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klasskru [66]
3 years ago
15

Solving an Equation for a Rate Problem Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail a

t an average rate of 5 miles per hour. He traveled for a total of 3 hours. The equation 3t = 5(3 – t) can be used to find the time it took Stu to hike one way. How long did it take Stu to hike the trail one way?
Mathematics
2 answers:
ohaa [14]3 years ago
6 0
Given:
speed = distance / time

walking: 3 miles per hour
running 5 miles per hour
for a total of 3 hours.

3t = 5(3-t)
3t = 15 - 5t
3t + 5t = 15
8t = 15
t = 15/8
t = 1 7/8 

7/8 * 60 mins = 52.50 minutes

t = 1 hour and 52.5 minutes

It took Stu 1 hour and 52.5 minutes to hike the trail one way.
Dafna11 [192]3 years ago
5 0

Answer:

It's B (3t = 5(3 – t))

Step-by-step explanation:

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Olin [163]

Answer:

(2,1)

Step-by-step explanation:

3 0
2 years ago
A pond forms as water collects in a conical depression of radius a and depth h. Suppose that water flows in at a constant rate k
Scrat [10]

Answer:

a. dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. πa² ≥ k/∝

Step-by-step explanation:

a.

The rate of volume of water in the pond is calculated by

The rate of water entering - The rate of water leaving the pond.

Given

k = Rate of Water flows in

The surface of the pond and that's where evaporation occurs.

The area of a circle is πr² with ∝ as the coefficient of evaporation.

Rate of volume of water in pond with time = k - ∝πr²

dV/dt = k - ∝πr² ----- equation 1

The volume of the conical pond is calculated by πr²L/3

Where L = height of the cone

L = hr/a where h is the height of water in the pond

So, V = πr²(hr/a)/3

V = πr³h/3a ------ Make r the subject of formula

3aV = πr³h

r³ = 3aV/πh

r = ∛(3aV/πh)

Substitute ∛(3aV/πh) for r in equation 1

dV/dt = k - ∝π(∛(3aV/πh))²

dV/dt = k - ∝π((3aV/πh)^⅓)²

dV/dt = K - ∝π(3aV/πh)^⅔

dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. Equilibrium depth of water

The equilibrium depth of water is when the differential equation is 0

i.e. dV/dt = K - ∝π(3a/πh)^⅔V^⅔ = 0

k - ∝π(3a/πh)^⅔V^⅔ = 0

∝π(3a/πh)^⅔V^⅔ = k ------ make V the subject of formula

V^⅔ = k/∝π(3a/πh)^⅔ -------- find the 3/2th root of both sides

V^(⅔ * 3/2) = k^3/2 / [∝π(3a/πh)^⅔]^3/2

V = (k^3/2)/[(∝π.π^-⅔(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝π^⅓(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝^3/2.π^½.(3a/h))]

V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. Condition that must be satisfied

If we continue adding water to the pond after the rate of water flow becomes 0, the pond will overflow.

i.e. dV/dt = k - ∝πr² but r = a and the rate is now ≤ 0.

So, we have

k - ∝πa² ≤ 0 ---- subtract k from both w

- ∝πa² ≤ -k divide both sides by - ∝

πa² ≥ k/∝

5 0
3 years ago
SOMEONE PLEASE HELP ME ASAP THIS IS ALMOST DUE ILL MARK BRAINLIEST!!!!
makkiz [27]

Answer:

153

Step-by-step explanation:

If the table adds up to 20 and opened toe counts for 45% of the total. then 45% of 340 is 153 !

3 0
2 years ago
I need please ASAP SOMEBODY I'll appreciate it
Setler [38]
It depends on the weather but ill go with the second one. U dont have to take my advice tho.
8 0
3 years ago
Nancy’s morning routine involves getting dressed , eating breakfast, making her bed , and driving to work . Nancy spends 1/3 of
grin007 [14]

Answer: Nancy needs 26 minutes to driving to work.

Explanation:

Since we have given that

Time taken in eating breakfast = 10 minutes

Time taken in making her bed = 5 minutes

Let the total time taken by her in doing routine activities be x

Time taken in getting dressed is given by

\frac{1}{3}x

So, According to question,

\frac{x}{3}+10+5=35\frac{1}{2}\\\\\frac{x}{3}+15=\frac{71}{2}\\\\\frac{x}{3}=\frac{71}{2}-15\\\\\frac{x}{3}=\frac{71-30}{2}=\frac{41}{2}\\\\x=\frac{123}{2}

Now, we need to find the time taken in driving to work which is given by

\frac{123}{{2}-\frac{71}{2}=\frac{52}{2}=26\ minutes

Hence, Nancy needs 26 minutes to driving to work.

6 0
3 years ago
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