Question

Simplify
(3a^-2b^3)^-4

Answer 1

A jet takes 8hours to travel a distance of 7168 miles against the wind, the. Return trip take 7 hours with the wind. What is the rate if the jet in still air and what is the rate of the wind

Answer 2

Write and equation for the expression p varies directly with f and inversely with u . Use k as the constant of proportionality

Answer 3

To simplify the expression, we can apply the exponent rules.

First, we can distribute the exponent of -4 to both the numerator and denominator of the expression.

Doing so, we get:
((3^-4) * (a^-2*-4) * (b^3*-4))

Next, we can simplify the exponents:
((1/3^4) * (a^8) * (b^-12))

Simplifying further, we get:
(a^8) / (81 * b^12)

Answer 4

Let's denote the rate of the jet in still air as "x" and the rate of the wind as "y".

Against the wind:
Rate = x - y
Time = 8 hours
Distance = 7168 miles

Using the formula Distance = Rate * Time, we can write the equation:
7168 = (x - y) * 8

With the wind:
Rate = x + y
Time = 7 hours
Distance = 7168 miles

Using the same formula, we can write the equation:
7168 = (x + y) * 7

We now have a system of equations:

8(x - y) = 7168
7(x + y) = 7168

Expanding and simplifying these equations, we get:

8x - 8y = 7168
7x + 7y = 7168

To solve the system of equations, we can multiply the second equation by 8 and subtract it from the first equation:

8x - 8y - (56x + 56y) = 7168 - (57264)

-48x = -50096

Dividing both sides by -48, we get:
x = 1046

Substituting this value into the first equation, we can find the value of y:

8x - 8y = 7168

8(1046) - 8y = 7168

8368 - 8y = 7168

-8y = -1200

Dividing both sides by -8, we get:
y = 150

Therefore, the rate of the jet in still air is 1046 mph and the rate of the wind is 150 mph.

Answer 5

The equation for the expression "p varies directly with f and inversely with u" can be written as:

p = k * (f/u)

In this equation, p represents the variable that varies directly with f and inversely with u. k is the constant of proportionality. Multiplying k by the ratio of f to u represents the direct variation with f and the inverse variation with u.