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lisov135 [29]
3 years ago
7

Y = 3 sin2x, y = 0, 0 ≤ x ≤ π; about the x−axis

Mathematics
1 answer:
Dominik [7]3 years ago
8 0
I assume you're revolving the region with those bounds about the x-axis, and supposed to find the volume.

Via the disk method,

\displaystyle\pi\int_0^\pi(3\sin2x)^2\,\mathrm dx=9\pi\int_0^\pi\sin^22x\,\mathrm dx

Recall the half-angle identity for sine:

\sin^2t=\dfrac{1-\cos2t}2
\implies\displaystyle\frac{9\pi}2\int_0^\pi(1-\cos4x)\,\mathrm dx
=\displaystyle\frac{9\pi}2\left(x-\frac14\sin4x\right)\bigg|_{x=0}^{x=\pi}
=\dfrac{9\pi^2}2
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jason runs 440 yards in 75 seconds.At this rate how many minutes does it take him to run a mile? (1 mile = 1,760 yards)​
Zepler [3.9K]

Answer: 5 minutes

Step-by-step explanation:

We know that 1760 yards are in a mile. We can convert the given info into a proportion. 440/75 = 1760/x, where x is the number of seconds it takes to run a mile. Cross-multiply to get 440x = 75*1760. Divide both sides by 440 to get x = 75*4 = 300 seconds. The problem asks for how many minutes so you have to convert 300 seconds to minutes. To do this, we have to divide 300 by 60 to get 5 minutes.

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3 years ago
The length of a rectangle is x² + 6x + 3 and the width is 3x² + 4x - 2. Which expression represents the are of the rectangle
miss Akunina [59]

Answer:

Step-by-step explanation:

area of rectangle=length×width

=(x²+6x+3)×(3x²+4x-2)

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7 0
3 years ago
Evaluate : 9⁴xa⁷b⁴/ 3⁵xa⁴b⁴ ​
hjlf

Answer:

27a³

Step-by-step explanation:

9⁴xa⁷b⁴ / 3⁵xa⁴b⁴

(3²)⁴xa⁷b⁴ / 3⁵xa⁴b⁴

3⁸xa⁷b⁴ / 3⁵xa⁴b⁴

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7 0
3 years ago
¿cuál es el vértice de una parábola que corta los ejes en los puntos (-1,0) , (5,0), (0,-10) ?​
kvasek [131]

Answer:

vertex: (2,-18)

Step-by-step explanation:

y = ax² + bx + c

(-1,0) : a - b + c = 0       ...(1)

(5,0) : 25a +5b +c = 0  ...(2)

(0,-10): 0a + 0b + c = -10        c=-10

(1) x5: 5a - 5b + 5c = 0  ...(3)

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(1): 2 - b -10 = 0     b = -8

Equation: y = 2x² - 8x -10 = 2 (x² -4x +4) - 18 = 2(x-2)² -18

equation: y = a(x-h)²+k     (h,k): vertex

vertex: (2,-18)

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3 years ago
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