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3 years ago

10

Find the measure of the angle indicated and show work please help I need this soon

1 answer:

kumpel [21]3 years ago

6 0

The answer is 120 degrees I hope this helps

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Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

If someone runs 4 meters per second, how many kilometers is that per hour?

Vesna [10]

Answer:

14.4 km/h

Step-by-step explanation:

When finding km/h given m/s always multiply by 3.6

When finding m/s given km/h do the vice versa (divide by 3.6)

So.. 4km/h x 3.6 = <u>14.4 km/h </u>

6 0

4 years ago

Read 2 more answers

¿ cuáles son los adjetivos? y ¿ cuáles son los adjetivos ? por favor es para hoy <br>

QveST [7]

Answer:

1) maldava y despota

2) pequenos

Step-by-step explanation:

4 0

3 years ago

{(24p – 66) = 3p + 43

Alenkinab [10]

$\text {Hello! Let's Solve this Equation!}$

$\text {\underline {The First Step is to Subtract 3p}}$

$\text {24p-66-3p=3p+43-3p}$

$\text {Your New Problem Is: 21p-66=43}$

$\text {\underline {The Next Step Is to Add 66}}$

$\text {21p-66+66=43+66}$

$\text {Your New Problem Is: 21p=109}$

$\text {\underline {The Final Step is to Divide 21}}$

$\text {21p/21=109/21}$

$\text {Your Answer Would Be:}$

$\fbox {p=109/21}$

$\text {Best of Luck!}$

5 0

3 years ago

8r - 4 (7r - 5) this is the question im struggling with

Ira Lisetskai [31]

i am pretty sure the answer is:

= -20r + 20

3 0

3 years ago