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HACTEHA [7]
2 years ago
11

Determine and state the coordinates of the center and the length of the radius of a circle whose equation is

Mathematics
1 answer:
Tpy6a [65]2 years ago
5 0

Answer:  center = (-3, 2)   radius = √23

<u>Step-by-step explanation:</u>

The equation of a circle is: (x - h)² + (y - k)² = r²

where center = (h, k) and radius = r

Complete the square for both x and y:

x^2+6x+\bigg(\dfrac{6}{2}\bigg)^2+y^2-4y+\bigg(\dfrac{-4}{2}\bigg)^2 = 10 +\bigg(\dfrac{6}{2}\bigg)^2+\bigg(\dfrac{-4}{2}\bigg)^2\\\\\\(x+3)^2+(y-2)^2=23\\\\\\\rightarrow (h,k)=(-3,2)\\\\\rightarrow r^2=23\quad \rightarrow r=\sqrt{23}

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JL = 28,<br> KL= 5x + 6, and<br> JK = 3x + 6,
Alexeev081 [22]

Answer:

KL = 16

Step-by-step explanation:

For this problem, JL is the sum of KL and JK.  So we can say this:

JK + KL = JL

( 3x + 6 ) + ( 5x + 6 ) = 28

8x + 12 = 28

8x = 16

x = 2

So, now we can find KL:

5x + 6 = ?

5(2) + 6 = ?

10 + 6 = ?

16 = ?

So the length of KL is 16.

Cheers.

7 0
3 years ago
A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set w
VashaNatasha [74]

Complete Question

A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set was split into 5 segments (each 6.4 seconds long), what is the resulting:

a)F minimum

b) F maximum

c) Frequency resolution

Answer:

a) Fmax=100Hz

b) Fmin=0Hz

c) F_r=0.0313

Step-by-step explanation:

From the question we are told that:

Time t=32sec

FrequencyF=200Hz

Segments \mu=5

Generally the equation for Frequency Range is mathematically given by

Fmax=\frac{F}{2}

Fmax=100Hz

Therefore

a) Fmax=100Hz

b) Fmin=0Hz

c)

Generally the equation for Frequency Resolution is mathematically given by

F_r=\frac{F}{N}

Where

N=The Total dat points

N=Sampling Frequency *Time

N=200*32

N=6400

Therefore

F_r=\frac{200}{6400}

F_r=0.0313

6 0
2 years ago
Solve the equation 1) 4.3^x+1 = 27+9^x<br> 2) 3^x+5= 3^x+3+8/3
Bad White [126]

Answer:

Step-by-step explanation:

4*3^x+1=27+(3^2)^x

(3^2)^x=(3^x)^2

3^x=t

4t+1=27+t^2

t^2-4t+27-1=0

t^2-4t+26=0

delta=4^2-4*1*26=16-84=-68<0

the  equation has not real solutions

3 0
3 years ago
A music school charges a registration fee in addition to a fee per lesson. Write an equation if each lesson costs $40 and a regi
Jobisdone [24]
T = total cost for music school
L = # of lessons

T = $1,190 + ($40 × L)
T = $1,190 + ($40 × 12)
T. = $1,190 + $480
T = $ 1,670 for 12 lessons
3 0
2 years ago
Plz answer this question:
d1i1m1o1n [39]

Yes, Lord Vader !

                                               2/3 x + 5   = 1/2

Multiply each side by  2 :       4/3 x + 10  =  1

Multiply each side by  3 :         4  x + 30  =  3  <== equivalent equation
                                                                                without fractions
 
Subtract  30  from each side:  4x             =  -27

Divide each side by  4 :            x              =  -27/4  =  -6.75 

6 0
3 years ago
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