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Yuliya22 [10]
3 years ago
12

Find the area between y=(x-2)ex and the x-axis from x=2 to x=4.

Mathematics
1 answer:
mojhsa [17]3 years ago
3 0

Answer:

e^4+e^2

Step-by-step explanation:

It can be found by integral.

First let's find the intersection points.

(x-2)e^x = 0

Only intersection point is x = 2.

And it is asked to find the area in the interval (2, 4).

\int\limits^4_2 (x-2)e^x \,dx=?

We will use integration by parts.

x-2=u\\dx=du\\e^xdx=dv\\e^x=v

\int\limits^4_2 (x-2)e^x \,dx=uv-\int vdu=(x-2)e^x-\int e^xdx=(x-2)e^x-e^x=\\\\=(x-3)e^x|^4_2=(4-3)e^4-(2-3)e^2=e^4+e^2

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Lisa [10]

Answer:

y = 2/3x + 4

Step-by-step explanation:

First, we look at where the equation intersects the y axis. It intersects at y = 4, which means that in the end of the equation there must be a "+4", so we can rule out the first two.

Second, we look at the slope of the line. Slope is defined as rise over run. As you can see in the graph, the line moves up 2 units while moving right 3 units. That means the coefficient of x (which is the slope) will be 2/3, which means the answer is y = 2/3x + 4.

4 0
2 years ago
Which graph corresponds to the equation: y=−3x−6 ?
Nonamiya [84]

Answer:

Step-by-step explanation:

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2 years ago
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randy has two 28 pound blocks of ice for his snow cone stand. if each snow cone requires 2/3 pound of ice, how many snow cones c
Mariana [72]
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4 0
2 years ago
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Triangle ABC has vertices at A(−1 , 2), B(4, 2), and C(3, −1). Classify the triangle according to the side lengths.
Orlov [11]

Answer:

B) Isosceles

Step-by-step explanation:

The given triangle has vertices at A(-1,2), B(4,2) and C(3,-1).

We must first determine the length of the sides of the triangle, before we can classify it.

We apply the distance formula to find length of the sides.

|AB|=\sqrt{(4--1)^2+(2-2)^2}

\Rightarrow |AB|=\sqrt{(4+1)^2+(2-2)^2}

\Rightarrow |AB|=\sqrt{5^2+(0)^2}

\Rightarrow |AB|=\sqrt{25}

\Rightarrow |AB|=5 units.

The length of side BC

|BC|=\sqrt{(3-4)^2+(-1-2)^2}

\Rightarrow |BC|=\sqrt{(-1)^2+(-3)^2}

\Rightarrow |BC|=\sqrt{1+9}

\Rightarrow |BC|=\sqrt{10}

The length of side AC

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We simplify to obtain;

|AC|=\sqrt{(3+1)^2+(-3)^2}

\Rightarrow |AC|=\sqrt{(4)^2+(-3)^2}

|AC|=\sqrt{16+9}

|AC|=\sqrt{25}

|AC|=5\:units

Since |AC|=5\:units=|AB|, the given triangle is an isosceles triangle.

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3 years ago
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