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
lakkis [162]
2 years ago
11

Help help help math math math

Mathematics
1 answer:
REY [17]2 years ago
6 0

Answer:

2048ft^3

Step-by-step explanation:

First, we find the radius. We get this by dividing the diameter by 2.

16 / 2 = 8

Then we solve the volume equation, using 3 for pi.

4/3 * 3 * 8^3

4/3 * 3 * 512

12/3 * 512

4 * 512 = 2048

You might be interested in
There was a bag of counters. 45 were large! For every large counters 3/5 were small! The green was 300% than yellow, there were
madreJ [45]

Answer:

12 is the correct answer

7 0
2 years ago
Help please? match each system of linear equation with the correct numbers of solutions ​
Ksenya-84 [330]

Answer:

Step-by-step explanation:

First system:  no solution, since the two lines are parallel; they never cross.

Second system:  one solution

Third system:  infinitely many solutions, since the second equation is a multiple of the first

4 0
3 years ago
Solve the following differential equation using using characteristic equation using Laplace Transform i. ii y" +y sin 2t, y(0) 2
kifflom [539]

Answer:

The solution of the differential equation is y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)

Step-by-step explanation:

The differential equation is given by: y" + y = Sin(2t)

<u>i) Using characteristic equation:</u>

The characteristic equation method assumes that y(t)=e^{rt}, where "r" is a constant.

We find the solution of the homogeneus differential equation:

y" + y = 0

y'=re^{rt}

y"=r^{2}e^{rt}

r^{2}e^{rt}+e^{rt}=0

(r^{2}+1)e^{rt}=0

As e^{rt} could never be zero, the term (r²+1) must be zero:

(r²+1)=0

r=±i

The solution of the homogeneus differential equation is:

y(t)_{h}=c_{1}e^{it}+c_{2}e^{-it}

Using Euler's formula:

y(t)_{h}=c_{1}[Sin(t)+iCos(t)]+c_{2}[Sin(t)-iCos(t)]

y(t)_{h}=(c_{1}+c_{2})Sin(t)+(c_{1}-c_{2})iCos(t)

y(t)_{h}=C_{1}Sin(t)+C_{2}Cos(t)

The particular solution of the differential equation is given by:

y(t)_{p}=ASin(2t)+BCos(2t)

y'(t)_{p}=2ACos(2t)-2BSin(2t)

y''(t)_{p}=-4ASin(2t)-4BCos(2t)

So we use these derivatives in the differential equation:

-4ASin(2t)-4BCos(2t)+ASin(2t)+BCos(2t)=Sin(2t)

-3ASin(2t)-3BCos(2t)=Sin(2t)

As there is not a term for Cos(2t), B is equal to 0.

So the value A=-1/3

The solution is the sum of the particular function and the homogeneous function:

y(t)= - \frac{1}{3} Sin(2t) + C_{1} Sin(t) + C_{2} Cos(t)

Using the initial conditions we can check that C1=5/3 and C2=2

<u>ii) Using Laplace Transform:</u>

To solve the differential equation we use the Laplace transformation in both members:

ℒ[y" + y]=ℒ[Sin(2t)]

ℒ[y"]+ℒ[y]=ℒ[Sin(2t)]  

By using the Table of Laplace Transform we get:

ℒ[y"]=s²·ℒ[y]-s·y(0)-y'(0)=s²·Y(s) -2s-1

ℒ[y]=Y(s)

ℒ[Sin(2t)]=\frac{2}{(s^{2}+4)}

We replace the previous data in the equation:

s²·Y(s) -2s-1+Y(s) =\frac{2}{(s^{2}+4)}

(s²+1)·Y(s)-2s-1=\frac{2}{(s^{2}+4)}

(s²+1)·Y(s)=\frac{2}{(s^{2}+4)}+2s+1=\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)}

Y(s)=\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)(s^{2}+1)}

Y(s)=\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}

Using partial franction method:

\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}=\frac{As+B}{s^{2}+4} +\frac{Cs+D}{s^{2}+1}

2s^{3}+s^{2}+8s+6=(As+B)(s²+1)+(Cs+D)(s²+4)

2s^{3}+s^{2}+8s+6=s³(A+C)+s²(B+D)+s(A+4C)+(B+4D)

We solve the equation system:

A+C=2

B+D=1

A+4C=8

B+4D=6

The solutions are:

A=0 ; B= -2/3 ; C=2 ; D=5/3

So,

Y(s)=\frac{-\frac{2}{3} }{s^{2}+4} +\frac{2s+\frac{5}{3} }{s^{2}+1}

Y(s)=-\frac{1}{3} \frac{2}{s^{2}+4} +2\frac{s }{s^{2}+1}+\frac{5}{3}\frac{1}{s^{2}+1}

By using the inverse of the Laplace transform:

ℒ⁻¹[Y(s)]=ℒ⁻¹[-\frac{1}{3} \frac{2}{s^{2}+4}]-ℒ⁻¹[2\frac{s }{s^{2}+1}]+ℒ⁻¹[\frac{5}{3}\frac{1}{s^{2}+1}]

y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)

3 0
3 years ago
Find the y intercept of the line above.
NISA [10]
The y-intercept is (0, 2), because it's the spot where the line crosses the y-axis. The other point showed on the graph is the x-intercept..
6 0
3 years ago
Given a sphere with a diameter of 6 cm, find its volume to the nearest whole<br> number.
mezya [45]

Answer:

Volume of the sphere is 1.13\times 10^{-4}m^3

Step-by-step explanation:

It is given diameter of the sphere d = 6 cm = 0.06 m

Radius of the sphere

r=\frac{d}{2}=\frac{0.06}{2}=0.03m

We know that volume of the sphere is given by

V=\frac{4}{3}\pi r^3

Therefore ,

V=\frac{4}{3}\times 3.14\times  0.03^3

=1.13\times 10^{-4}m^3

Therefore volume of the sphere is 1.13\times 10^{-4}m^3

6 0
3 years ago
Other questions:
  • Marcus needs 108 inches of wood to make a frame. How many feet of wood does Marcus need for the frame?
    5·1 answer
  • Solve the question. show your work. check your answer. 3x -7 = 5x + 19
    10·2 answers
  • Change 4700g into kilograms
    11·2 answers
  • There are 9 cherry cokes, 3 diet cokes, and 4 coke zeros in a cooler. What is the proabiliyt of selecting a drink and getting a
    14·1 answer
  • Identify the domain and range
    15·1 answer
  • Solve for x 0.03x+20=0.07x+5
    9·1 answer
  • G(x)=3x-2;find g(7)​
    12·2 answers
  • Find the value of the variable.
    10·2 answers
  • Twenty boxes of paper weights 460 pounds. What is the ratio of boxes to pounds?​
    8·1 answer
  • A family of 2 adults and 3 children went out to dinner. The total bill was $42. Each child's dinner cost $4. How much did each a
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!