an oil storage tank ruptures and oil leaks from the tank at a rate of r(t)= 100e^(-0.01t) liters per minute. How much oil leaks out during the first hour?

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]\\\displaystyle V=\int\limits^{60}_0 {100*e^{-0.01*t}} \, dx \\\\=-\frac{100}{0.01} *\Bigg [e^{-0.01*t}\Bigg ]^{60}_0\\\\=-10000*(e^{-0.60}-1)\\\\=4511.883663.... (liters)[/tex]


Related Questions

Could you help please i really dont get it

Answers

Answer:

[tex]3.4 \: apple \: pounds = 5.61 \: dollars \\ 1 \: apple \: pound = \{ \frac{(1 \times 5.61)}{3.4} \} \: dollars \\ \\ = { \boxed{ \boxed{1.65 \: dollars \: per \: pound}}}[/tex]

Answer:

1.65

Step-by-step explanation:

5.61/3.4=1.65

There are 6 times as many dogs as cats . If the total number of dogs and cats is 21 , how many dogs are there?

Answers

3 cause 3x6=18 18+3=21

Answer:

126 cats .................

126 dogs........

Fitness 19 charges a $44 sign up fee and $30 per month. LA fitness charges a $99 sign up and $25 per month. For what number of months is the cost the same?

Answers

Answer:

11 months

Step-by-step explanation:

Let x = months

y = total cost

Since Fitness 19 charges $30 a month, we multiply x by 30 like this: 30x

$44 is already added on the cost, so the Fitness 19 equation will look like this:

y = 30x + 44

Since LA Fitness charges $25 a month, multiply x by 25 like this: 25x

$99 is already added to the cost, so the LA Fitness equation will look like this:

y = 25x + 99

We need to find the point where they are both the same

30x + 44 = 25x + 99

First, move like terms to one side by subtracting 25x from both sides

30x + 44 = 25x + 99

- 25x         - 25x

5x + 44 = 99

Then, subtract 44 from both sides

5x + 44 = 99

     - 44 - 44

5x = 55

Finally, isolate the variable, x, by dividing both sides by the coefficient, 5

5x/5 = 55/5

x = 11

If two functions are inverses of each other, which 2 statements are true?
A The graph of an inverse of a function is a reflection of the function across the line y=x. B f(g(x)) = x and g(f(x)) = x
C The graph of an inverse of a function is a reflection of the function across the line y=0. D f(g(x)) =1 and g(f(x)) = 1

Answers

Answer:

A and B

Step-by-step explanation:

To be inverses, the inverse composite functions must equal x, since the input and output must be equal as how much you used as your input, which is x. B proves that. Also, the graph must reflect over y = x, which is the line that runs through the origin

please help!!!!!!!!!​

Answers

110 feet of fencing is needed to make four gardens

Answer:

110

Step-by-step explanation:

First, find the perimeter of 1 fence.

55/2 or [tex]27\frac{1}{2}[/tex]

Multiply by the number of fences (4)

110

I hope this helps!

Please explain how to solve this problem

The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 400 pounds of the new blend. The selling price of the new blend is to be $4.50 per​ pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are​ required?

The blend should have _ pounds of Earl Grey and _ pounds of Orange Pekoe.

Answers

9514 1404 393

Answer:

100 pounds Earl Grey300 pounds Orange Pekoe

Step-by-step explanation:

Let x represent the number of pounds of Earl Gray tea in the mix. Then the total cost of the mix is ...

  6x +4(400-x)=4.50(400)

  2x +1600 = 1800 . . . . . . . simplify

  2x = 200 . . . . . . . . . . . subtract 1600

  x = 100 . . . . . . . . . . . divide by 2. Pounds of Earl Grey

  (400 -x) = 300 . . . . . Pounds of Orange Pekoe

The blend should have 100 pounds of Earl Grey and 300 pounds of Orange Pekoe.

_____

Additional comment

It is easy to show that the relationship between the quantities of high-cost (H) and low-cost (L) items in the mix (M) is ...

  fraction of mix that is H is (M -L)/(H -L)

Here, we have H=6, L=4, M=4.5, so the fraction of the mix that is Earl Grey is ...

  (4.5 -4)/(6 -4) = 0.5/2 = 0.25

There are 400 pounds of mix, so 0.25(400) = 100 pounds is Earl Grey.

The solution above is essentially 2-step, so using this relation doesn't necessarily save any steps. It just makes it possible to solve the problem in your head.

In exercises 1-2, solve the formula for the indicated variable.

1: Surface area of a cylinder: S=2πr^2+2πrh: Solve for h.

2: Area of a trapezoid: A=1/2h(b1 + b2); Solve for b2.
The 1 and 2 are supposed to be under to the side of b like this.​

Answers

Answer:

area of a trapezoid A =1

Step-by-step explanation:

2

PLEASE HELP MARKING BRAINLIEST

Answers

The answer is B, I believe.

How to solve -3/9 + ( -2 9/10)
[tex] - 3 \sqrt{8 + ( - 2 \times \frac{9}{10} } [/tex]

Answers

9514 1404 393

Answer:

-3 7/30-7.46994

Step-by-step explanation:

We understand this to be two separate problems.

  -3/9 +(-2 9/10) = -(3/9 +2 9/10)

  = -(10/30 +87/30) = -97/30 = -3 7/30

__

  -3√(8 +(-2(9/10))) = -3√(8 -1.8) = -3√6.2 ≈ -7.46994

__

Additional comment

A calculator can help with these, especially if it is able to deal with rational numbers. (Many graphing calculators and some scientific calculators will do that more or less nicely. My favorite Android calculator app makes arithmetic with fractions and mixed numbers very easy.)

Find the area of this figure. round your answer to the nearest hundredth.

Answers

Answer:

49.12 ft^2

Step-by-step explanation:

The triangle:

Area = 1/2 * base * height

= 1/2 * 6 * 8

= 24

The semicircle:

Area = 1/2 * 3.14 * 4^2

= 25 .12

Total area = 24 + 25.12

= 49.12 fT^2

14 644 552 + 25 625 568




ayud estoy haciendo tarea :3

Answers

Answer:

14644552+25625568

=40270120

Step-by-step explanation:

is right answer

c(ge + p) = n +j

Solve for c: C=​

Answers

Answer:

[tex]c(ge + p) = n + j \\ \\ \frac{c(ge + p)}{(ge + p)} = \frac{n + j}{(ge + p)} \\ \\ { \boxed{ \boxed{c = \frac{n + j}{ge + p} }}}[/tex]

A nut-raisin mix costs $5.26 per pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is

Answers

$81.53 Is the estimated cost

$81.53 is the cost of nut-raisin mix

Find(f−g)(x) f(x)=x2−6xandg(x)=−2x+3
A x2−4x+3
B x2+4x−3
C x2−4x−3
D x2+4x+3

Answers

Answer:

option C is the answer......

Loretta earns $10 a week
and puts $7.50 a week
into savings account and spends
the rest. How much does she
spend in six weeks?​

Answers

She spends 2.50 a week times 6 weeks is 15$

solve for x. y = 1/3 (x + w)

Answers

Step 1: get rid of the 1/3 by multiplying both sides by 3

3 • y = 3 • 1/3(x+w)

3y = x + w

Step 2: get the x by itself by subtracting away the w

3y - w = x + w - w

3y - w = x

You’ve got your answer.

Write the given phrase as an algebraic expression. Use the variable x to represent each unknown number.
A number divided by eleven.
The answer is

(Answer quickly)

Answers

Answer:

x/11

Step-by-step explanation:

The prompt states to use x for each unknown number and then the question says A number divided by eleven so x divided by 11 = x/11

K = [ 14 -13 0 3 8 -1 -10 -2 5 ] find the determinant of K

Answers

I suppose K is the matrix

[tex]K = \begin{bmatrix}14 & -13 & 0 \\ 3 & 8 & -1 \\ -10 & -2 & 5\end{bmatrix}[/tex]

To compute det(K), you can use a simple cofactor expansion along the first row:

[tex]\det(K) = 14\times\det\begin{bmatrix}8 & -1 \\-2 & 5\end{bmatrix} - (-13)\times\det\begin{bmatrix}3 & -1 \\ -10 & 5\end{bmatrix} + 0\times\det\begin{bmatrix}3 & 8 \\ -10 & -2\end{bmatrix} \\\\ \det(K) = 14\times(8\times5-(-1)\times(-2)) + 13\times(3\times5-(-1)\times(-10)) + 0 \\\\ \det(K) = 14\times38 + 13\times5 = \boxed{597}[/tex]

Solve for the value of R

Answers

Answer:

13

Step-by-step explanation:

Since the angles form 180 degrees, it will be what the equation is equal to.

Make the equation:

8r + 5 + 5r + 6 = 180

Combine like terms:

8r + 5 + 5r + 6 = 180

13r + 5 + 6 = 180

13r + 11 = 180

Solve:

13r + 11 = 180

       -11     -11

---------------------

     13r = 169

    ------   ------

      13      13

        r = 13

Hope this helped.

I think 13 I don’t know for sure though

If you can make 12 cookies in 10 minutes, how long does it take to make 200 cookies

Answers

Answer:

12 cookies = 10minutes

200 cookies = x minutes

cross multiply

200×10 = 12x

2000= 12x

divide both sides by 12

X = 166.67 minutes

Step-by-step explanation:

that is 200 cookies will take 166.67 minutes

Answer:

[tex]12 \: cookies \: in \: 10 \: minut \: \\ 1 \: cookie \: in \: \frac{10}{12} = \frac{5}{6} \: minute \\ for \: 200 \: cookies = \frac{5}{6} \times 200 = 166.67 \: minute \\ thank \: you[/tex]


-.0666
Rational or
Irrational?
WHY

Answers

Answer:

It's irrational

Step-by-step explanation:

An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point.

Answer:

Rational

Step-by-step explanation:

Irrational numbers go on FOREVER.

An example is

1. π

2.[tex]\sqrt{2}[/tex]

....

Surds are irrational. A surd is a square root of a number that goes on forever.

Some irrational numbers have recurring digits (repeating digits)

10/3 is an example:

3. 333333333333333333333333333333333333333333............

if (a^-1+b^-1)(a+b)^-1=a^mb^n.prove that a^(m-n)=1.​

Answers

Answer:

46666

Step-by-step explanation:

Find the area of this triangle. Round to the nearest tenth. 8m, 62°, 12m.

Answers

9514 1404 393

Answer:

  42.4 m²

Step-by-step explanation:

The area can be found from the formula ...

  Area = 1/2ab·sin(C)

  Area = (1/2)(8 m)(12 m)sin(62°) ≈ 42.4 m²

Please help me with this problem

Answers

Answer:

18e90w002

919293939

jwiwoqo1919

2kw29w9w9ww9

91022929292929 91901

19190193939

19292920202

5 + (-8) - (-10)

please help

Answers

Answer:

-7

Step-by-step explanation:

5 + (-8) - (-10)

5 - 8 + 10

-3 + 10

7

Answer:

7

Step-by-step explanation:

TUrns into 5-8-(-10)

5-8+10

PEMDAS the answer and youll get 7

A motorist drives on a state road to and from work each day and pays $3.50 on tolls one-way.
(a) Write a model for the cost for tolls C (in S) for x working days.
(b) The department of transportation has a prepaid toll program that discounts tolls for high-volume use. The motorist can buy a pass for $112 per month. How many working days are required for the motorist to save money by buying the pass?
The model for the tolls cost is C= ?​

Answers

Answer:

Step-by-step explanation:

please help will give you brainly

Answers

Answer:

-1/2

Step-by-step explanation:

3(y+13 )=36

y+13=12

y=-1

(1/2) x -1 = -1/2

3(y + 13) = 36

Distribute the 3

3y + 39 = 36

Subtract 39 from both sides.

3y = -3

Divide both sides by 3

y = -1

1/2y = 1/2(-1) = -1/2

Hello Brainly User please help me I will mark brainliest. Its really east math please help me

Answers

1. not function
not function
not function (i’m pretty sure)

2. not function
function

Find the coordinates of the vertices of each figure after the given transformation.
dilation of 2.5 about the origin
Q(-1,-1), R(-2, 1), S(0, 2), T(2,0)

Answers

Step-by-step explanation:

Q(-1,-1), R(-2, 1), S(0, 2), T(2,0)

after dilation, all the numbers should be multiplied by 2.5.

so, the correct answer is d.

Q'(-2.5 ,-2.5), R'(-5, 2.5), S'(0, 5), T'(5,0)

.Si un juguete vale s/ 95 me lo rebajan en s/ 27.¿Cuanto me costara?

Answers

Answer:

Vale 95.

Me rebajan 27.

95-27=68

Me costará 68.

Step-by-step explanation:

Other Questions
China only had one of five dynasties in..... Convert 120 Ibs to kilograms Crane Company had these transactions during the current period. June 12 Issued 79,500 shares of $1 par value common stock for cash of $298,125. July 11 Issued 3,650 shares of $105 par value preferred stock for cash at $113 per share. Nov. 28 Purchased 3,200 shares of treasury stock for $8,800.Prepare the journal entries for the Crane Company transactions shown above. Find the inverse of the function: f(x)=1/5x+4A f1(x)=x4B f1(x)=5x20C f1(x)=5x4D f1(x)=4x5 What were the consequences of the accident for Lauda and for the race? A researcher wonders if children who engage in active play for at least 10 minutes a day have a lower obesity rate than children who do not. Staff from her laboratory shadow 100 children for 1 week and record the number of minutes of active play each child participated in each day. They also record the child's weight and BMI to assess obesity. What type of study is this? Lawrence's check at Fresh Catchery is $23.09. In order to leave a 13% tip, how much should he pay? Round to the nearest cent. It takes 5 workers 3 days to build 120 birdhouses. How long will it take 3 workers to build 95 birdhouses? HELP WILL GIVE BRAINLIEST ruchi cooked rice ___? (doesnt she/dont she/didnt she) Choose the word that needs correcting: "I had to go to school on foot last week because my bike was being fixing."A. had toB. becauseC. was beingD. fixing SpongeBob loves to garden and wants to grow lots of pink flowers for his pal Sandy.special Flower Power fertilirer to see if will help plants produce more flowers. He plants two plants ofthe same size in separate containers with the same amount of potting soil. He places one plant in a sunnywindow and waters it every day with fertilized water. He places the other plant on a shelf in a closet andwaters it with plain water every other day.What should SpongeBob do to test the effectiveness of Flower Power fertilizer? Write an experiment. Which equation has a constant of proportionality equal to 2? pls some help im so stuck im stuck as a cat in a tree dude plz help iill give u 100 pointes Cal went to the store to buy half liter bottle of water . One bottom cost 3$ but he saw one liter bottle that cost 5$ what is the unit price of a half liter bottle and a one liter Find the equation of this line Alexander earns $11.50 per hour working at the nearby grocery store last week Alexander worked for 13 1/2 hours how much money did Alexander earn last week round your answer to the nearest penny. Ill mark u as brainliest!! solve these two equations n show ya work !! Evaluate each expression if a = -1 and b = 6: a + b ab Determine what value(s) for the variable would make each algebraicequation a true number sentence.2 = 81 is true for ____________________.6 = 3 + 2 + is true for ____________________. + 74 = 74 is true for ____________________.