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vivado [14]
3 years ago
7

A raft travels down river at a rate of 6 miles per hour. The total distance d in miles that the raft travels is equal to the rat

e times the number of hours h. What is the independent variable? * What is the dependent variable? * Write an equation for this situation. (using h and d) *
Mathematics
1 answer:
Fudgin [204]3 years ago
8 0

Answer:

d=6h

Step-by-step explanation:

Speed of the raft= 6 miles per hour

Total distance (d) of the raft= rate × number of hours

d=r*h

Independent variable is the number of hours(h)

Dependent variable is the distance (d)

Equation for the situation

d=r*h

d=distance

r=rate

h=number of hours

From the question,

r=6 miles per hour

Therefore,

The equation is

d=r*h

d=6*h

d=6h

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Answer:

(A) h(x) = 1/4x -2

Step-by-step explanation:

Given: f(x)=4x+8

Rewrite with y: y=4x+8

Switch x and y: x=4y+8

Solve for y: x-8=4y

(x-8)/4=y

1/4x-2=y

y=1/4x-2

This means that h(x) = 1/4x -2 is the correct answer

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now,

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TEA [102]

Answer: the rate at which the distance between the boats is​ increasing is 68 mph

Step-by-step explanation:

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Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

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Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

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z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

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68dz/dt = 4624

dz/dt = 4624/68

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