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
Talja [164]
3 years ago
10

SCALCET8 3.9.005.MI. A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m3/min. How fast is the height

of the water increasing
Mathematics
1 answer:
Lana71 [14]3 years ago
8 0

Answer:

The height of the water is increasing at a rate of 0.05m/min.

Step-by-step explanation:

Volume of a cylinder:

The volume of a cylinder, with radius r and height h, is given by:

V = \pi r^2h

Radius 5 m

This means that r = 5, and so:

V = 25\pi h

How fast is the height of the water increasing?

We have to differentiate V and h implictly in function of t. So

\frac{dV}{dt} = 25\pi\frac{dh}{dt}

Being filled with water at a rate of 4 m3/min

This means that \frac{dV}{dt} = 4. The questions asks \frac{dh}{dt}. So

\frac{dV}{dt} = 25\pi\frac{dh}{dt}

4 = 25\pi\frac{dh}{dt}

\frac{dh}{dt} = \frac{4}{25\pi}

\frac{dh}{dt} = 0.05

The height of the water is increasing at a rate of 0.05m/min.

You might be interested in
How many ways can a person with five ​nickels, three​ dimes, and two quarters make a 75-cent purchase from the​ machine?
DIA [1.3K]
2 quarters, 2 dimes, and 1 nickel
8 0
3 years ago
I really need it to be sold in imaginary numbers
Yuliya22 [10]
Solving a 5th grade polynomial

We want to find the answer of the following polynomial:

x^5+3x^4+3x^3+19x^2-54x-72=0

We can see that the last term is -72

We want to find all the possible numbers that can divide it. Those are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

We want to factor this polynomial in order to find all the possible x-values. In order to factor it we will have to find some binomials that can divide it using the set of divisors of -72.

We know that if

(x - z) is a divisor of this polynomial then z might be a divisor of the last term -72.

We will verify which is a divisor using synthetic division. If it is a divisor then we can factor using it:

Let's begin with

(x-z) = (x - 1)

We want to divide

\frac{(x^5+3x^4+3x^3+19x^2-54x-72)}{x-1}

Using synthetic division we have that if the remainder is 0 it will be a factor

We can find the remainder by replacing x = z in the polynomial, when it is divided by (x - z). It is to say, that if we want to know if (x -1) is a factor of the polynomial we just need to replace x by 1, and see the result:

If the result is 0 it is a factor

If it is different to 0 it is not a factor

Replacing x = 1

If we replace x = 1, we will have that:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ 1^5+3\cdot1^4+3\cdot1^3+19\cdot1^2-54\cdot1-72 \\ =1+3+3+19-54-72 \\ =-100 \end{gathered}

Then the remainder is not 0, then (x - 1) is not a factor.

Similarly we are going to apply this until we find factors:

(x - z) = (x + 1)

We replace x by -1:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ (-1)^5+3\cdot(-1)^4+3\cdot(-1)^3+19\cdot(-1)^2-54\cdot(-1)-72 \\ =-1+3-3+19+54-72 \\ =0 \end{gathered}

Then, (x + 1) is a factor.

Using synthetic division we have that:

Then:

x^5+3x^4+3x^3+19x^2-54x-72=(x+1)(x^4+2x^3+x^2+18x-72)

Now, we want to factor the 4th grade polynomial.

Let's remember our possibilities:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

Since we verified ±1, let's try with ±2 as we did before.

(x - z) = (x - 2)

We want to divide:

\frac{x^4+2x^3+x^2+18x-72}{x-2}

We replace x by z = 2:

\begin{gathered} x^4+2x^3+x^2+18x-72 \\ \downarrow \\ 2^4+2\cdot2^3+2^2+18\cdot2-72 \\ =16+16+4+36-72 \\ =0 \end{gathered}

Then (x - 2) is a factor. Let's do the synthetic division:

Then,

x^4+2x^3+x^2+18x-72=(x-2)(x^3+4x^2+9x+36)

Then, our original polynomial is:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =\mleft(x+1\mright)\mleft(x^4+2x^3+x^2+18x-72\mright) \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \end{gathered}

Now, let's prove if (x +2) is a factor, using the new 3th grade polynomial.

(x - z) = (x + 2)

We replace x by z = -2:

\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-2)^3+4(-2)^2+9(-2)+36 \\ =-8+16-18+36 \\ =26 \end{gathered}

Since the remainder is not 0, (x +2) is not a factor.

All the possible cases are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

let's prove with +4

(x - z) = (x + 4)

We want to divide:

\frac{x^3+4x^2+9x+36}{x+4}

Let's replace x by z = -4 in order to find the remainder:

\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-4)^3+4(-4)^2+9(-4)+36 \\ =-64+64-36+36 \\ =0 \end{gathered}

Then (x + 4) is a factor. Let's do the synthetic division:

Then,

x^3+4x^2+9x+36=(x+4)(x^2+9)

Since

x² + 9 cannot be factor, we have completed our factoring:

\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \\ =(x-1)(x-2)(x+4)(x^2+9) \end{gathered}

Now, we have the following expression:

(x-1)(x-2)(x+4)(x^2+9)=0

Then, we have five posibilities:

(x - 1) = 0

or (x - 2) = 0

or (x + 4) = 0

or (x² + 9) = 0

Then, we have five solutions;

x - 1 = 0 → x₁ = 1

x - 2 = 0 → x₂ = 2

x + 4 = 0 → x₃ = -4

x² + 9 = 0 → x² = -9 → x = ±√-9 = ±√9√-1 = ±3i

→ x₄ = 3i

→ x₅ = -3i

<h2><em>Answer- the solutions of the polynomial are: x₁ = 1, x₂ = 2, x₃ = -4, x₄ = 3i and x₅ = -3i</em></h2>

7 0
1 year ago
Mandy and karissa swam laps in the pool to train for the upcoming swim meet. The ratio to the number of laps Mandy swam to the n
Goryan [66]
Set up a proportion.
2/3 = 12/x. Cross multiply the proportion.
2x = 36. Solve for x.
x = 18.
8 0
3 years ago
I’m now sure how to work this out... my teacher had shown us this today at the end of class.
Kipish [7]
That's "5 to the negative seventh power," and is equal to

      1            1
---------- = --------- .  I would accept "1/(5^7)" as correct.
    5^7       78125
4 0
3 years ago
Choose the correct description of the graph of the compound inequality: x − 2 &gt; −3 and 3x less than or equal to 12
STALIN [3.7K]
<span>X - 2 > -3 x > -3 + 2 x > -1 A number line with an open circle -1, closed circle on 4 and shading in between.,when dividing/multiplying by a negative, the inequality sign changes. An open circle is used when there is no equal sign involved. A closed circle is used when there is an equal sign involved. If it is greater then, shading goes to the right. If it is less then, shading goes to the left</span>
4 0
3 years ago
Read 2 more answers
Other questions:
  • The vertices of a rectangle are given in the columns of the matrix (picture 1).
    15·1 answer
  • Help please i only have a little bit of time
    7·2 answers
  • Solve the two-step equation.
    5·1 answer
  • An arithmetic sequence is represented by the explicit formula A(n) = 2 + 9(n - 1). What is the recursive formula?. . A. A(n) = A
    12·2 answers
  • I need help on number 6
    5·1 answer
  • Here is a list of numbers:<br> 0, 10,-18, 7, -14,-7,7,-14,13,0<br> State the median.
    8·1 answer
  • One hundred sixty people who suffer from painful diabetic neuropathy have volunteered to participate in a study. Eighty are sele
    15·1 answer
  • Find the area of a rectangle whose vertices are (2,1), (2,11), (9,1), and (9,11).
    13·1 answer
  • HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
    12·2 answers
  • I NEED HELP WILL GIVE BRAINLIEST. PLZZZZ
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!