What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −2/3

Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How

aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight = $(\frac{1}{K})$

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe = $(\frac{1}{K-3})$

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them = $(\frac{1}{2})$

⇒ Per hour rate of ( Dwight + Joe) = $(\frac{1}{2} )$

$\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})$

Now, solving for the value of K , we get:

$(\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0$

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

8 0

3 years ago

Will give brainliest answer

vovangra [49]

Answer:

A=50.26548246units^2

Step-by-step explanation:

Radius is 4 because half the diameter (8) is the radius (4)

A=πr^2

A=π(4)^2

A=50.26548246units^2

8 0

3 years ago

Read 2 more answers

A construction crew built miles of road in days. What is the unit rate in miles per day? Write your answer as a fraction or a mi

vovikov84 [41]

Complete question :

A construction crew built 1/2 miles of road in 1/8 days. What is the unit rate in miles per day? Write your answer in simplest form.

Answer:

3 miles per day

Step-by-step explanation:

Given that:

1/2 miles of road takes 1/8 days

Unit Rate in miles per day :

Miles of road built / number of days taken

1/2 miles ÷ 1/8 days

1/2 * 8/1

= (1*8) / (2*1)

= 8/2

= 4

Unit Rate = 4 miles per day

4 0

3 years ago

A half-filled cylindrical water tank has a water level of 20 feet high. The tank can hold 6000 cubic feet of water. Find the dia

OleMash [197]

Answer:

Diameter of tank = 19.5 ft

Step-by-step explanation:

Volume of cylinder = Base area x Height.

Base area = Area of circle

$\texttt{ Area of circle}=\frac{\pi d^2}{4}$

Height = 20 ft.

Volume of tank = 6000 cubic feet .

$\texttt{ Volume of cylinder = Base area x Height.}\\\\6000=\frac{\pi d^2}{4}\times 20\\\\d^2=381.97\\\\d=19.5ft$

Diameter of tank = 19.5 ft

4 0

3 years ago

Scott sends an email to 3 people and each of those people will send the email to 3 more people, and so on. Which

Naddika [18.5K]

Answer:

12 I think I counted it hope it's correct

5 0

3 years ago