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3 years ago

Find an equation of the sphere that passes through the origin and whose center is (1, -7, 9

1 answer:

6 0

The distance between any point on the sphere and its center is the radius. The origin is on the sphere, so the radius $r$ satisfies

$r^2=(1-0)^2+(-7-0)^2+(9-0)^2=131$

This means the equation of the circle is

$(x-1)^2+(y+7)^2+(z-9)^2=131$

You might be interested in

What is the solution to the quadratic equation 8m^2+7m-15=-7 ?

Aleks04 [339]

Make equal to zero
add7 both sides
8m^2+7m-8=0
quadratic fomrula

if you have
ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

8m^2+7m-8=0
a=8
b=7
c=-8

x= $\frac{-7+/- \sqrt{7^{2}-4(8)(-8)} }{2(8)}$
x= $\frac{-7+/- \sqrt{49+256} }{16}$
x= $\frac{-7+/- \sqrt{305} }{16}$

x= $\frac{-7+ \sqrt{305} }{16}$ or x= $\frac{-7- \sqrt{305} }{16}$

aprox
x=-1.52902 or 0.654016

4 0

3 years ago

Y = -2x + 8<br> y = x^2 - 9x + 18<br><br> solve the system of nonlinear equation

ryzh [129]

Substitution

-2x+8=x^2-9x+18

x^2-7x+10=0

Factoring, we get

(x-5)(x-2)=0

x=5, x=2

If x equals 5,

y=-2(5)+8=

-10+8=

-2

Therefore, we derive our first solution:

Now we solve for our second x

If x=2,

y=-4+8=

Therefore, we derive our second solution:

-Hunter

3 0

2 years ago

The letters in the word Mississippi are put into a bag. What’s the probability of randomly selecting a vowel from the bag ?

Zinaida [17]

4/11 is the correct answer.

3 0

3 years ago

Find the value of x.

Gala2k [10]

Answer:

$\large\boxed{2\sqrt7}$

Step-by-step explanation:

Look at the picture.

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

$\dfrac{AC}{AD}=\dfrac{AB}{AC}$

We have

$AC=x,\ AD=2,\ AB=2+12=14$

Substitute:

$\dfrac{x}{2}=\dfrac{14}{x}$ <em>cross multiply</em>

$x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7$

5 0

3 years ago

Can someone help me in this question

BlackZzzverrR [31]

Answer:

The average speed of the athlete for the entire competition is approximately 21.23 km/hr

Step-by-step explanation:

The given parameters of the athlete performance in the triathlon are;

The length the athlete swims = 750 m = 0.75 km

The time the athletes spends swimming = 15 minutes = 0.25 hours

The speed with which the athlete cycles = 40 km/hr.

The time the athletes spends while cycling = 30 minutes = 0.5 hours

The distance the athlete ran = 5 km

The average speed with which the athlete ran = 3 m/s = 10.8 km/hr.

The formula for average speed, s is Average speed = Total distance/(Total time)

The distance, ∑d, the athlete covered in the entire competition is given as follows;

∑d = 0.75 km + 0.5 hr. × 40 km/hr. + 5 km = 0.75 km + 20 km + 5 km = 25.75 km

The distance, ∑t, the athlete spends in the entire competition is given as follows;

∑t = 0.25 hr. + 0.5 hr. + 5 km/(10.8 km/hr.) = 0.25 hr. + 0.5 hr. + 0.463 hr. ≈ 1.213 hr.;

Therefore;

The average speed of the athlete for the entire competition, s = ∑d/∑t = 25.75 km/(1.213 hr.) ≈ 21.23 km/hr.

6 0

3 years ago