Mathematics, 15.07.2020 21:01 starwars77

Please help The answer is 0.8284 unit2.

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Answer from: JavyHart9695

0.8284 units²

Step-by-step explanation:

To find the area between curves, we need to use the integral. We can see that both sides of the shaded region are equal to each other. Therefore, we can find the area of one shaded part and multiply it by 2 for the 2 shaded regions. For the integral, we can find the area of the shaded region on the left side, on the interval from 0 to π/4.

Now that we know the integral, we can figure out the function. We do this by subtracting the top curve by the bottom curve. The top curve on the left shaded region, is y=cosx. The bottom curve on the shaded region is y=sinx. Therefore, we will subtract cosx-sinx.

$2\int\limits^\frac{\pi }{4} _0 {cosx-sinx} \, dx$

Now that we have the integral, we can solve by splitting the integral into 2 separate integrals by the Sum Rule. Let's disregard the multiply by 2 for now, but we will make sure to multiply by 2 at the end.

$\int\limits^\frac{\pi }{4} _0 {cosx} \, dx -\int\limits^\frac{\pi }{4} _0 {sinx} \, dx$

Now, we can solve each integral separately.

$\int\limits^\frac{\pi }{4} _0 {cosx} \, dx =sinx]^\pi^ /^40$

*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.

$sin(\frac{\pi }{4} )-sin(0)=\frac{\sqrt{2} }{2} -0=\frac{\sqrt{2} }{2}$

Now, we can find the integral of sinx.

$\int\limits^\frac{\pi }{4} _0 {sinx} \, dx=-cos]^\pi ^/^40$

*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.

$-cos(\frac{\pi }{4} )-(-cos(0))=-\frac{\sqrt{2} }{2} -(-1)=-\frac{\sqrt{2} }{2} +1$

Now that we have the integral of each integral, we can subtract them, and multiply by 2.

$\frac{\sqrt{2} }{2} -(-\frac{\sqrt{2} }{2} +1)=\sqrt{2}+1$

$2(\sqrt{2} +1)=0.8284 units^2$

Answer from: Quest

she would want to sell 10 full-year subscriptions and at least 9 half-year subscriptions to get a total of at least $300.

i hope this answer you! if you have any further questions or concerns, feel free to ask! : )

step-by-step explanation:

mark brainliest!

Kelly sells magazine subscriptions after work. the half-year subscriptions cost $12, and the full-ye

Answer from: Quest

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a. $y = 60(1) - 90 \\ y = 60 - 90 \\ y = - 30$ this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b. $y = 60(1) - 150 \\ y = 60 - 150 \\ y = - 90$ this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

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