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3 years ago

Find an equation of the line through (2,7) and parallel to y=3x-6 Y=

Mathematics

1 answer:

Sliva [168]3 years ago

6 0

As we know the formula to calculate the line of equation is y - y1 = m (x - x1)

Where m is the slope. y1 is the first y co ordinate. x1 is the first x co ordinate.

Now we do know that the slope of parallel line is the same as the slope of the original line.

So parallel line slope is 3 so slope for our line is 3. Hence equation is y - 7 = 3 (x - 2) which becomes y = 3x + 1.

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PASSAGE:

Art [367]

The shortest distance separating Julio from Sarah is 111.8ft

To know the distance of the shortest bridge between Julio and Sarah, the following procedure must be carried out.

We know that Julio walked 100ft to one side and Sarah walked 20ft to the opposite side, that is, on the <em>y-axis</em> they are 120ft apart.

On the other hand, Julio stayed by the river and Sarah walked 9ft away from the river, that is, on the <em>x-axis</em> they are separated by a distance of 59ft (assuming that the width of the river is 50ft).

To know the linear distance that separates them, it is necessary to use the following formula of the Pythagorean theorem.

c² = a² + b²

c= $\sqrt{a^{2} + b^{2} }$

From this operation we know the value of a and b:

a = 120ft

b = 59ft

Now we just have to replace the values in the formula.

c = $\sqrt{120^{2} + 59^{2} }$

c = $\sqrt{14400 + 3481}$

c = $\sqrt{17881}$

c = 133,7

However, 133.5ft is not the value of the bridge distance because Sarah went 9ft away form the river. Then a portion must be subtracted from her to calculate the exact portion of the distance above the river.

For this we must calculate the distance that separates them that is above the Earth, for this we use the same mathematical formula.

c = $\sqrt{20^{2} + 9^{2} }$

c = $\sqrt{400 + 81}$

c = $\sqrt{481}$

c = 21,9ft

So the distance a part of the Earth covers is 21.9ft. To find out how far the bridge should be over the river, we subtract 21.9ft from the total distance 133.7ft

133,7ft - 21,9ft = 111,8ft

Note: This question is incomplete because it has missing information (the length and width of the river).

Learn more in: brainly.com/question/25292638

5 0

3 years ago

A plane flying over the ocean is on course to land on an aircraft carrier. The diagonal distance between the plane and the aircr

fomenos

Answer:

the plane's current height above the ocean is 3.42 miles

Step-by-step explanation:

Given that the diagonal distance between the plane and the aircraft carrier is 10 miles.

What we need to find is the vertical distance between the plane and the aircraft carrier which is the plane's current height above the ocean. This can be gotten using sine rule.

For sine rule, you need a side and its opposite angle. For this question the triangle formed is a right angle triangle with diagonal distance, vertical distance and horizontal distance.

let a = diagonal distance = 10 miles

let the opposite angle to the diagonal distance be A = 90° (right angle)

let the vertical distance = b

let the opposite angle to the vertical distance be B = 20°

Sine rule states that $\frac{a}{sin(A)} = \frac{b}{sin(B)}$