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3 years ago

Write the equation of a circle centered at the

Mathematics

1 answer:

Fudgin [204]3 years ago

3 0

Answer:

$(x+4)^2+(y+6)^2=100$

Step-by-step explanation:

Given a circle centred at the point P(-4,-6) and passing through the point

R(2,2).

To find its equation, we follow these steps.

Step 1: Determine its radius, r using the distance formula

For point P(-4,-6) and R(2,2)

$\text{Distance Formula=}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\text{Radius=}\sqrt{(2-(-4))^2+(2-(-6))^2} \\=\sqrt{(2+4))^2+(2+6)^2}\\=\sqrt{6^2+8^2}\\=\sqrt{100}\\Radius=10$

Step 2: Determine the equation

The general form of the equation of a circle passing through point (h,k) with a radius of r is given as: $(x-h)^2+(y-k)^2=r^2$

Centre,(h,k)=P(-4,-6)

r=10

Therefore, the equation of the circle is:

$(x-(-4))^2+(y-(-6))^2=10^2\\\\(x+4)^2+(y+6)^2=100$

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Solve. (K+1)(k-5)=0<br> Explin how to solve ???

Anna71 [15]

Alright remember, if any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
k+1=0
k-5=0
Set the first factor equal to 0 and solve
k=-1
Set the next factor equal to 0 and solve
k=5
The final solution is all the values that make (k+1)(k-5)=0 true.
k=-1, 5

Hope this helped you out :)

5 0

3 years ago

Read 2 more answers

if a number line plot starts from 2 (including the point) and extends towards positive infinity, the corresponding inequality is

murzikaleks [220]

Answer:

$2 \leqslant y \leqslant \infty$

Step-by-step explanation:

y is equal to 2 and goes up to infinity

6 0

2 years ago

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

3 years ago

A principal of $2800 is invested at 8% interest, compounded annually. How much will the investment be worth after 9 years?

Helga [31]

Answer:

2,016

Step-by-step explanation:

You do 2800 x 0.08 in ur calculator which is 224 and multiply that by 9

3 0

3 years ago

The Length of a standard jewel case is 7cm more than its width. The area of the rectangular top of the case is 408cm. Find the l

salantis [7]

Answer:

The length of the case is 24 cm and its width is 17cm.

Step-by-step explanation:

The Length of a standard jewel case is 7cm more than its width.

Let the length be represented by L and the width be represented by W, this means that:

L = 7 + W

The area of the rectangular top of the case is 408cm². The area od a rectangle is given as:

A = L * W

Since L = 7 + W:

A = (7 + W) * W = 7W + W²

The area is 408 cm², hence:

408 = 7W + W²

Solving this as a quadratic equation:

=> W² + 7W - 408 = 0

W² + 24W - 17W - 408 = 0

W(W + 24) - 17(W + 24) = 0

(W - 17) (W + 24) = 0

=> W = 17cm or -24 cm

Since width cannot be negative, the width of the case is 17 cm.

Hence, the length, L, is:

L = 7 + 17 = 24cm.

The length of the case is 24 cm and its width is 17cm.

4 0

3 years ago