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2 years ago

Find the area between the graph please

Mathematics

1 answer:

vagabundo [1.1K]2 years ago

4 0

The area of the region shown in the coordinate plane is 2.7823 units square.

<h3>What is integration?</h3>

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

The graph of a function:

y = sinx

And a line segment passed through:

(0, 0) and (7π/6, -1/2)

First, find the equation of the line:

y = (-1/2)/(7π/6)[x]

y = (-3/7π)x

The area by definite integration:

$\rm Area = \int\limits^{7\pi/6}_0 {[sinx - (-3/7\pi)x]} \, dx$

$\rm Area = \int\limits^{7\pi/6}_0 {[sinx +3x/7\pi ]} \, dx$

After solving the above definite integral:

Area = 2.7823 units square

Thus, the area of the region shown in the coordinate plane is 2.7823 units square.

Learn more about integration here:

brainly.com/question/18125359

#SPJ1

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Please Help me answer all 4 questions with a full explanation so I can solve the rest on my own.

Nata [24]

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$\\ \rm\Rrightarrow (2x^4y^3)^3.2x^4y^4=8x^{12}y^6.2x^4y^4=16x^{16}y^{10}$

$\\ \rm\Rrightarrow (m^3n^0(2m^3n^2)^4)^2=(m^316m^{12}n^8)^2=(16m^{15}n^8)^2=256m^{30}n^{16}$

$\\ \rm\Rrightarrow (2xy^3)^2.2x^2y^0=4x^2y^6.2x^2=8x^4y^6$

6 0

2 years ago

An airplane makes a 400-mile trip against a head wind in 4 hours. The return trip takes 2.5 hours, the wind now being a tall win

tangare [24]

Answer:

$v_p=130\ miles/h$

$v_w=30\ miles/h$

Step-by-step explanation:

Lets call $v_p$ the the still-air speed of the plane and $v_w$ the speed of the wind. On the first part the speed of the plane relative to the ground will be $v_1=v_p-v_w$ , and on the second part it will be $v_2=v_p+v_w$ .

We know that the distance d=400 miles on the first and second parts are the same, so by the definition of velocity we will have:

$v_1=\frac{d}{t1}$

$v_2=\frac{d}{t2}$

Or:

$v_p-v_w=\frac{d}{t1}$

$v_p+v_w=\frac{d}{t2}$

Adding both equations:

$(v_p-v_w)+(v_p+v_w)=2v_p=\frac{d}{t1}+\frac{d}{t2}$

$v_p=\frac{1}{2}(\frac{d}{t1}+\frac{d}{t2})$

Which for our values is:

$v_p=\frac{1}{2}(\frac{400\ miles}{4h}+\frac{400\ miles}{2.5h})=130\ miles/h$

If instead of adding, we substact, we would have:

$(v_p+v_w)-(v_p-v_w)=2v_w=\frac{d}{t2}-\frac{d}{t1}$

$v_w=\frac{1}{2}(\frac{d}{t2}-\frac{d}{t1})$

Which for our values is:

$v_w=\frac{1}{2}(\frac{400\ miles}{2.5h}-\frac{400\ miles}{4h})=30\ miles/h$

6 0

4 years ago

Sketch the graph of the given data on the accompanying coordinate plane. a)choose ad state an appropriate scale so that all of t

vodomira [7]

Part A
A good scale for y to use would be 100, since it fits in all of the f(x)'s and the next value (243) is obviously not going to fit.
As for x, you can use 4 or 5. If you do 5, you're not going to get to it though, because f(x) will be 243.

Part B
When our input increases by 1, our output multiplies by 3.
Multiplying by 3 $x$ times can be represented as $3^x$ .
We start at 1, so we'd want to have $1\times3^x$ . However, 1 times anything doesn't change its value, so we can leave it out because it is redundant.

As for making the graph, just label your y axis 0 to 100, and your x axis 0 to 5.
Then mark out (0, 1), (1, 3), (2, 9), (3, 27), and (4, 81).
Draw a curve that includes all of these. It should hit y=100 a little after x=4, since x=5 is all the way at y=243.

6 0

3 years ago

I need help simplifying:

Alex787 [66]

1. 3/5
2. doesnt simplify
3.3/32

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4 years ago

Find the period of the function

Ostrovityanka [42]

Answer:

6π

Step-by-step explanation:

The period indicates after which time the sine wave repeats.

You divide 2π by the factor in front of your function variable. This is 1/3 for your function.

So 2π/(1/3) = 6π

4 0

3 years ago