 days) = 7/3

Answer:

Area is 30cm^2 if thats what your asking

Step-by-step explanation:

Answer:

X = 5

Step-by-step explanation:

You need to use the Pythagorean theory to solve this question.

[tex] {13}^{2} = {x}^{2} + {(x + 7)}^{2} [/tex]

[tex]169 = {x}^{2} + ( {x}^{2} + 14x + 49)[/tex]

[tex]169 = 2 {x}^{2} + 14x + 49[/tex]

[tex]0 = 2 {x}^{2} + 14x + 49 - 169[/tex]

[tex]0 = 2 {x}^{2} + 14x - 120[/tex]

Now simply the equation by dividing everything by 2.

[tex]0 = {x}^{2} + 7x - 60[/tex]

[tex]0 = (x - 5)(x + 12)[/tex]

Now, you can find the possible solutions by setting each bracket to 0.

[tex]0 = x - 5[/tex]

[tex]5 = x[/tex]

OR

[tex]0 = x + 12[/tex]

[tex] - 12 = x[/tex]

However, a measurement on a triangle cannot be negative. Therefore, we can ignore -12 and say that the answer is x = 5.

Answer:

20.5 degrees

Step-by-step explanation:

So when the arc is being made from two lines coming out from the center, the measure of the arc is the same as the angle of the lines.

So the measurement of 41 degrees for the arc is also the angle of line OB and line OC.

Now that center line is the diameter, which means it is 180 degrees

So you can find the angle of line OA and OB:

180 - 41 = 139

Then, to find x you need to recognize that OB and OA is actually the radius of the circle, which means they are the same length.

This makes it an isosceles triangle. So, the angle of OB and BA is the same as OB and BA. The measurement of all the angles in a truianbgle is 180 degrees, so to find the measurement of x, you need to subtract 139 from 180:

180-139 = 41

And then divide by two to find the remaining two angles:

41/2 = 20.5

and that is x :)

Answer:

2

Step-by-step explanation:

1 ⅚ + ⅙ = 1 6/6, also known as, 2

Answer: 15 miles per gallon

Step-by-step explanation:

135 divided by 9

15 miles per gallon

rate:

[tex]\sf \dfrac{distance}{amount \ of \ oil}[/tex]

[tex]\rightarrow \dfrac{135}{9}[/tex]

[tex]\sf \rightarrow15 \ miles \ per \ gallon[/tex]

Step-by-step explanation:

I think the answer is x=70

Answer:

Step-by-step explanation:

The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.

Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...

  1100x +1300(x+0.03) = 255

  2400x +39 = 255 . . . simplify

  2400x = 216 . . . . . . subtract 39

  x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x

Rosa invested $1100 at 9%, and $1300 at 12%.

Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.

At the null hypothesis, we test if the proportion is of 50.3%, hence:

[tex]H_0: p = 0.503[/tex]

We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:

[tex]H_1: p \neq 0.503[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, the parameters are:

[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]

Hence:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]

[tex]z = 2.32[/tex]

Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.

More can be learned about the z-distribution at https://brainly.com/question/26454209

it's interpreted as 28 - 21 = 7