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3 years ago

Right now, it's colder than 80ºF outside. Which inequality represents t, the temperature outside?n have?

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

4 0

Answer:

t<80°

Step-by-step explanation:

if the value is less than, use <

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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

H(9z)<br><img src="https://tex.z-dn.net/?f=h%28y%29%20%3D%20y%20%2B%203" id="TexFormula1" title="h(y) = y + 3" alt="h(y) = y + 3

Diano4ka-milaya [45]

Not enough informatio dawg

4 0

4 years ago

3! + 4! = 5040 30 or 16

makkiz [27]

Answer:

None of those

Step-by-step explanation:

3! = 3*2*1 = 6

4! = 4*3*2*1 = 24

24 * 6 = 144

144 is none of the choices

6 0

3 years ago

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GIVING BRAINLIEST Write an equation to represent the number puzzle. Use x as the

amid [387]

Answer:

It's C

Step-by-step explanation:

When I wrote it out I got x^2+7=7x-5

3 0

4 years ago

In the figure above a || b. If <1=34, find the measure of <2

MA_775_DIABLO [31]

Its also 34 ....hope u got ur answer

5 0

3 years ago

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