P varies inversely with x. If P = 14 when x= 16, find the value of P when x = 21.

Mathematics

1 answer:

Oliga [24]2 years ago

7 0

Answer:

Option C. 32/3

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form $p*x=k$ or $p=k/x$

we know that

For p=14, x=16

Find the value of k

$k=p*x$

substitute the values

$k=(14)*(16)=224$

The equation is equal to

$p=\frac{224}{x}$

Find the value of p when x=21

substitute the value of x in the equation

$p=\frac{224}{21}$

simplify

Divide by 7 both numerator and denominator

$p=\frac{32}{3}$

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Rina8888 [55]

I would recommend taking a picture of the instructions because I am not sure if you need to find the equation of the line that is parallel or perpendicular, so I will do both.

1. (3 , 2); y = 3x - 2

If the line is parallel to the given equation, the slopes have to be the SAME, so the slope(m) is 3

y = mx + b

y = 3x + b

To find b you plug in the point (3, 2) into the equation

2 = 3(3) + b

2 = 9 + b

-7 = b

The equation of the line that is parallel to the given equation is:

y = 3x - 7

To find the equation of the line that is perpendicular to the given equation, the slope has to be the exact opposite of the given slope. (you flip the sign and the number of the given slope to get the perpendicular line's slope)

The given slope is 3, the perpendicular slope is $-\frac{1}{3}$