Answer:
cubic units
Step-by-step explanation:
We are to find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.
f(x)=2x+1, y=0, x=0, x=4.
The picture is given as shaded region.
This is rotated about x axis
Limits for x are already given as 0 and 4
f(x) is a straight line
The solid formed would be a cone
Volume = ![\pi \int\limits^a_b {(2x+1)^2} \, dx \\= \pi \int\limits^4_0 {(4x^2+4x+1)} \, dx \\=\pi [\frac{4x^3}{3} +2x^2+x]^5_0\\\\=\pi[\frac{4*4^3}{3}+2*4^2+4-0]\\=\frac{364\pi}{3}](https://tex.z-dn.net/?f=%5Cpi%20%5Cint%5Climits%5Ea_b%20%7B%282x%2B1%29%5E2%7D%20%5C%2C%20dx%20%5C%5C%3D%20%5Cpi%20%5Cint%5Climits%5E4_0%20%7B%284x%5E2%2B4x%2B1%29%7D%20%5C%2C%20dx%20%5C%5C%3D%5Cpi%20%5B%5Cfrac%7B4x%5E3%7D%7B3%7D%20%2B2x%5E2%2Bx%5D%5E5_0%5C%5C%5C%5C%3D%5Cpi%5B%5Cfrac%7B4%2A4%5E3%7D%7B3%7D%2B2%2A4%5E2%2B4-0%5D%5C%5C%3D%5Cfrac%7B364%5Cpi%7D%7B3%7D)
Answer:
B 480 in.³
Step-by-step explanation:
Volume of a rectangular prism is given by
V = l*w*h
V = 8*12*5
V =480 in ^3
Answer:
Probably A, or 1
Step-by-step explanation:
You see, a square root function actually looks like a sideways parabola, just missing one side because of the domain of a square root. Now, the reason I can tell them apart is because our vertex is below the y-axis, and the only equation that has a negative y-intercept is the first one, or A.
Hope this helps!
This question is an example of what we call "system of equations". We can use two separate equations to help us solve.
Let a = number of touchdowns
Let b = number of field goals
a + b = 43
7a + 3b = 301
We can solve this system using the elimination method.
1. a + b - b = 43 + -b (add - b to both sides)
a = -b + 43
2. substitute -b + 43 for a in 7a + 3b = 301
7 (-b +43) + 3b = 301
-4b + 301 = 301 (simplify both sides of the equation)
-4b + 301 - 301 = 301 - 301 (add -301 to both sides)
-4b = 0
b = 0
Since b = 0, and b is the number of field goals, we know that Liam's team did not score any field goals. Which means the only points from his team came from touchdowns. So, 43 touchdowns were scored, and 0 field goals were scored, for a total of 301 points.
