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solong [7]
2 years ago
6

Region R is bounded by the curves y = 4x^2 and y = 4. A solid has base R, and cross sections perpendicular to the y-axis are sem

icircles with the diameter lying in R. The volume of this solid is
A. pi/4
B. pi/2
C. pi
D. 2pi

Mathematics
1 answer:
vlada-n [284]2 years ago
6 0

Each cross section has a diameter equal the horizontal distance between the two "halves" of the parabola. We have

y = 4x²   ⇒   x = ±√y/2

so the diameter for some given y would be √y/2 - (-√y/2) = √y.

The volume of a cross section with thickness ∆y is then

π/2 (√y/2)² ∆y = π/8 y ∆y

The total volume of the solid would then be

\displaystyle \int_0^4 \frac\pi8 y \, dy = \frac\pi8 \times \frac12 y^2 \bigg|_{y=0}^{y=4} = \boxed{\pi}

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Answer:

a=21

b=69

c=42

d=138

Step-by-step explanation:

c is supplementary to d (which is 138), so c=180-138= 42.

angle b is on the edge of the central angle 138, so b is 1/2, therefore, b=69.

angle a is complementary to angle b because any triangle that includes the diameter is a right angle, so angle a=90-69=21.

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Step-by-step explanation:

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<em>(a), (d)</em>

Step-by-step explanation:

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3 years ago
A road rises 50 feet over a horizontal distance of 600 feet. What is the slope of the road?
Hatshy [7]

Answer:

1/12 (or 0.833)

Step-by-step explanation:

Recall that the definition of "slope" is the change in vertical distance divided by the change in the horizontal distance. (aka. rise ÷ run)

it is given that rise = 50 feet and the horizontal distance (i.,e "run") = 600feet

hence slope = rise / run = 50 / 600 = 1/12 (or 0.833)

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Ben and Alyssa play a game in which they earn the same number of points for each goal and lose the same number of points for eac
Nadya [2.5K]

Answer:

Each goal gives 5 points and a penalty costs 7 points.

Step-by-step explanation:

Let a penalty cost = x points

And a goal gives = y points

Ben makes 7 goals and 2 penalties ending the game with 21 points,

7y - 2x = 21 --------(1)

Alyssa makes 10 goals and 8 penalties ending the game with (-6) points,

10y - 8x = -6

5y - 4x = -3 --------(2)

Equation (1) multiplied by 2, then subtracted from equation (2),

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Therefore, each goal gives 5 points and a penalty costs 7 points.

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