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leva [86]
3 years ago
15

Refer to the equation 2x − 3y = 18.

Mathematics
1 answer:
xenn [34]3 years ago
7 0
First, you should rearrange your equation using simple algebra

2x-3y-18=0
2x-18=3y
(2x/3)-6=y

the y intercept has an x coordinate of 0, so substitute 0 as x in your equation to find the y-int.

the x intercept has a y coordinate of 0, so substitute 0 as y in your equation and algebraically solve for the x-int

to make the table of values, just substitute different values in for x in the equation
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The kittens, Annie and Josie, are pushing a ball, Annie with a force magnitude of 80 N in a direction of 133 degrees, and Josie
kvv77 [185]

Answer: Then the magnitude of the force is 37.86N, and the direction is 54.35°

Step-by-step explanation:

We can write the forces as vectors.

We know that Annie pushes with a magnitude of 80N in a direction of 133° (Remember that the angles are always measured from the x-axis)

The components of this force, (Ax, Ay), are then:

Ax = 80N*cos(133°)

Ay = 80N*sin(133°)

And we know that Josie pushes with a magnitude of 95N in direction of 290°

The components of this force, (Jx, Jy), are:

Jx = 95N*cos(290°)

Jy = 95N*sin(290°)

When we add these forces, the total force acting on the ball is:

F = (80N*cos(133°) ,  80N*sin(133°)) + (95N*cos(290°), 95N*sin(290°))

F = (80N*cos(133°) + 95N*cos(290°), 80N*sin(133°) + 95N*sin(290°))

Now, the third kitten wants to do a force K, in a direction θ, such that the net force acting on the ball is zero.

Then we must have that, each component of the force of the third cat (K*cos(θ)  on the x-axis and k*sin(θ) on the y-axis), is such that:

K*cos(θ) + 80N*cos(133°) + 95N*cos(290°) = 0

k*sin(θ)  + 80N*sin(133°) + 95N*sin(290°) = 0

Now we need to solve that system for k and θ

if we simplify the equations we get:

k*cos(θ) - 22.07N = 0

k*sin(θ)  -30.76N  = 0

Now we can rewrite them as:

k*cos(θ) = 22.07N

k*sin(θ)   = 30.76N  

Now we can take the quotiet between both equations to get:

(k*sin(θ))/(k*cos(θ)) = 30.76N/22.07N

Tan(θ) = 1.394

θ = Atan(1.394) = 54.35°

Now that we know the angle, we can find the value of the magnitude k, by using one of the two equations of the system:

k*cos(54.35°) = 22.07N

k = 22.07N/cos(54.35°) = 37.86N

Then the magnitude of this force is 37.86N, and the direction is 54.35°

7 0
2 years ago
Construct a triangle whose sides are 3 in., 1 1/2 in., 2 3/8 in., 2 in., 3 1/2 in.
Luda [366]
That's 5 lengths for a three sided shape... Are you sure that is the instructions?
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The graph shows the height of a hiker above sea level. The hiker walks at a constant speed for the entire trip. What are the var
Scorpion4ik [409]
It is shown that he goes down in a slower time than he does going up.
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The graph of the function B is shown below. If B(x) = -1, then what is x?
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The answer is c, 2.To find this, look on the graph for a point with the y value of -1. (2,-1) is the solution.
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Albania is an Eastern European country that uses a currency called the Albanian Lek (ALL). Right now, $1 (1 USD) exchanges for 1
rosijanka [135]

Answer:

$9398.50

Step-by-step explanation:

Given

\$1 = 106.40\ ALL

Required

Equivalent of 1,000,000 ALL

We have:

\$1 = 106.40\ ALL

and

\$x = 1000000\ ALL

Cross Multiply

x * 106.40 = 1 * 1000000

106.40x = 1000000

Solve for x

x = 1000000/106.4

<em></em>x = \$9398.50<em> -- Approximated</em>

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