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2 years ago

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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point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below

enot [183]

Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

To find angle CAB and;
Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using cosine rule to determine angle CAB, we have:

$\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}$

Here:

$\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}$

$\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}$

$\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}$

$\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}$

$\mathbf{Sin \hat {CAB} = 0.3451}$

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

$\mathbf{Tan \theta = \dfrac{GF}{BF}}$

$\mathbf{Tan \ 35.19 = \dfrac{1.8 \ m }{BF}}$

$\mathbf{BF = \dfrac{1.8 \ m }{Tan \ 35.19}}$

$\mathbf{BF = \dfrac{1.8 \ m }{0.7052}}$

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

8 0

2 years ago

I forgot what to do

kvv77 [185]

Pretty sure it would be 21x^2+16x+17y

8 0

2 years ago

Succesive approximation

borishaifa [10]

The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.

<h3>What is the iterations about?</h3>

In the equation given:

Note that:

x²-3x+2 = square root √x-2 + 2

Therefore:

x⁴-6x³+9x²= square root x-2

x² = 3.375

Convert 3.35 into fractions and will get 27/8. So, The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.

Learn more about Successive approximation from

brainly.com/question/27278132

#SPJ1

3 0

1 year ago

Which statements about the circle are correct? Check all that apply Arc PQ is congruent to arc SR. The measure of arc QR is 150

m_a_m_a [10]

Answer:

1st 2nd 4th 5th

6 0

2 years ago

How do i solve this????? plz plz plz help!!!!!!

Ahat [919]

Hello there! I can help you! So, we would shift two units to the right, which means that we would subtract, and we go down 7 units, which would also make us subtract. For the original equation of y = x - 3, the line would only go down 3 units. The line of the original equation does not go left or right, because there are no absolute value signs between it. With the equation translation of 7 units, you would go down anouther 7 units, and 7 + 3 is 10. So the equation of the new line is y = |x - 2| - 10.
The original equation is where the line infinitely when up and down on a slanted line. In other words, it has no vertex. In the new equation, however, the graph has a vertex, and the lines go up from there. Both graphs have the same slope, except that for the left side of the new equation, the slope is -1, because the line goes down.

7 0

3 years ago