1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Greeley [361]
2 years ago
5

Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio

n barrels of oil in the well; six years later barrels remain.At what rate was the amount of oil in the well decreasing when there were barrels remaining
Mathematics
1 answer:
JulijaS [17]2 years ago
7 0

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

Initial =1\ million

6\ years\ later = 500,000

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

\frac{dA}{dt} = kA

Where k represents the constant of proportionality

\frac{dA}{dt} = kA

Multiply both sides by dt/A

\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}

\frac{dA}{A}  = k\ dt

Integrate both sides

\int\ {\frac{dA}{A}  = \int\ {k\ dt}

ln\ A = kt + lnC

Make A, the subject

A = Ce^{kt}

t = 0\ when\ A =1\ million i.e. At initial

So, we have:

A = Ce^{kt}

1000000 = Ce^{k*0}

1000000 = Ce^{0}

1000000 = C*1

1000000 = C

C =1000000

Substitute C =1000000 in A = Ce^{kt}

A = 1000000e^{kt}

To solve for k;

6\ years\ later = 500,000

i.e.

t = 6\ A = 500000

So:

500000= 1000000e^{k*6}

Divide both sides by 1000000

0.5= e^{k*6}

Take natural logarithm (ln) of both sides

ln(0.5) = ln(e^{k*6})

ln(0.5) = k*6

Solve for k

k = \frac{ln(0.5)}{6}

k = \frac{-0.693}{6}

k = -0.1155

Recall that:

\frac{dA}{dt} = kA

Where

\frac{dA}{dt} = Rate

So, when

A = 600000

The rate is:

\frac{dA}{dt} = -0.1155 * 600000

\frac{dA}{dt} = -69300

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

You might be interested in
crater Lake in Oregon in shaped like a circle with a diameter of about 5.5 miles. What is the area of the surface of crater lake
N76 [4]

Answer:

Given the statement: Crater Lake in Oregon in shaped like a circle with a diameter of about 5.5 miles.

Area of circle is given by:

A = \pi \frac{d^2}{4}

where

A represents the area of a circle

d represents the diameter of a circle.

then;

It is given that Surface of Crater lake is shaped like a circle.

Substitute the given values, we have;

Area of a circle = \pi \frac{(5.5)^2}{4}

= 3.14 \times \frac{30.25}{4} =3.14 \times 7.5625 = 23.74625 square miles

therefore, the area of a surface of a crater lake is, 23.74625 square miles.

3 0
3 years ago
A conical-shaped umbrella has a radius of 0.4 m and a height of 0.45 m. Calculate the amount of fabric needed to manufacture thi
bonufazy [111]

Answer:

The correct answer will be "0.756596 m²".

Step-by-step explanation:

The given values are:

The radius of an umbrella,

r = 0.4 m

The height of an umbrella,

h = 0.45 m

As we know,

The lateral surface of an umbrella will be:

⇒  \pi r\sqrt{r^2+h^2}

On substituting the values, we get

⇒  \pi \times 0.4\sqrt{(0.4)^2=(0.45)^2}

⇒  0.756596 \ m^2

So that the amount of fabric needed will be "0.756596 m²".

7 0
3 years ago
If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building?
elena55 [62]

The closer Diana gets to the building, the smaller the angle becomes

Diana is 17.6 feet closer to the building

<h3>How to calculate the distance from the building</h3>

To calculate the distance between her and the building, we make use of the following tangent ratio

\tan(\theta) = \frac{h}{d}

Where:

  • \theta = 40^o
  • h represents the height of the building; h = 130
  • d represents the distance from the building

So, we have:

\tan(40) = \frac{130}{d}

Make d the subject

d = \frac{130}{\tan(40)}

Evaluate tan(40)

d = \frac{130}{0.8391}

d = 154.93

Initially, Diana is at a distance of 172.53.

The difference in both distance is:

\Delta d = 172.53 - 154.93

\Delta d = 17.6

Hence, Diana is 17.6 feet closer to the building

Read more about trigonometry ratios at:

brainly.com/question/4326804

7 0
2 years ago
How many ways are there to select a 5-card hand from a regular deck such that the hand contains at least one card from each suit
Snezhnost [94]

Answer:

There are 685464 ways of selecting the 5-card hand

Step-by-step explanation:

Since the hand has 5 cards and there should be at least 1 card for each suit, then there should be 3 suits that appear once in the hand, and one suit that apperas twice.

In order to create a possible hand, first we select the suit that will appear twice. There are 4 possibilities for this. For that suit, we select the 2 cards that appear with the respective suit. Since there are 13 cards for each suit, then we have {13 \choose 2} = 78 possibilities. Then we pick one card of all remaining 3 suits. We have 13 ways to pick a card in each case.

This gives us a total of 4*78*13³ = 685464 possibilities to select the hand.

6 0
3 years ago
PLEASE HELP. WILL GIVE BRAINLEST
swat32

Answer:

i would say A. The initial cost for renting a snowmobile is $75, with each hour of use costing an additional $25.

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • PLEASE HELP !!! First and right answers I will mark brainliest !!!!
    5·2 answers
  • One-half a number minus 6 is 4. what is the number​
    13·1 answer
  • I don’t even know how to answer this lol it’s too early for me. So confused plz help
    11·2 answers
  • 4x^2-x-3=0<br> Solve by completing the square.<br> x= ?
    9·1 answer
  • Simplify 8n + 3 - 4 + 4n show work pls
    11·2 answers
  • Which is the correct graph and solution for the following system of equations y=2x+3 y=-x-6
    7·2 answers
  • Whatss the Median??????????????????????///
    14·1 answer
  • 1) x 20+ 5 = 4
    12·2 answers
  • Ima be posting a lot of questions so...cash in. (ONLY if you know the answers)
    5·2 answers
  • A bag contains 9 pennies , 8 nickels, and 5 dimes. How many quarters should be added to the bag so the probability of drawing a
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!