You need to set it up as a fraction and make the fractions equal each other.
2/3 (2 of their books for 3 of yours)
x/18 (x amount of their books for 18 of yours)
(2/3)=(x/18)
multiply both sides by 18
and you get
36/3 which reduces to 12
so your answer is 12
we have that
−4+8−16+32−.....
a1=-2*(-2)-----> -4
a2=-4*(-2)-----> +8
a3=+8*(-2)-----> -16
a4=-16*(-2)----> +32
a5=+32*(-2)----> -64
a6=-64*(-2)-----> +128
a7=+128*(-2)-----> -256
The sum of the first 7 terms of the series is
<span>[a1+a2+a3+a4+a5+a6+a7]-----> [-4+8-16+32-64+128-256]------->
-172</span>
<span>
the answer is -172</span>
Answer would be 58.5 yd^2 .
You should take the base of the triangle multiplied by the height.
Formula: 1/2×base×height
In this case, you know that base is 13yd and height is 9 yd.
So, apply the formula.
Area = 1/2(13yd)(9yd) = 58.5 yd^2
*Do not include the " invisible length as it is not part of the actual triangle.
*Do not include 32yd as it is a hypotenuse and not a base. Hypotenuse is a side that is opposite a right angle triangle.
If you're using the app, try seeing this answer through your browser: brainly.com/question/2264253_______________
Evaluate the indefinite integral:
Trigonometric substitution:
then,
![\begin{array}{lcl} \mathsf{x=sin\,\theta}&\quad\Rightarrow\quad&\mathsf{dx=cos\,\theta\,d\theta\qquad\checkmark}\\\\\\ &&\mathsf{x^2=sin^2\,\theta}\\\\ &&\mathsf{x^2=1-cos^2\,\theta}\\\\ &&\mathsf{cos^2\,\theta=1-x^2}\\\\ &&\mathsf{cos\,\theta=\sqrt{1-x^2}\qquad\checkmark}\\\\\\ &&\textsf{because }\mathsf{cos\,\theta}\textsf{ is positive for }\mathsf{\theta\in \left[\dfrac{\pi}{2},\,\dfrac{\pi}{2}\right].} \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Blcl%7D%20%5Cmathsf%7Bx%3Dsin%5C%2C%5Ctheta%7D%26%5Cquad%5CRightarrow%5Cquad%26%5Cmathsf%7Bdx%3Dcos%5C%2C%5Ctheta%5C%2Cd%5Ctheta%5Cqquad%5Ccheckmark%7D%5C%5C%5C%5C%5C%5C%20%26%26%5Cmathsf%7Bx%5E2%3Dsin%5E2%5C%2C%5Ctheta%7D%5C%5C%5C%5C%20%26%26%5Cmathsf%7Bx%5E2%3D1-cos%5E2%5C%2C%5Ctheta%7D%5C%5C%5C%5C%20%26%26%5Cmathsf%7Bcos%5E2%5C%2C%5Ctheta%3D1-x%5E2%7D%5C%5C%5C%5C%20%26%26%5Cmathsf%7Bcos%5C%2C%5Ctheta%3D%5Csqrt%7B1-x%5E2%7D%5Cqquad%5Ccheckmark%7D%5C%5C%5C%5C%5C%5C%20%26%26%5Ctextsf%7Bbecause%20%7D%5Cmathsf%7Bcos%5C%2C%5Ctheta%7D%5Ctextsf%7B%20is%20positive%20for%20%7D%5Cmathsf%7B%5Ctheta%5Cin%20%5Cleft%5B%5Cdfrac%7B%5Cpi%7D%7B2%7D%2C%5C%2C%5Cdfrac%7B%5Cpi%7D%7B2%7D%5Cright%5D.%7D%20%5Cend%7Barray%7D)
So the integral
becomes
Integrate
by parts:
Substitute back for the variable x, and you get
I hope this helps. =)
Tags: <em>integral inverse sine function angle arcsin sine sin trigonometric trig substitution differential integral calculus</em>
Question:
If all the edges of prism A are multiplied by 5 to create prism B. The volume of prism B will be __________ times the volume of prism A?
* 5
* 125
* 50
* 25
Answer:
* 5 times.
Step-by-step explanation:
Let us represent all the edges of prism A as = X
Prism B = All the edges of Prism A × 5
Prism B = X × 5
= 5X
Let's assume the prism is a cube
Volume of a Prism(cube) = L × W × H
Volume of Prism A = L × W × H
Volume of Prism B = 5 (L × W × H)
Therefore, The volume of prism B will be 5 times the volume of prism A
