Answer:
22
Step-by-step explanation:
The midsegment is always half as long as the base, so
2(6 + 4x) = 5x + 24
12 + 8x = 5x + 24
3x = 12
x = 4
Replace the 4 in for x,
6 + 4(4) = 22
Answer:
Area of polygon = 42.63 mm²
Step-by-step explanation:
Given:
To find the area of the polygon (rectangle), multiply the length with the width.
⇒ Area of polygon = LW
<u>Substitute the values into the area:</u>
⇒ Area of polygon = (8.7)(4.9) [L = 8.7 mm; W = 4.9 mm]
⇒ Area of polygon = 42.63 mm²
The equation to find the volume of a sphere is V=4/3(pi)r^3.
So I cubed 12, times by 4, and divided by 3, so the volume of the beach ball is 2,304(pi) cubic inches. Hope this helps.
Please express the eqn of the parab by <span>y = 2x^2. " ^ " indicates exponentiation.
Find the equation of the tangent line to </span>y = 2x^2 at (1,2):
dy/dx = 4x; now let x = 1. Thus, the slope of the TL at (1,2) is 4(1) = 4, and the eqn of the TL is y-2 = 4(x-1), or y-2 = 4x -4, or y = 4x -2.
To find the area bounded by the parabola, the line y = 4x-2 and the x-axis, we need to use horizontal strips and integrate with respect to y instead of to x.
The smallest y value will be 0 (this is the x-axis), and the largest will be 2 (this comes from the given point, (1,2) ).
Solve y = 2x^2 for x: x^2 = y/2, so that x = sqrt(y/2) for y = 0 to y = 2.
y+2
Solve y = 4x - 2 for x: 4x = y + 2, so that x = -------
4
Thus, the length of each horiz. strip of width dy is given by
(y+2)
------- - sqrt(y/2), since the first term represents the larger x-value and the
4 second term represents the smaller x-value.
Then the area is the integral from y=0 to y=2 of
(y+2)
[ -------- - sqrt(y/2) ] dy
4
Can you do this integration? If not, ask specific questions so that I could help you further.
Answer:
0.2773
Step-by-step explanation:
Please see attachment.