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2 years ago

The number line shows the distance in meters of two birds ,A and B from a worm located at point x:

Mathematics

1 answer:

juin [17]2 years ago

7 0

Distance between the 2 birds is 2.5 - (-2.5), or 5.0 (units).

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If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

Sauron [17]

<h2>Answer:</h2>

$2\vec{v}-6\vec{u}=(-52,48) \\ \\ ||2\vec{v}-6\vec{u}||=75.28}$

<h2>Step-by-step explanation:</h2>

In this problem we have two vectors:

$\vec{u}=(5,-7) \ and \ \vec{v}=(-11,3)$

So we need to find two things:

$2\vec{v}-6\vec{u}$

and:

$||2\vec{v}-6\vec{u}||$

FIRST:

In this case we have the multiplication of vectors by scalars. A scalar is a simple number, so:

$2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}$

SECOND:

If we name:

$\vec{w}=2\vec{v}-6\vec{u}$

Then, $||2\vec{v}-6\vec{u}||$ is the magnitude of the vector $\vec{w}$ . Therefore:

$||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}$

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2 years ago

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Simplify <br> ( 5w + 13 ) + ( 2w + 1)

Vadim26 [7]

Answer:

10w^2 + 24w + 13

Step-by-step explanation:

use Foil method

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3 years ago

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The region bounded by y = e−x2, y = 0, x = 0, and x = b (b > 0) is revolved about the y-axis. (Round your answers to three de

kari74 [83]

Answer:

0.982 * $\pi$ = 3.085 cubic units

Step-by-step explanation:

To find the volume of the solid generated by a region that is bounded by lines where x = 0 , x (b) = 2 we apply the formula given in the attachment below

the required region boundaries are

y = e^-x2 , y = 0 , x = 0, x = b ( b >0)

attached below is a detailed solution of the problem