Answer:
<h3>Q1</h3>
- This is acute angle since 75° < 90°
<h3>Q2</h3>
- This is an isosceles triangle
<h3>Q3</h3>
<u>Exterior angle is the sum of non-adjacent interior angles:</u>
- 4x + 7 + 6x - 9 = 118
- 10x - 2 = 118
- 10x = 120
- x = 12
m∠L = 4*12 + 7 = 48 + 7 = 55°
<h3>Q4</h3>
<u>The triangles are congruent and corresponding sides are equal:</u>
- 3x - 5 = 2x + 1
- 3x - 2x = 1 + 5
- x = 6
<u>Side lengths are:</u>
Answer:
The surface area of a sphere is calculated by formula:
A = 4 x pi x radius^2
=> radius = sqrt(A/(4 x pi) = sqrt(4534.16/(4 x pi)) = 19 (cm)
Hope this helps!
:)
The coefficient would be 18. The exponent for g would be 18. The exponent for h would be 9.
Add the exponents of the same variable and multiply the coefficents.
Answer:
Let the no. of messages Jina send be x.
No. of messages Kevin send=x-5
No. of messages Chang send=3(x-5)
=3x-15
x+(x-5)+(3x-15)=130
x+x-5+3x-15=130
x+x+3x-5-15=130
5x-20=130
5x=130+20
=150
x=150÷5
=30
No. of messages Jina sent=30
No. of messages Kevin sent=30-5
=25
No. of messages Chang sent=3(30)-15
=90-15
=75
Answer:
Step-by-step explanation:
The formula for the volume for a solid of revolution about the x-axis on an interval [a,b] is
If y = 4 - ½x, a = 1, and b = 2,
![\displaystyle V = \int_{1}^{2} \pi (4 - \frac{1}{2}x)^{2}dx = \pi \int_{1}^{2} \left(\dfrac{8-x }{2}\right)^{2}dx=\dfrac{\pi }{4}\int_{1}^{2} \left(8-x\right)^{2}dx\\\\=-\dfrac{\pi }{4}\times \dfrac{1}{3}\left[ 8 - x)^{3}\right]_{1}^{2}= -\dfrac{\pi }{12 }\left [512 - 192x + 24x^{2}-x^{3} \right ]_{1}^{2}\\\\=-\dfrac{\pi }{12}(512 - 384 + 96-8) + \dfrac{\pi }{12}(512 - 192 +24 -1)\\\\= -\dfrac{216\pi }{12} + \dfrac{343\pi }{12} = \mathbf{\dfrac{127 \pi}{12}\approx 33.25}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%20%3D%20%5Cint_%7B1%7D%5E%7B2%7D%20%5Cpi%20%284%20-%20%5Cfrac%7B1%7D%7B2%7Dx%29%5E%7B2%7Ddx%20%3D%20%5Cpi%20%5Cint_%7B1%7D%5E%7B2%7D%20%5Cleft%28%5Cdfrac%7B8-x%20%7D%7B2%7D%5Cright%29%5E%7B2%7Ddx%3D%5Cdfrac%7B%5Cpi%20%7D%7B4%7D%5Cint_%7B1%7D%5E%7B2%7D%20%5Cleft%288-x%5Cright%29%5E%7B2%7Ddx%5C%5C%5C%5C%3D-%5Cdfrac%7B%5Cpi%20%7D%7B4%7D%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%5Cleft%5B%208%20-%20x%29%5E%7B3%7D%5Cright%5D_%7B1%7D%5E%7B2%7D%3D%20-%5Cdfrac%7B%5Cpi%20%7D%7B12%20%7D%5Cleft%20%5B512%20-%20192x%20%2B%2024x%5E%7B2%7D-x%5E%7B3%7D%20%5Cright%20%5D_%7B1%7D%5E%7B2%7D%5C%5C%5C%5C%3D-%5Cdfrac%7B%5Cpi%20%7D%7B12%7D%28512%20-%20384%20%2B%20%2096-8%29%20%2B%20%5Cdfrac%7B%5Cpi%20%7D%7B12%7D%28512%20-%20192%20%2B24%20-1%29%5C%5C%5C%5C%3D%20-%5Cdfrac%7B216%5Cpi%20%7D%7B12%7D%20%2B%20%5Cdfrac%7B343%5Cpi%20%7D%7B12%7D%20%3D%20%5Cmathbf%7B%5Cdfrac%7B127%20%5Cpi%7D%7B12%7D%5Capprox%2033.25%7D)
The solid looks like the graph below.
