All categories

4 years ago

A circle is centered at P(0,0). The point W(-6, √37) is on the circle. Where does the point Z(8,3) lie?

Mathematics

1 answer:

olga_2 [115]4 years ago

3 0

Answer:

On the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

The radius is the distance from the centre to a point on the circle.

To calculate r use the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 6, $\sqrt{37}$ )

r = $\sqrt{(-6-0)^2+(\sqrt{37-0)^2} }$

= $\sqrt{36+37}$ = $\sqrt{73}$

Hence

x² + y² = ( $\sqrt{73}$ )²

x² + y² = 73 ← equation of circle

Substitute (8, 3) into the left side of the equation and

value < 73 → lies inside circle

value = 73 ← lies on the circle

value > 73 ← lies outside circle

(8, 3) → 8² + 3² = 64 + 9 = 73

(8, 3) lies on the circle

You might be interested in

Define a new random variable by y = 2px. show that, as p l 0, the mgf of y converges to that of a chi squared random variable wi

Mandarinka [93]

The moment generating function (mgf) of y is given by

$M_y(t)=E(e^{ty})=E(e^{2pxt})=M_x(2pt)=p(1-e^{2pt}(1-p))^{-1}$

Since the momoent generating function of x is given by $M_x(t)=p(1-e^{t}(1-p))^{-1}$

When p tends to 0, we have

$\lim_{p \to 0} M_y(t)= \lim_{p \to 0} \frac{p}{1-e^{2pt}(1-p)} = \frac{0}{0}$

Applying L'Hopital's rule we have:

$\lim_{p \to 0} M_y(t)=\lim_{p \to 0} \frac{1}{e^{2pt}+2te^{2pt}+2pte^{2pt}} = \frac{1}{1+2t} , \ \ \ t\ \textless \ \frac{1}{2}$

This shows that y converges to <span>a chi squared random variable with 2r degrees of freedom</span>.

5 0

4 years ago

What is 1000×2000×3000×4000×5000

Sophie [7]

Answer:

120000000000000000

Step-by-step explanation:

1.2*10^17

6 0

2 years ago

Read 2 more answers

HELP PLEASE SOMEONE!!!

AnnyKZ [126]

Answer:

3 units right, 4 down = (x+3, y-4)

3 units left, 4 up = (x-3, y+4)

4 units right, 3 down = (x+4, y-3)

Step-by-step explanation:

8 0

2 years ago

Which fraction is closest to 1?<br> 5/6, 11/20 or -9/10

ivann1987 [24]

5/6 is closest to 1.

6 0

4 years ago

Read 2 more answers

Why is 4X +5 a linear function <br> Why is y=X2 a nonlinear function

andreev551 [17]

y = 4x+5 is in the form y = mx+b which is slope intercept form. Anything in y = mx+b form is linear. It graphs out a straight line.

Contrast this with y = x^2 which is nonlinear because it graphs a curve that isnt a straight line. All quadratics like this graph out a parabola which resembles a bowl shaped curve.

4 0

3 years ago