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9 months ago

#3 Determine the constant of proportionality of the graph 4

Mathematics

1 answer:

miss Akunina [59]9 months ago

6 0

Explanation

Step 1

choose two points from the line

$\begin{gathered} P1(0,0) \\ \text{and} \\ P2(2,40) \end{gathered}$

Step 2

the constant of proportionality is given by

$\begin{gathered} C=\frac{f(b)-f(a)}{b-a} \\ C=\frac{y_{p2}-y_{p1}}{x_{p2}-x_{p1}} \\ \text{replace} \\ C=\frac{40-0}{2-0} \\ C=\frac{40}{2} \\ C=20 \end{gathered}$

so, the answer is 20

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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

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JulsSmile [24]

Answer:

$2y + {4}^{2} = 64 \\ 2y + 16 = 64 \\ 2y = 64 - 16 \\ 2y = 48 \\ \\ y = \frac{48}{2} \\ \\ y = 24$

I hope I helped you^_^

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How much interest is earned on $2,700 in one year if it is invested at 3%?

tester [92]

On this part, you can use the formula for compound interest:

F = P(1+i)^n
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P = present worth of $
i=interest
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So interest = 2781-2700 = $81

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

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Archy [21]

Answer:

If 5x-2 = 3x+4, then x=3

Step-by-step explanation:

5x-2=3x+4

Add 2 to both sides, and you get 5x=3x+6. Subtract 3x from both sides, and you get 2x=6. Divide both sides by 2, and what's left is x=3. Hope this helps. :)

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The diagram below is NOT drawn to scale. Are lines j and k parallel? How can you tell?

Artemon [7]

Answer:

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Step-by-step explanation:

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