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3 years ago

Which equation represents a circle at (-3,-5) and radius of 6 units

Mathematics

2 answers:

Liono4ka [1.6K]3 years ago

8 0

Answer:

(x+3)^2 (y+5)^2=36

Step-by-step explanation:

Hope this helped

Elden [556K]3 years ago

7 0

Answer:

The equation of the circle is (x + 3)² + (y + 5)² = 36

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- The center-radius form of the circle equation is in the format

(x – h)² + (y – k)² = r², where the center is the point (h, k) and

the radius is r.

- This form of the equation is helpful, because you can easily find

the center and the radius.

* Now lets solve the problem

∵ The center of the circle is (-3 , -5)

∵ The center of the circle in the equation is (h , k)

∴ h = -3

∴ k = -5

∴ The equation of the circle is (x - -3)² + (y - -5)² = r²

∴ The equation is (x + 3)² + (y + 5)² = r²

* Now lets find the value of r²

∵ The length of the radius of the circle is 6 units

∴ r = 6

∴ r² = (6)² = 36

∴ The equation of the circle is (x + 3)² + (y + 5)² = 36

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Is the point (5,8) a solution to the system of equations shown below? Justify your response

AlladinOne [14]

Step-by-step explanation:

For the point (5,8) to be a solution to the equations, when you insert x=5 and y=8 , they have to equal to the given values

substituting (5,8) into 4x+y

4(5)+8

=20+8

=28

substituting(5,8) into x-y=3

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5 0

2 years ago

A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas

Fittoniya [83]

Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

$#V=pi r^2 h#$

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

$#V=pi (5m)^2 h#$

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

$#(dV)/(dt)=(25 m^2) pi (dh)/(dt)#$

In the problem, we are given $#3(m^3)/min# which is #(dV)/(dt)#.$

So we need to substitute this in:

$#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#$

Hence, Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>Formula used: </h3>

$#V=pi r^2 h#$

To Learn more visit:

brainly.com/question/4313883

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4 0

2 years ago

Read 2 more answers

Item cost $430 before taxes and the sales tax is $38.70 find a sales tax

natulia [17]

Answer:

sales tax= 9 %

Step-by-step explanation:

sales tax= cost x %tax

38.70 = 430 x %tax

%tax = 38.7/430 = 0.09 = 9 %

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8 0

3 years ago

lukranit [14]

Answer:

Step-by-step explanation:

The y-coordinate of the point where both lines intersect will give us the same solution for x.

At y = 4, both equations will have a corresponding x-value of 1.

Therefore, the value of y that that will make both equations have the same solution of x is 4.

7 0

3 years ago

En un examen calificado del 0 al 10, 3 personas obtuvieron 5 de nota, 5 personas obtuvieron 4 de nota, y 2 personas obtuvieron 3

Nastasia [14]

Answer:

Media = 4.1

Mediana = 4

Moda = 4

Step-by-step explanation:

3 personas obtuvieron 5 puntos

5 personas obtuvieron 4 puntos

2 personas lograron 3 puntos

a. La media se da como:

Media = suma total de marcas / número de personas

Por lo tanto, la media será:

$M = \frac{((3 * 5) + (5 * 4) + (2 * 3)}{10}\\ \\M = \frac{15 + 20 + 6}{10} \\\\M = \frac{41}{10}\\ \\M = 4.1$

b. Para obtener la mediana, tenemos que organizar los términos en consecuencia y encontrar el número en el medio.

3, 3, 4, 4, 4, 4, 4, 5, 5, 5

Como no hay un número único en el medio, la mediana es:

(4 + 4) / 2 = 8/2 = 4

c. La moda es el número que aparece más, y eso es 4

8 0

3 years ago