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I am Lyosha [343]
3 years ago
13

What is the equation of the line through (3,7) that is perpendicular to the line through points (-1,-2) and (5,3)?

Mathematics
2 answers:
Svetlanka [38]3 years ago
7 0
<span>the line through points (-1,-2) and (5,3)
slope=(3-(-2))/(5-(-1))=5/6
for a perpendicular line slope =-6/5=-1.2
y=(-6/5)x+b
7=(-6/5)*3+b
7=-18/5+b
7=-36/10+b
7=-3.6+b
b=10.6
y=-1.2x+10.6</span>
fomenos3 years ago
3 0

Answer:

The equation of the line would by y = -6/5x + 53/5

Step-by-step explanation:

In order to find this, we must first find the slope of the original line. We can do this with the slope formula.

m (slope) = (y2 - y1)/(x2 - x1)

m = (3 - -2)/(5 - -1)

m = (3 + 2)/(5 + 1)

m = 5/6

Now that we have the slope of this line, we can find the slope to the other line by using the reciprocal and opposite of it. So we flip 5/6 to get 6/5 and then we make it negative to get -6/5. Now that we have this, we can use the slope and a point in point-slope form to find the line.

y - y1 = m(x - x1)

y - 7 = -6/5(x - 3)

y - 7 = -6/5x + 18/5

y = -6/5x + 53/5

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Cone W has a radius of 8 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W. Paul and Manuel
sergij07 [2.7K]

This question is incomplete because it lacks the appropriate attachment containing the argument of Paul and Manuel

Kindly find attached the appropriate attachment necessary to solve this question.

The attachment was sourced online

Answer:

a) Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X

Step-by-step explanation:

From the above question, we are given two shapes: Cone W and Square Pyramid

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Volume of a Cone = 1/3 πr²h

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Volume of Cone X = 1/3 × 3.14 × 8² × 5

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Volume = 1/3 × Base Area × Height

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Where π = 3.14

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Height of Square pyramid X = Height of Cone W = 5cm

Volume of Square pyramid = 1/3 ×200.96cm² × 5cm

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Therefore, from my above calculation and compared with the arguments of Paul and Manuel, Option a) "Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X" is the correct option.

The reason why is because the correct formula for the volume of a square pyramid = 1/3 × Base area × Height

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Manuel on the other hand used the formula: Base Area × Height to find the volume of cone W. This formula is wrong.

Option a, is the correct answer.

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