Determine the equation of the circle graphed below.

Answer:

XY is a tangent

Step-by-step explanation:

Given

[tex]XY = 12[/tex]

[tex]WY = 20[/tex]

[tex]WZ = 8[/tex]

Required

Is XY a tangent?

XY is a tangent if:

[tex]WY^2 = XY^2 + WX^2[/tex]

Because XY should make a right angle at point X with the circle

Where

[tex]WX = 2 * WZ[/tex]

So, we have:

[tex]WY^2 = XY^2 + WX^2[/tex]

[tex]WY^2 = XY^2 + (2*WZ)^2[/tex]

[tex]WY^2 = XY^2 + (2WZ)^2[/tex]

[tex]WY^2 = XY^2 + 4WZ^2[/tex]

This gives:

[tex]20^2 = 12^2 + 4*8^2[/tex]

[tex]400 = 144 + 256[/tex]

[tex]400 = 400[/tex]

Yes, XY is a tangent

Answer: Did this all by myself 1/6 is closer to 0 and 5/8 is closer to 1/2 so the answer is 1/2  0 then 1/2 then 1/3 again

Step-by-step explanation:  

1/ 6   -5 /8 =(1 × 4  6 × 4)  – (5 × 3  8 × 3)  = 4 /24  – 15 /24  =  4 – 15  24 = – 11  24

Answer:

[tex] \displaystyle 5\sqrt{2}[/tex]

Step-by-step explanation:

we have a right angle isosceles triangle

in order to figure out the length of each leg we can consider Pythagoras theorem given by

[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]

remember that,

isosceles triangle has two equal legs so a=b and given that the the hypotenuse is 10

substitute:

[tex] \displaystyle {a}^{2} + {a}^{2} = {10}^{2} [/tex]

simplify addition:

[tex] \displaystyle {2a}^{2}= 100[/tex]

simplify square:

divide both sides by 2:

[tex] \displaystyle {a}^{2}= 50[/tex]

square root both sides:

[tex] \displaystyle {a}^{}= \sqrt{50}[/tex]

[tex] \displaystyle {a}^{}= 5\sqrt{2}[/tex]

hence,

the length of each leg is 5√2

Answer:

11.17

Step-by-step explanation:

arc length = 2πr(θ/360)

= 2π(8)(80/360)

= 11.1701072...

= 11.17 to nearest hundredth

Answer:

Error term

Step-by-step explanation:

Given :

In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the _____. slope error term variance standard error of the mean standard deviation

To find :

Fill in the blanks.

Now, In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the Error term.

Because we use the error term in the regression analysis difference between the actual value of [tex]Y[/tex] and the approximate value of [tex]Y[/tex] which is above of actual value or below of actual value.

 As [tex]Y[/tex]is an actual value and [tex]Y_0[/tex] is an approximate value then,

[tex]|Y-Y_0|[/tex] is an error.

It is a vertical distance between the actual value and the approximate value  of [tex]Y[/tex].

So, the error term is always positive.

Answer:

I think the answer is 3:5

Answer:

3.5

Step-by-step explanation:

Answer:

d. 63%

Step-by-step explanation:

percent, will be white?

A41% b50% c59% d63%

The probability of white = P (w) = 41/65= 0.63

The  probability of yellow = P (y)= 24/65= 0.369=0.37

The probability of choosing white is 0.63 . When rounded to  nearest percent gives

0.63*100/100

=0.63*100 percent

= 63 percent

= 63%

the probability of getting   the next marble white is the same as the probability of getting a white.

Answer: (b)

Step-by-step explanation:

Given

The function is given as

[tex]f(x)=\dfrac{x^2-12x+20}{x-2}[/tex]

Solving the function

[tex]f(x)=\dfrac{x^2-2x-10x+20}{x-2}\\\\f(x)=\dfrac{(x-2)(x-10)}{(x-2)}\\\\f(x)=x-10[/tex]

for [tex]x=2[/tex]

[tex]f(2)=2-10\\f(2)=-8[/tex]

The function is continuous at [tex]x=2[/tex] because [tex]\lim_{x \to 2} f(x)[/tex] exists.

If the limit exists at a point, then the function is continuous.  

Answer:

on edge its fs not b or c

Step-by-step explanation:

Answer: Prism

Step-by-step explanation:

Answer:

[tex]\frac{8x^{18} }{y^{2} }[/tex]

Step-by-step explanation:

Answer:

Hence, the [tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex] and approximately value of [tex]y(t)[/tex] is [tex]-0.844[/tex].

Given :

 [tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]

Where  [tex]m=2[/tex] kilograms

           [tex]c=8[/tex] kilograms per second

           [tex]k=80[/tex] Newtons per meter

          [tex]F(t)=20\sin (6t)[/tex] Newtons

Explanation :

(1)

Solve the initial value problem. [tex]y(t)[/tex]

   [tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]

[tex]\Rightarrow 2y''+8y'+80y=20\sin (6t)[/tex]

[tex]\Rightarrow y''+4y'+40y=10\sin (6t)[/tex]

Auxilary equations :[tex]F(t)=0[/tex]

[tex]\Rightarrow r^2+4r+40=0[/tex]

[tex]\Rightarrow r=\frac{-4\pm\sqrt{4^2-4\times 1\times 40}}{2\times 1}[/tex]

[tex]\Rightarrow r=\frac{-4\pm\sqrt{16-160}}{2}[/tex]

[tex]\Rightarrow r=\frac{-4\pm\sqrt{-144}}{2}[/tex]

[tex]\Rightarrow r=\frac{-4\pm12i}{2}[/tex]

[tex]\Rightarrow r=-2\pm6i[/tex]

The complementary solution is [tex]y_c=e^{-2t}\left(c_1\cos 6t+c_2\sin 6t\right)[/tex]

The particular Integral, [tex]y_p=\frac{1}{f(D)}F(t)[/tex]

[tex]y_{y} &=\frac{1}{D^{2}+4 D+40} 25 \sin (6 t) \\\\ y_{y} &=\frac{25}{-6^{2}+4 D+40} \sin (6 t) \quad\left(D^{2} \text { is replaced with }-6^{2}=-36\right) \\\\y_{y} &=\frac{25}{4 D+4} \sin (6 t) \\\\y_{y} &=\frac{25}{4(D+1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(D+1)(D-1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4\left(D^{2}-1\right)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(-36-1)} \sin (6 t) \\\\y_{y} &=-\frac{25}{148}(D-1) \sin (6 t) \\y_{y} &=-\frac{25}{148}\left(\frac{d}{d t} \sin (6 t)-\sin (6[/tex]

Hence the general solution is :[tex]y=y_c+y_p=e^{-2t}(c_1\cos 6t+c_2\sin 6t)-\frac{25}{148}(6\cos 6t-\sin 6t)[/tex]

Now we use given initial condition.

[tex]y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\y(0) &=e^{-\alpha 0)}\left(c_{1} \cos (0)+c_{2} \sin (0)\right)-\frac{25}{148}(6 \cos (0)-\sin (0)) \\\\0 &=\left(c_{1}\right)-\frac{25}{148}(6) \\\\c_{1} &=\frac{75}{74} \\\\y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\[/tex]

[tex]y^{\prime}(t)=-2 e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)+e^{-2 t}\left(-6 c_{1} \sin 6 t+6 c_{2} \cos 6 t\right)-\frac{25}{148}(-36 \sin (6 t)-6 \cos (6 t)) \\\\y^{\prime}(0)=-2 e^{0}\left(c_{1} \cos 0+c_{2} \sin 0\right)+e^{0}\left(-6 c_{1} \sin 0+6 c_{2} \cos 0\right)-\frac{25}{148}(-36 \sin 0-6 \cos 0) \\\\0=-2\left(c_{1}\right)+\left(6 c_{2}\right)-\frac{25}{148}(-6) \\\\0=-2 c_{1}+6 c_{2}+\frac{75}{74} \\\\0=-2\left(\frac{75}{74}\right)+6 c_{2}+\frac{75}{74} \\\\[/tex][tex]\begin{array}{l}0=-\frac{150}{74}+6 c_{2}+\frac{75}{74} \\\\\frac{150}{74}-\frac{75}{74}=6 c_{2}\end{array}[/tex]

[tex]\begin{array}{l}c_{2}=\frac{25}{148}\\\\\text { Substitute } c_{1} \text { and } c_{2} \text { in } y(t) \text { . Then }\\\\y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex]

(2)

[tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\left(\frac{75}{74} e^{-2 t} \cos 6 t+\frac{75}{148} e^{-2 t} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\frac{75}{74}\left(e^{-2 t}-1\right) \cos 6 t+\frac{25}{148}\left(3 e^{-2 t}+1\right) \sin 6 t \\\\|y(t)| \leq \frac{75}{74} e^{-2 t}-1|\cos 6 t|+\frac{25}{148}\left|3 e^{-2 t}+1\right||\sin 6 t| \\\\[/tex]

[tex]|y(t)| \leq \frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right| \\\\\lim _{t \rightarrow \infty} y(t) \leq \lim _{t \rightarrow \infty}\left\{\frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right|\right\} \\\\\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}\left|\lim _{t \rightarrow \infty}\left(e^{-2 t}-1\right)\right|+\frac{25}{148}\left|\lim _{t \rightarrow \infty}\left(3 e^{-2 t}+1\right)\right|\right\} \\[/tex]

[tex]\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}(-1)+\frac{25}{148}(1)\right\}=-\frac{75}{74}+\frac{25}{148}=-\frac{-150+25}{148}=-\frac{125}{148} \approx-0.844[/tex]

Answer:

[tex](6\sqrt{3},\,\frac{5\pi}{6})[/tex]

Step-by-step explanation:

The radius  r  can be found from the relationship

 [tex]r^2=x^2+y^2\\r^2=(-9)^2+(3\sqrt{3})^2\\r^2=81+27=108\\r=\sqrt{108}\\r=6\sqrt{3}[/tex]

The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.

[tex]\cos{\theta}=\frac{x}{r}=\frac{-9}{6\sqrt{3}}\\\cos{\theta}=-\frac{9}{6\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\\\cos{\theta}=-\frac{9\sqrt{3}}{6\cdot3}\\\cos{\theta}=-\frac{\sqrt{3}}{2}\\\\\cos^{-1}\frac{-\sqrt{3}}{2}}=\frac{5\pi}{6}[/tex]

See the attached image.

Answer:

y= 12x

Step-by-step explanation:

36/3=12

12× x =y

________________________

Answer:

C) 96i – 280j

Step-by-step explanation:

Multiplying vector by constant:

When a vector is multiplied by a constant, each component of the vector is multiplied by this constant.

In this question:

u = -12i + 35j

-8u = -8(-12i + 35j) = (8*12i - 8*35j) = 96i - 280j.

The answer is C) 96i – 280j

Answer:

I believe it would be "505 times n"

Step-by-step explanation:

If tis is not what you are looking for I am sorry, but the question was vague.

Answer:

Since there are 7.5 gallons in each cubic foot, multiply the cubic feet of the pool by 7.5 to arrive at the volume of the. 3.14 x 25 ft x 3 ft x 7.5 = 1766.25 gallons

Step-by-step explanation:

Answer:

26 customers

Step-by-step explanation:

First:  determine the z score from standard normal probability table with an indicative area of 0.1

Z-score from probability table  = - 1.28

mean   = 3.5 minutes

std  = 3 minutes

next determine the Z-score based on the information given in the question

Z = ( std -  mean )  / processing time

  = ( 3 - 3.5 ) / 2 = -0.25

Finally determine the number of customers

N = [tex](\frac{-1.28}{-0.25} )^2[/tex]  = 1.6384 / 0.0625 = 26.21 ≈ 26 customers  

Answer:

X = 65 degrees

Step-by-step explanation:

180 = 70 + 45 + X

180 = 115 + X

X = 65 degrees

Answer:

9

Step-by-step explanation:

Substitute 8 in place of x

f(x) = 2*8-7

f(x) = 9

Answer:

9

Step-by-step explanation:

plug in 8 where x is so it would look like

2(8)-7 = 9

do 2 *8 first which is 16

then do 16-7 which gives you 9

Using the sine rule,

[tex] \frac{a}{sin(a)} = \frac{b}{sin(b)} = \frac{c}{sin(c)} [/tex]

Here we are going to use the values of A and C,

[tex] \frac{12}{sin(a)} = \frac{14}{sin(90)} \\ \frac{12}{sin(a)} = \frac{14}{1} \\ sin(a) = 12 \div 14 \\ sin(a) = 0.8571[/tex]

So sin(A) = 12/14 = 6/7 = 0.8571, but since the question says in its simplest radical form, I think the closest answer to it should be

[tex] \frac{ \sqrt{3} }{2} [/tex]

Answer: 44.59 or 44.6

Step-by-step explanation:

30^2+33^2= 900+ 1089

= 1989^2

square root = 44.6

hope this helps

Answer:

1/20

Step-by-step explanation:

According to G0ogle 5 percent equals 1/20 in lowest terms.

Answer:

5% equals 5/100 which is 1/20 in lowest terms.

Step-by-step explanation:

5% is basically equivalent to 5/100. 5/100 in lowest terms is 1/20 since you divide the numerator and denominator by 5.

I hope this helps, have a nice day.

Answer:

you should multiply or add

Step-by-step explanation:

Answer:

u=−x2−x+1

Step-by-step explanation:

Let's solve for u.

2x−u−1x^2−3x+3=2

Step 1: Add x^2 to both sides.

−x2−u−x+3+x2=2+x2

−u−x+3=x2+2

Step 2: Add x to both sides.

−u−x+3+x=x2+2+x

−u+3=x2+x+2

Step 3: Add -3 to both sides.

−u+3+−3=x2+x+2+−3

−u=x2+x−1

Step 4: Divide both sides by -1.

−u/−1=x2+x−1

−1/u=−x2−x+1

Answer:

u=−x2−x+1

Answer:

Solution given:

x²-12x+11=0

Comparing above equation with ax²+bx+c

we get

a=1

b=-12

c=11

By using Vieta's theorem

X1+X2=[tex] \frac{-b}{a} [/tex]=[tex] \frac{- -12}{1} [/tex]=12

again

X1X2=[tex] \frac{c}{a} [/tex]=[tex] \frac{11}{1} [/tex]=11

x1.x2=11

x1+x2=12

Answer:

x=52   y=116

Step-by-step explanation:

because they give you the angle 116.

those two are actually equal.

y=116

since that is true, you can do 180-116=64.

now, you subtract 64-12

which is 52.