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3 years ago

Find the coordinates of the center and the measure of the radius for a circle whose equation is (x-3)^2 + (y-7)^2=2

Mathematics

1 answer:

igomit [66]3 years ago

6 0

Answer:

fourth option

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 3)² + (y - 7)² = 2 ← is in standard form

with centre = (h, k) = (3, 7) and r² = 2 ⇒ r = $\sqrt{2}$

You might be interested in

Find the derivative of f(x) = -9/x at x = 6

Svet_ta [14]

F(x)=-9/x which is equal to:

f(x)=-9x^(-1) So the power rule for differentiation is used...

Power rule: f(x)=x^e, df/dx=ex^(e-1) so:

df/dx=-9(-1)x^(-1-1)

df/dx=9x^(-2) or if you prefer...

df/dx=9/x^2

df/dx(6)=9/36=1/4

3 0

4 years ago

A Ferris Wheel 22.0m in diameter rotates once every 12.5s. What is the ratio of a persons apperenet weight to her real weight (a

AnnZ [28]

<span>Acceleration of a passenger is centripetal acceleration, since the Ferris wheel is assumed at uniform speed:
a = omega^2*r

omega and r in terms of given data:
omega = 2*Pi/T
r = d/2

Thus:
a = 2*Pi^2*d/T^2

What forces cause this acceleration for the passenger, at either top or bottom?

At top (acceleration is downward):
Weight (m*g): downward
Normal force (Ntop): upward

Thus Newton's 2nd law reads:
m*g - Ntop = m*a

At top (acceleration is upward):
Weight (m*g): downward
Normal force (Nbottom): upward

Thus Newton's 2nd law reads:
Nbottom - m*g = m*a

Solve for normal forces in both cases. Normal force is apparent weight, the weight that the passenger thinks is her weight when measuring by any method in the gondola reference frame:
Ntop = m*(g - a)
Nbottom = m*(g + a)

Substitute a:
Ntop = m*(g - 2*Pi^2*d/T^2)
Nbottom = m*(g + 2*Pi^2*d/T^2)

We are interested in the ratio of weight (gondola reference frame weight to weight when on the ground):
Ntop/(m*g) = m*(g - 2*Pi^2*d/T^2)/(m*g)
Nbottom/(m*g) = m*(g + 2*Pi^2*d/T^2)/(m*g)

Simplify:
Ntop/(m*g) = 1 - 2*Pi^2*d/(g*T^2)
Nbottom/(m*g) = 1 + 2*Pi^2*d/(g*T^2)

Data:
d:=22 m; T:=12.5 sec; g:=9.8 N/kg;

Results:
Ntop/(m*g) = 71.64%...she feels "light"
Nbottom/(m*g) = 128.4%...she feels "heavy"</span>

7 0

4 years ago

Read 2 more answers

Is prime a composite number, a prime number, both or neither? Pease explain.

Annette [7]

Composite number is made up of 2 or more prime numbers
a prime number is only made up of itself and 1

composite and prime numbers are like oposites

a prime is not a composite but it is a prime number
confusing quesiton

5 0

3 years ago

Starting in the 1970s, medical technology allowed babies with very low birth weight (VLBW, less than 1500 grams, about 3.3 pound

cluponka [151]

Answer:

The test statistic value using the VLBW babies as group 1 is z=-2.76±0.01 and the P-value for the test (±0.0001) is 0.0030.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of persons with normal birth weight that graduates from high school is significantly greater than the proportion of persons with very low birth weight that graduates from high school.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0$

The significance level is 0.05.

The sample 1 (VLBW group), of size n1=244 has a proportion of p1=0.77049.

$p_1=X_1/n_1=188/244=0.77049$

The sample 2 (control group), of size n2=247 has a proportion of p2=0.79757.

$p_2=X_2/n_2=197/247=0.79757$

The difference between proportions is (p1-p2)=-0.02708.

$p_d=p_1-p_2=0.77049-0.79757=-0.02708$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{188+197}{244+247}=\dfrac{385}{491}=0.988$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.988*0.012}{244}+\dfrac{0.988*0.012}{247}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00005}=\sqrt{0.0001}=0.0098$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.02708-0}{0.0098}=\dfrac{-0.02708}{0.0098}=-2.76$

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=P(t$

As the P-value (0.0030) is smaller than the significance level (0.05), the effect issignificant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of persons with normal birth weight that graduates from high school is significantly greater than the proportion of persons with very low birth weight that graduates from high school.

3 0

3 years ago

Hey can anyone help me find the missing side lengths please and thank you

alex41 [277]

Answer:

choice a

Step-by-step explanation:

angle 45 means, its a isosceles triangle.

so y = √3

x^2 = 3+3= 6

x = √6

3 0

2 years ago