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3 years ago

What Percent of 60m is 9m?

Mathematics

2 answers:

fomenos3 years ago

5 0

The percent of 60m and 9m is 15%

skelet666 [1.2K]3 years ago

4 0

The answer is 15%

Nope this helped :)

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Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

3 years ago

1. Michael buys a chocolate bar which has 50% extra free. The chocolate bar usually weighs 200g. (a) How much extra chocolate do

KiRa [710]

Answer:

1/2 more chocalte or 50% more or 100g more

300g is the new weight

Step-by-step explanation:

200/2=100(50%)

100+200=300g

5 0

3 years ago

A bedroom wall is 12 feet long. A decorator places the center of a square painting that has side lengths of 3 feet in the exact

antiseptic1488 [7]

the answer is 9 feet

cuz 12-3=9

8 0

3 years ago

Shawn incorrectly graphed the inequality -x-2y≥8 as shown below Explain shawn mistake rotate phone if u need to

Aleks04 [339]

Answer:

He failed to flip the inequality

y ≤-1/2x-4

Step-by-step explanation:

-x-2y ≥8

Add x to each side

-x+x-2y ≥x+8

-2y ≥x+8

Divide by -2. Remember to flip the inequality

-2y/-2 ≤-1/2 x +8/-2

y ≤-1/2x-4

Shawn shaded the wrong side of the line.

Y is less than or equal to . He failed to flip the inequality

3 0

3 years ago

Oil spill spreads 25 m² every 1/6 hour how much area does the oil spill cover after two hours

Delvig [45]

1/6 of an hour is 10 minutes because there are 60 minutes in an hour so 60/6=10
so it's 25m^2/10minutes
now just multiply 25 by 12 ( 12 lots of 10 minutes in 2 hours)
25*12=300
answer is 300m^2

hope this helped

6 0

3 years ago

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What Percent of 60m is 9m?​

What Percent of 60m is 9m?