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
Effectus [21]
2 years ago
15

The sum of the areas of two circles is 80n square meters. Find the length of a radius of each circle if

Mathematics
1 answer:
astra-53 [7]2 years ago
4 0

Answer:

8 meters.

Step-by-step explanation:

Let the 2 radii be x and 2x, then
π x^2 + π (2x)^2 = 80π

π x^2 + π 4x^2= 80π

x^2 + 4x^2= 80

5x^2 = 80

x^2 = 16

x = 4.

So the radius of the larger circle = 2*4 = 8 m.

You might be interested in
A mass weighing 16 pounds stretches a spring (8/3) feet. The mass is initially released from rest from a point 2 feet below the
mezya [45]

Answer with Step-by-step explanation:

Let a mass weighing 16 pounds stretches a spring \frac{8}{3} feet.

Mass=m=\frac{W}{g}

Mass=m=\frac{16}{32}

g=32 ft/s^2

Mass,m=\frac{1}{2} Slug

By hook's law

w=kx

16=\frac{8}{3} k

k=\frac{16\times 3}{8}=6 lb/ft

f(t)=10cos(3t)

A damping force is numerically equal to 1/2 the instantaneous velocity

\beta=\frac{1}{2}

Equation of motion :

m\frac{d^2x}{dt^2}=-kx-\beta \frac{dx}{dt}+f(t)

Using this equation

\frac{1}{2}\frac{d^2x}{dt^2}=-6x-\frac{1}{2}\frac{dx}{dt}+10cos(3t)

\frac{1}{2}\frac{d^2x}{dt^2}+\frac{1}{2}\frac{dx}{dt}+6x=10cos(3t)

\frac{d^2x}{dt^2}+\frac{dx}{dt}+12x=20cos(3t)

Auxillary equation

m^2+m+12=0

m=\frac{-1\pm\sqrt{1-4(1)(12)}}{2}

m=\frac{-1\pmi\sqrt{47}}{2}

m_1=\frac{-1+i\sqrt{47}}{2}

m_2=\frac{-1-i\sqrt{47}}{2}

Complementary function

e^{\frac{-t}{2}}(c_1cos\frac{\sqrt{47}}{2}+c_2sin\frac{\sqrt{47}}{2})

To find the particular solution using undetermined coefficient method

x_p(t)=Acos(3t)+Bsin(3t)

x'_p(t)=-3Asin(3t)+3Bcos(3t)

x''_p(t)=-9Acos(3t)-9sin(3t)

This solution satisfied the equation therefore, substitute the values in the differential equation

-9Acos(3t)-9Bsin(3t)-3Asin(3t)+3Bcos(3t)+12(Acos(3t)+Bsin(3t))=20cos(3t)

(3B+3A)cos(3t)+(3B-3A)sin(3t)=20cso(3t)

Comparing on both sides

3B+3A=20

3B-3A=0

Adding both equation then, we get

6B=20

B=\frac{20}{6}=\frac{10}{3}

Substitute the value of B in any equation

3A+10=20

3A=20-10=10

A=\frac{10}{3}

Particular solution, x_p(t)=\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

Now, the general solution

x(t)=e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

From initial condition

x(0)=2 ft

x'(0)=0

Substitute the values t=0 and x(0)=2

2=c_1+\frac{10}{3}

2-\frac{10}{3}=c_1

c_1=\frac{-4}{3}

x'(t)=-\frac{1}{2}e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+e^{-\frac{t}{2}}(-c_1\frac{\sqrt{47}}{2}sin(\frac{\sqrt{47}t}{2})+\frac{\sqrt{47}}{2}c_2cos(\frac{\sqrt{47}t}{2})-10sin(3t)+10cos(3t)

Substitute x'(0)=0

0=-\frac{1}{2}\times c_1+10+\frac{\sqrt{47}}{2}c_2

\frac{\sqrt{47}}{2}c_2-\frac{1}{2}\times \frac{-4}{3}+10=0

\frac{\sqrt{47}}{2}c_2=-\frac{2}{3}-10=-\frac{32}{3}

c_2==-\frac{64}{3\sqrt{47}}

Substitute the values then we get

x(t)=e^{-\frac{t}{2}}(-\frac{4}{3}cos(\frac{\sqrt{47}t}{2})-\frac{64}{3\sqrt{47}}sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

8 0
3 years ago
10 One of the legs of a right triangle has vertices with coordinates (-2,4) and (10,0).
jeka57 [31]

The equation of the line of the other leg of the right triangle if it shares the vertice of (10,0) is y = -1/3x + 10/3

<h3>How to find the equation of a line?</h3>

The equation of a line in slope-intercept form is expressed as y = mx + b

where

m is the slope

b is the y-intercept

Given the coordinate points (-2, 4) and (10, 0)

Find the slope

Slope = -4/12
Slope = -1/3

Determine the y-intecept

0 = -1/3(10) + b

b = 10/3

Determine the equation

y = -1/3x + 10/3

Hence the equation of the line of the other leg of the right triangle if it shares the vertice of (10,0) is y = -1/3x + 10/3

Learn more on equation of a line here: brainly.com/question/13763238

7 0
2 years ago
What is the length of a rectangle with an area of (4
Luda [366]

I think 54 is the answer of this puestion

5 0
2 years ago
14) What is the distance between −2 + 1 and 4 + 5 a) √10 b
Svetllana [295]

Answer:

\sqrt52

Step-by-step explanation:

(-2,1)=(x1,y1)

(4,5)=(x2,y2)

d=?

d=\sqrt(4+2)2 + (5-1)2\\\sqrt(6)2+(4)2\\\sqrt36+16\\\sqrt52\\

7 0
3 years ago
If you deposit $100 in a savings account that earns simple interest at a rate of 1.5% per year how much interest will you have e
Alexus [3.1K]
Equation: L=P*R*T

P=100
R=1.5%=0.015
T=5

Multiply and you get 7.5 as the interest.

7 0
3 years ago
Read 2 more answers
Other questions:
  • A saleswoman earns 5% commission on all the merchandise that she sells. Last month she sold $9000 worth of merchandise. How much
    5·2 answers
  • Can somebody help me with this question?
    6·2 answers
  • A line has a slope of -4 and a y-intercept of 1. What is the equation of the line in slope-intercept form?
    5·1 answer
  • A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.
    6·1 answer
  • PLEASE HELPP!<br><br>Triangles FGH and WXY are similar.
    15·1 answer
  • 994 multiplied by 239
    14·2 answers
  • Please help Identify the domain of the function shown in the graph. A. 0 ≤ x ≤ 5 B. x is all real numbers. C. –5 ≤ x ≤ 5 D. x &g
    14·1 answer
  • Below is the list the highway gas mileages (in miles per gallon) of the randomly selected Honda car models. 22, 24, 26, 26, 28,
    5·1 answer
  • If y=30 when x=6 what is the value of y when x=12
    12·2 answers
  • Need help asap. Need answer and how to solve it please
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!