All categories

4 years ago

1 The White House is one of the most famous buildings in the world, and the north face

Mathematics

1 answer:

pogonyaev4 years ago

7 0

Answer:

what are we supposed to answer? im confused.. i can help i just dont know what to answer

Step-by-step explanation:

You might be interested in

Find the slope of the line.. Use the two points shown. PLEASE HELP ME

leonid [27]

The answer is 7/2 i believe

4 0

3 years ago

83 students choose to attend one of three after school activities: football, tennis or running. There are 53 boys. 36 students c

Neko [114]

Answer:

38.55% or 32/83

Step-by-step explanation:

First of all, we need to write down the amount of students in each activity:

Football = 36

Tennis = 15

Running = 18 girls + 14 boys (the remainder of the 83 students) so 32 students.

So 32/83 as a percentage is 38.55%

Thus, the chance of the randomly selected student being in the Running category is 38.55% or 32/83.

5 0

3 years ago

4. Courtney wants to sell her grandfather's antique 1932 Ford. She begins to set her price by looking at ads and finds these pri

Vera_Pavlovna [14]

Answer:

$22,320

Step-by-step explanation:

1. Understanding

Mean is the average of a given set

2. Solving

We have to find the average of all of these numbers.

How do I find the average?

I add all of the numbers and divide by the number of numbers I added. Example:

(x + x + x + x)/4 or,

(x+x)/2 and examples in numbers:

(3+4)/2 or,

(9+4+8+5+7)/5

See what I mean? Dividing by the number of numbers I have.

Ok, now we know that, we can solve!

Here is the equation for this problem:

(24,600+19,000+33,000+15,000+20,000)/5 (We have 5 numbers)

We have to do Parentheses First

(24,600+19,000+33,000+15,000+20,000)/5 --> 111,600/5

111,600/5 = 22,320

22,320 is the average number of all of the numbers, which is the mean

Hope this helps :)

-jp524

8 0

2 years ago

Perry traveled at an average speed of 55 miles per hour for 3.5 hours and then traveled at an average speed of 60 miles per hour

Alex

Answer:

342.5

Step-by-step explanation:

Take 55 and multiply it by 3.5

Then multiply 60 by 2.5

Then add those two numbers that you come up with and add them together.

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%20%5Cdisplaystyle%20%5Cint%20%5Climits_%7B0%7D%5E%7B%20%5Cfrac%7B%20%5Cpi%7D%7B2%7D%20%7D%

murzikaleks [220]

Let $x = \arcsin(y)$ , so that

$\sin(x) = y$

$\tan(x)=\dfrac y{\sqrt{1-y^2}}$

$dx = \dfrac{dy}{\sqrt{1-y^2}}$

Then the integral transforms to

$\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_{y=\sin(0)}^{y=\sin\left(\frac\pi2\right)} \frac{y}{\sqrt{1-y^2}} \ln(y) \frac{dy}{\sqrt{1-y^2}}$

$\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy$

Integrate by parts, taking

$u = \ln(y) \implies du = \dfrac{dy}y$

$dv = \dfrac{y}{1-y^2} \, dy \implies v = -\dfrac12 \ln|1-y^2|$

For 0 < y < 1, we have |1 - y²| = 1 - y², so

$\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = uv \bigg|_{y\to0^+}^{y\to1^-} + \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy$

It's easy to show that uv approaches 0 as y approaches either 0 or 1, so we just have

$\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy$

Recall the Taylor series for ln(1 + y),

$\displaystyle \ln(1+y) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n y^n$

Replacing y with -y² gives the Taylor series

$\displaystyle \ln(1-y^2) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n (-y^2)^n = - \sum_{n=1}^\infty \frac1n y^{2n}$

and replacing ln(1 - y²) in the integral with its series representation gives

$\displaystyle -\frac12 \int_0^1 \frac1y \sum_{n=1}^\infty \frac{y^{2n}}n \, dy = -\frac12 \int_0^1 \sum_{n=1}^\infty \frac{y^{2n-1}}n \, dy$

Interchanging the integral and sum (see Fubini's theorem) gives

$\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy$

Compute the integral:

$\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy = -\frac12 \sum_{n=1}^\infty \frac{y^{2n}}{2n^2} \bigg|_0^1 = -\frac14 \sum_{n=1}^\infty \frac1{n^2}$

and we recognize the famous sum (see Basel's problem),

$\displaystyle \sum_{n=1}^\infty \frac1{n^2} = \frac{\pi^2}6$

So, the value of our integral is

$\displaystyle \int_0^{\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \boxed{-\frac{\pi^2}{24}}$

6 0

3 years ago