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10 months ago

Are A and B parallel?

Mathematics

1 answer:

lawyer [7]10 months ago

4 0

Answer:

Gradient of line A = 0.8

Gradient of line B = 0.75

Therefore the lines are not parallel

Step-by-step explanation:

1. Rearrange the equation of line A into the form Y=mX + C in order to find the gradient of line A which m in the equation represents the gradient.

2. Use the gradient formula, (y2-y1)/(x2-x1) to find the gradient of line B

Since the both have different gradient. It means that they are not parallel

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Something to remember is how to multiply terms with same bases, but different exponents:

$a^b \cdot a^c = a^{(b+c)}$

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Using the information above, we can find our answer:

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2 years ago

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2 years ago

The height of an object from a distance

olga55 [171]

Y = height
x = distance from tower

tan(19.9) = y/x

tan(21.8) = y/(x-50) ( x is 50 feet closer so subtract 50 from x)

find the tan of the angles:
tan19.9 = 0.362
tan21.8 = 0.400

replace those values in the equations:
0.362 = y /x
0.400 = y / (x-50)

rewrite to solve for height:
0.362x = y
0.400(x-50) = y distribute the 0.400 and rewrite as 0.400x-20 =y

now solve:

0.362x = 0.400x-20

add 20 to each side:
0.362x +20 = 0.400x

subtract 0.362x from each side:

20 = 0.038x

divide both sides by 0.038
x = 20 / 0.038 = 526.3 feet

now that x is known replace x in the original equation and solve for y:

tan19.9 = y /x

0.362 = y / 526.3
y = 0.362 x 526.3
y = 190.5

the height of the tower is 190.5 feet

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2 years ago