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3 years ago

Graph each circle given below right the center and radius of each circle

Mathematics

2 answers:

kotegsom [21]3 years ago

7 0

Answer:

The center of circle is (-3,-2) and radius of circle is √6.

Step-by-step explanation:

We have given an equation of circle.

(x+3)²+(y+2) = 6

We have to plot the graph of circle.

(x-h)²+(y-k)² = r² where (h,k) is center and r is radius of circle.

Given equation is (x-(-3))²+(y-(-2))² = (√6)²

comparing above equation with standard equation, we have

(h,k) = (-3,-2) and r = √6

Hence, the center of circle is (-3,-2) and radius of circle is √6.

expeople1 [14]3 years ago

5 0

Answer:

Center: (-3,-2)

Radius: √6

The graph is attached.

Step-by-step explanation:

The equation of the circle has the form:

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

Where (h,k) is the point of the center of the circle and r is the radius of the circle.

The equation given in the problem is

$(x +3)^{2}+(y+2)^{2}=6$

Therefore:

h=-3

k=-2

The center is at (-3,-2)

And the radius is:

$r^2=6\\r=\sqrt{6}$

Then, you can graph it has you can see in the image attached.

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Suppose theta is an angle in the standard position whose terminal side is in quadrant 4 and cot theta = -6/7. find the exact val

zimovet [89]

First off, let's notice that the angle is in the IV Quadrant, where sine is negative and the cosine is positive, likewise the opposite and adjacent angles respectively.

Also let's bear in mind that the hypotenuse is never negative, since it's simply just a radius unit.

$\bf cot(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{opposite}{-7}}\qquad \impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{6^2+(-7)^2}\implies c=\sqrt{36+49}\implies c=\sqrt{85} \\\\[-0.35em] ~\dotfill$

$\bf tan(\theta)=\cfrac{\stackrel{opposite}{-7}}{\stackrel{adjacent}{6}} ~\hfill csc(\theta)=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{opposite}{-7}} ~\hfill sec(\theta)=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{adjacent}{6}} \\\\\\ sin(\theta)=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{sin(\theta)=\cfrac{-7}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies sin(\theta)=-\cfrac{7\sqrt{85}}{85}}$

$\bf cos(\theta)=\cfrac{\stackrel{adjacent}{6}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{cos(\theta)=\cfrac{6}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies cos(\theta)=\cfrac{6\sqrt{85}}{85}}$

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2 years ago

On an August day in Fairbanks, Alaska, the temperature changed by an average of 1.5° C per hour from its low of 5° C at 5:00 am.

zhuklara [117]

Answer:

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Step-by-step explanation:

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The frequency table was made using a box containing slips of paper. Each slip of paper was numbered 0, 1, 2, 3, or 4.

inna [77]

In order to make a frequency plot first we need to find the proportion of each outcome.

Total number of results = 15+20+5+5+5 = 50

Frequency of 0 = 15
Proportion of 0 = 15/50 = 0.3

Frequency of 1 = 20
Proportion of 0 = 20/50 = 0.4

Frequency of 2 = 5
Proportion of 2 = 5/50 = 0.1

Frequency of 3 = 5
Proportion of 3 = 5/50 = 0.1

Frequency of 4 = 5
Proportion of 4 = 5/50 = 0.1

Now we need to plot the data on a frequency plot. The x-axis shows the outcomes from 0 to 4 and y-axis shows the frequency of each outcomes. The frequency plot is shown in the figure attached with.