The value of angle E is 43 degeree.
Number of books each of them have:
Jaime: x
Grant: x - 6
Ky: 3 (x - 6)
There are 176 books in total, so we can write it down as:
176 = x + x - 6 + 3 (x - 6)
176 = x + x - 6 + 3 * x + 3 * (-6)
176 = x + x - 6 + 3x - 18
176 = 2x - 6 + 3x - 18
176 = 5x - 24 / + 24 (both sides)
5x = 200 / ÷ 5 (both sides)
x = 40
Doublecheck:
Jamie: 40
Grant: 40 - 6 = 34
Ky: 3 (40 - 6) = 3 * 34 = 102
102 + 34 + 40 = 176, so it's correct :)
Answer:
Crayola Classic: 5 Packs; Crayola Tropical: 4 Packs
Step-by-step explanation:
Keep multiplying by both until you get a number equal to eachother
1. 8 x 2 = 16, 10 x 2 = 20
2. 8 x 3 = 24, 10 x 3 = 30
You may notice that the numbers are getting farther apart. This is normal because the boxes are not equal and are getting multiplied further. That means that your answer will have different factors in both the equations.
3. 8 x 4 = 32, 10 x 4 = 40
4. 8 x 5 = 40
Both of those equations (in bold) have the same answer and he wanted the same crayons from both. So, the answer is:
10 x 4 = 40
8 x 5 = 40
(how much packs of each you need to get the same amount)
Hope this helps :)
-jp524
Using the disk method, the volume of the solid is
![\displaystyle \pi \int_3^8 \left(\dfrac1{2x-1}\right)^2 \, dx = \pi \int_3^8 \frac{dx}{(2x-1)^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cpi%20%5Cint_3%5E8%20%5Cleft%28%5Cdfrac1%7B2x-1%7D%5Cright%29%5E2%20%5C%2C%20dx%20%3D%20%5Cpi%20%5Cint_3%5E8%20%5Cfrac%7Bdx%7D%7B%282x-1%29%5E2%7D)
Substitute
and
.
![\displaystyle \pi \int_3^8 \frac{dx}{(2x-1)^2} = \frac\pi2 \int_5^{15} \frac{du}{u^2} \\\\ ~~~~~~~~ = -\frac\pi2 \frac1u \bigg|_5^{15} \\\\ ~~~~~~~~ = -\frac\pi2 \left(\frac1{15} - \frac15\right) = \boxed{\frac\pi{15}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cpi%20%5Cint_3%5E8%20%5Cfrac%7Bdx%7D%7B%282x-1%29%5E2%7D%20%3D%20%5Cfrac%5Cpi2%20%5Cint_5%5E%7B15%7D%20%5Cfrac%7Bdu%7D%7Bu%5E2%7D%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20-%5Cfrac%5Cpi2%20%5Cfrac1u%20%5Cbigg%7C_5%5E%7B15%7D%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20-%5Cfrac%5Cpi2%20%5Cleft%28%5Cfrac1%7B15%7D%20-%20%5Cfrac15%5Cright%29%20%3D%20%5Cboxed%7B%5Cfrac%5Cpi%7B15%7D%7D)
Answer:
5 gallons
Step-by-step explanation:
area of wall is 435 sq ft
100 sq ft requires 1 gallon so 435 sq ft requires at least 5 gallons