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3 years ago

Can you write the equation for a circle if the given point does not lie on the circle? Explain .

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

The equation of a circle with center (a,b) and radius r is given as:

${(x - a)}^{2} + {(y - b)}^{2} = {r}^{2}$

If a given point (x,y) does not lie on this circle, it will not satisfy its equation.

This means the distance from the point to the center is not equal to the radius.

It is either less or greater than the radius.

Hence you cannot write the equation of the circle.

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Solve the equation on the interval [0, 27r). 4(sin x)2 - 2 = 0

Ket [755]

$4[sin(x)]^2 - 2 = 0\implies 4[sin(x)]^2=2\implies [sin(x)]^2=\cfrac{2}{4}\implies [sin(x)]^2=\cfrac{1}{2} \\\\\\ sin(x)=\pm\sqrt{\cfrac{1}{2}}\implies sin^{-1}[sin(x)]=sin^{-1}\left( \pm\sqrt{\cfrac{1}{2}} \right)\implies x=sin^{-1}\left( \pm\sqrt{\cfrac{1}{2}} \right)$

$x=sin^{-1}\left( \pm\cfrac{\sqrt{1}}{\sqrt{2}} \right)\implies x=sin^{-1}\left( \pm\cfrac{1}{\sqrt{2}} \right)\implies x=sin^{-1}\left( \pm\cfrac{\sqrt{2}}{2} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x=\cfrac{\pi }{4}~~,~~\cfrac{3\pi }{4}~~,~~\cfrac{5\pi }{4}~~,~~\cfrac{7\pi }{4}~\hfill$

Check the picture below.

4 0

2 years ago

Teresa is building a scale model of the JP Morgan chase Tower in Houston.In her scale model, 1.5 inches represents 61 meters. Si

Jet001 [13]

Answer:

Teresa should build 7.5 inches model.

Step-by-step explanation:

Consider the provided information.

Teresa is building a scale model of the JP Morgan chase Tower in Houston.

Her scale model, 1.5 inches represents 61 meters.

The actual building is 305 meters tall,

First find how many 61's are there in 305.

For this divide 305 by 61.

$\frac{305}{61}= 5$

Actual building is 5 times taller than 61. Thus the model should be 5 times taller than 1.5.

multiply 1.5 with 5 gives us:

$1.5\times 5=7.5$

Hence, Teresa should build 7.5 inches model.

7 0

3 years ago

What is the missing fraction for 1/6 1/8 1/4 ?/? = 1whole

denis23 [38]

The answer is 11/24.

5 0

3 years ago

If p stays constant and u is doubled what happens to e? given U=EP

Stolb23 [73]

We are given the expression:

U = E * P

The equality symbol “ = “ means that for all cases, the value of U and E * P must always be equal. This means that whatever happens on the left side, must equally happen on the right side.

So what this actually means is that, if we double U so we must also double the expression E * P, that is:

2 U = 2 (E * P)

However since P stays constant in the process, therefore only E is changed, hence:

2 U = P * 2 E

So we can see that E is also doubled.

4 0

3 years ago

Part III: Bailey works part-time at a movie theater. The theater pays employees an hourly wage based on their length of employme

frutty [35]

Given the following table showing the hourly wages of employees of a movie theater based on their length of employment.

Length of employment (months) Hourly wage (dollars/hour)
6 months 7.55
12 months 7.85
18 months 8.15
24 months 8.45

To obtain an algebraic expression that describes how much Bailey’s employer pays part-time workers, we take two points from the table.

Recall that the equation of a linear function satisfying two points
$(x_1,y_1)$ and $(x_2,y_2)$
is given by
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Given the two points (6, 7.55) and (12, 7.85), the algebraic expression relating the two points is given by
$\frac{y-7.55}{x-6} = \frac{7.85-7.55}{12-6} = \frac{0.3}{6} \\ \\ 6(y-7.55)=0.3(x-6) \\ \\ 6y-45.3=0.3x-1.8 \\ \\ 0.3x-6y=-43.5$

Therefore, the algebraic expression that describes how much Bailey’s employer pays part-time workers is
$0.3x-6y=-43.5$

5 0

3 years ago