So first you plug 6 into the equation which is 4(6)-10.
Using PEMDAS, you solve what’s in the parenthesis first and you get 24-10.
24-10=14
f(6)=14
Alright, so the first step we are gonna do to solve this problem is subtract since Mason ate 5 ounces of the peanuts and so, we need to subtract 5 out of 29.8.
29.8 - 5 = 24.8
So, now there is 24.8 ounces.
Now we move onto the next step which is division. As you can see in the question it says "Then he divides the rest of the peanuts equally among 4 friends."
24. 8 ÷ 4 = 6.2
Since the answer is supposed to be a decimal..that's your answer!
So overall, each of Mason's friends get 6.2 ounces of peanuts.
Hope this helps!
If you are needing any more help, comment below this comment for any contact of mine. I'll be glad to help!
- Kana
Answer:
V = 2000r³/3
Step-by-step explanation:
We know that the base is a circular disk, so it creates a circle on the xy plane. It would be in the form x² + y² = r². In other words x² + y² = (5r)². Let's isolate y in this equation now:
x² + y² = (5r)²,
x² + y² = 25r²,
y² = 25r² - x²,
y = √25r² - x² ---- (1)
Now remember that parallel cross sections perpendicular to the base are squares. Therefore Area = length^2. The length will then be = 2√25r² - x² --- (2). Now we can evaluate the integral from -5r to 5r, of [ 2√25r² - x² ]² dx.
![\int _{-5r}^{5r}\:\left[\:2\sqrt{\left(25r^2\:-\:x^2\right)}\:\right]\:^2\:dx\\=\int _{-5r}^{5r}4\left(25r^2-x^2\right)dx\\\\= 4\cdot \int _{-5r}^{5r}25r^2-x^2dx\\\\= 4\left(\int _{-5r}^{5r}25r^2dx-\int _{-5r}^{5r}x^2dx\right)\\\\= 4\left(250r^3-\frac{250r^3}{3}\right)\\\\= 4\cdot \frac{500r^3}{3}\\\\= \frac{2000r^3}{3}](https://tex.z-dn.net/?f=%5Cint%20_%7B-5r%7D%5E%7B5r%7D%5C%3A%5Cleft%5B%5C%3A2%5Csqrt%7B%5Cleft%2825r%5E2%5C%3A-%5C%3Ax%5E2%5Cright%29%7D%5C%3A%5Cright%5D%5C%3A%5E2%5C%3Adx%5C%5C%3D%5Cint%20_%7B-5r%7D%5E%7B5r%7D4%5Cleft%2825r%5E2-x%5E2%5Cright%29dx%5C%5C%5C%5C%3D%204%5Ccdot%20%5Cint%20_%7B-5r%7D%5E%7B5r%7D25r%5E2-x%5E2dx%5C%5C%5C%5C%3D%204%5Cleft%28%5Cint%20_%7B-5r%7D%5E%7B5r%7D25r%5E2dx-%5Cint%20_%7B-5r%7D%5E%7B5r%7Dx%5E2dx%5Cright%29%5C%5C%5C%5C%3D%204%5Cleft%28250r%5E3-%5Cfrac%7B250r%5E3%7D%7B3%7D%5Cright%29%5C%5C%5C%5C%3D%204%5Ccdot%20%5Cfrac%7B500r%5E3%7D%7B3%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B2000r%5E3%7D%7B3%7D)
As you can see, your exact solution would be, V = 2000r³/3. Hope that helps!
Answer:
120 degrees
Step-by-step explanation:
plugged into calculator
cos inverse of -1/2
Please mark Brainliest if you feel like it:)
Answer:
D) 65°
Step-by-step explanation:
Remember, all the angles of a triangle are 180 degrees and 75 + 40 + 65 = 180 degrees. Please if you can, support my channel. In the images you can find the information ;)