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2 years ago

How would you teach something you have learned this year in Math to someone younger than you? Write more than 5 sentences.

1 answer:

4 0

I would start by saying how much I enjoyed this lesson and how it has helped me in many ways I would also like to state how it was difficult at first but once I started to understand it, it became really easy and would like to thanks the teacher for teaching it.

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A mountain climber started at 150 feet below sea level. What would he

Ber [7]

Answer:

3150 feet for both

Step-by-step explanation:

correct?

4 0

2 years ago

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

Solve b to the second power=77

zubka84 [21]

Answer:

$\large\boxed{b=\pm\sqrt{77}}$

Step-by-step explanation:

$b^2=77\iff b=\pm\sqrt{77}\\\\\text{because}\\\\(-\sqrt{77})^2=77\ \text{and} \ (\sqrt{77})^2=77$

3 0

3 years ago

A farmer had 63 sheep.<br> She sold 1/7 of them.<br> How many sheep had she left?

kykrilka [37]

63 dives by 7 is 9 so 63-9 is 54
Answer 54

3 0

3 years ago

Greatest common factor of three univariate monomials

ryzh [129]

Answer:

Step-by-step explanation:

The GCF is the largest number that is a factor of the numbers listed. In this case, since one of the numbers is a constant the GCF will not have a variable. However, all of the numbers can be divided by 3. This is because 3 is the GCF.

3 0

3 years ago

How would you teach something you have learned this year in Math to someone younger than you? Write more than 5 sentences.​

How would you teach something you have learned this year in Math to someone younger than you? Write more than 5 sentences.