All categories

1 year ago

Which of the following is a result of shifting a circle with equation (x+3)^2+(y-2)^2=36 up 3 units

Mathematics

2 answers:

Rufina [12.5K]1 year ago

7 0

Answer:

The general equation of the circle is given by:

$(x-h)^2+(y-k)^2=r^2$ where r is the radius of the circle and (h, k) is the center of the circle.

To shift any function upwards b units , then the center of the circle becomes;

(h, k+b)

As per the given statement:

equation of the circle is given by:

$(x+3)^2+(y-2)^2=36$

Center of this circle is: (-3, 2) and radius(r) = 6

to shift this equation of circle 3 units up then;

(h, k+3) = (-3, 2+3) = (-3, 5)

then;

the equation of circle 3 units upwards with radius = 6 units and center = (-3, 5) become:

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

Therefore, the result of shifting a circle with equation

$(x+3)^2+(y-2)^2=36$ up 3 units is:

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

sdas [7]1 year ago

4 0

Answer: A result of shifting a circle with equation (x+3)^2+(y-2)^2=36 up 3 units is: (x+3)^2+(y-5)^2=36

To shift a graph "a" units up, we must replace in the equation "y" by "y-a" when y is not isolated; or if y is isolated, you add "a" to the right side of the equation.
In this case we want to shift the graph of the circle 3 units up, then a=3, and we must replace in the equation of the circle "y" by "y-3":
(x+3)^2+[(y-3)-2]^2=36→
(x+3)^2+(y-3-2)^2=36→
(x+3)^2+(y-5)^2=36

Answer: A result of shifting a circle with equation (x+3)^2+(y-2)^2=36 up 3 units is: (x+3)^2+(y-5)^2=36

You might be interested in

Poiseuille's Law states that the volume, V, of blood flowing through an artery in a unit of time at a fixed pressure is directly

eimsori [14]

Answer:

11.58%

Step-by-step explanation:

The initial volume if blood flowing through the artery is given by

$V=kr^4$

To achieve a new volume of 155% (55% increase) of the initial volume, the new radius must be:

$V'= 1.55V\\1.55V=k(r')^4\\1.55kr^4 = k(r')^4\\(\sqrt[4]{1.55}*r)^4=(r')^4 \\(1.1158*r)^4=(r')^4 \\r'=1.1158*r$

Since the new radius is 1.1158 times larger than the initial radius, the percentage increased is:

$I=(1.1158 - 1)*100\%\\I= 11.58\%$

7 0

2 years ago

erin has $50. she wants to purchase a cell phone ($20) and spend the rest in music cds each cd costs $8. write an inepuality for

HACTEHA [7]

She can buy 3 because 50-20=30 30/8=3.75 so u round down cause you don't have enough money to buy 4

3 0

1 year ago

How can Ari simplify the following expression? StartFraction 5 Over a minus 3 EndFraction minus 4 divided by 2 + StartFraction 1

Zielflug [23.3K]

Answer:

$-\frac{8}{3}$

Step-by-step explanation:

Given

$\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}$

Required

Simpify

The very first step is to take LCM of the given expression

$\frac{-10 -4 - 2}{6}$

Perform arithmetic operations o the numerator

$-\frac{16}{6}$

Divide the numerator and denominator by 2

$-\frac{16/2}{6/2}$

$-\frac{8}{3}$

The expression can't be further simplified;

Hence, $\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}$ = $-\frac{8}{3}$

8 0

1 year ago

On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2.

koban [17]

Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

3 0

1 year ago

Which function has the domain x>or= -11

iogann1982 [59]

I'm assuming this is multiple choice and you forgot to post the answers. I'll take a guess and say it probably looks something like this:
$y = \sqrt{x + 11}$
Because you can't take the square root of a negative number without getting an imaginary result, resulting in the function having a closed domain limit.

6 0

2 years ago