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2 years ago

Find the area and the circumference of a circle with radius 4 yd

Mathematics

1 answer:

Romashka [77]2 years ago

4 0

First, let's find the area! The formula to find the area of a circle is πr²

πr²

3.14 · 4²

50.24 yds²

Now let's find the circumference. The formula for this is 2πr

2πr

2 · 3.14 · 4

25.12 yds

Hope this helps!

You might be interested in

Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +

Veronika [31]

Answer:

Verified

$y(x) = \frac{3Ln(x) + 3}{x}$

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}$

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

$x^2y' +xy = 3$

- A general solution to the above ODE is also given as:

$y = \frac{3Ln(x) + C }{x}$

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

$y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x) }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}$

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

$-\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3$

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3$

- Therefore, the complete solution to the given ODE can be expressed as:

$y ( x ) = \frac{3Ln(x) + 3 }{x}$

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)$

- Therefore, the complete solution to the given ODE can be expressed as:

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}$

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6 0

2 years ago

WHAT IS THE RELATIONSHIP BETWEEN THE ANGLE OF ELEVATION AND THE ANGLE OF DEPRESSION? GIVE AN EXAMPLE OF AN APPLICATION USING THE

Makovka662 [10]

Angles of Elevation and Depression are used in measuring heights and distances in trigonometric applications using right triangles. These angles are made when we look up or down to view objects. Devices are available to measure angles of elevation and depression. These measured angles can be used in measuring heights and distance which are either tedious or impractical to measure, by modelling the situation into right triangles

6 0

3 years ago

Read 2 more answers

Charley and Sarah went to the candy store.

Pepsi [2]

Answer:

rtt6655r55

Step-by-step explanation:

4 0

3 years ago

What could be the intersection of the plane PRS and plane QRS

MrRa [10]

The plane PRS passes through the points P, R and S. So it contains the line RS. Also the plane QRS passes through the points Q, R and S. So it contains the line RS as well. Since both the planes contain the line RS, the line RS must be the intersection of plane PRS and QRS

6 0

2 years ago

3 ⅕ -⅔ divided by 2 ⅘

spin [16.1K]

Answer:

160/196

Step-by-step explanation:

it would be easier if you converted all fractions to improper fractions

so 3 1/5 would equal 16/5 and 2 4/5 would equal to 14/5

$\frac{14}{5} - \frac{2}{3}$ : to solve this you would need the same common denomenator,

to do this you can multiply 5 and 3 by something to make the lowest common denominator, which would be 15

thus

multiplying first fraction by 3 and the second by 5

42/15 - 10/15 = 32/15

now 32/15 divided by 14/5

the rule for dividing fractions, is flipping the fraction which you will be using to divide, and then multiplying it to the first fraction:

$\frac{32}{14}$ multiplied by $\frac{5}{14}$

thus, answer is 160/196

8 0

2 years ago