Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of y=sinx and y=cosx.

1 answer:

3 0

since sin and cos = each other at pi/4; take your integrals from 0 to pi/4
[S] cos(t) dt - [S] sin(t) dt ;[0,pi/4]

to revolve it around the x axis;
we do a sum of areas [S] 2pi [f(x)]^2 dx

take the cos first and subtract out the sin next; like cutting a hole out of a donuts.
pi [S] cos(x)^2 dx - [S] sin(x)^2 dx ; [0,pi/4]

cos(2t) = 2cos^2 - 1
cos^2 = (1+cos(2t))/2

1/sqrt(2) - (-1/sqrt(2) +1)
1/sqrt(2) + 1/sqrt(2) -1
(2sqrt(2) - sqrt(2))/sqrt(2) = sqrt(2)/sqrt(2) = 1

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Maranda praticed a total of 52 hours in 4 weeks to prepare for a piano recital. If she practiced the same number of hours each w

RUDIKE [14]

The number of practice hours per week for Maranda's piano recital is 13 hours

Overall practice hours = 52 hours

Number of weeks of practice = 4 weeks

Since, the number of practice hours per week is the same ;

Number of hours practiced each week can be obtained by dividing the overall practice hours by the number of weeks of practice.

Number of practice hours per week = Overall practice hours ÷ Number of weeks of practice

Number of practice hours = (52 ÷ 4) = 13 hours

Therefore, Marana practiced for 13 hours each week.

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erica [24]

Answer:

3 cups of sugar.

Step-by-step explanation:

Han drinks 3/4 of a cup of sugar each day when she drinks iced tea. She drinks 3 gallons, and each contains 3/4. If each contains only 3/4, we will have to multiply 3/4 by 3 gallons to find our answer to this question.

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