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WITCHER [35]
3 years ago
14

Use the given information to answer the following questions. center (3, -9, 3), radius 5 (a) Find an equation of the sphere with

the given center and radius. (b) What is the intersection of this sphere with the yz-plane?
Mathematics
1 answer:
lianna [129]3 years ago
7 0

Answer: The equation of the sphere with the center and radius

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

Step-by-step explanation:

a) The equation of the sphere having center (h,k,l) and radius r is

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

Given center of the sphere  (3, -9, 3) and radius 5

(x-3)^{2}+(y+9)^2+(z-3)^2 = 5^2

on simplification , we get solution

x^{2} -6 x+9+y^{2} +18 y+81+z^{2}-6 z+9=25

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

Final answer :-

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

y^{2} +z^{2}+18 y-6 z+74=0

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Which inequality is true? Use the number line to help​
wlad13 [49]

Answer:

Option D.

Step-by-step explanation:

In order to resolve this problem, we are going to transform every fraction on a decimal number.

A) 2\frac{1}{2} is a mixed fraction. To get a proper fraction, we let the denominator as 2, and to get the numerator we multiply 2 by 2, and we add 1, as seen on the attached picture.

So:

2\frac{1}{2}=\frac{5}{2}

We divide 5 by 2 and we get 2,5.

So, the first option is not true, as 1.5 is smaller than 2,5.

B) We divide 1 by 2 and get 0,5. They are equal numbers, we can't say that 0,5 is bigger than 0,5.

C) -2.5 is smaller than -1,5 so this option is not true.

D) -3\frac{1}{2}=\frac{-7}{2}

We divide 7 by 2 and we get -3,5. In fact, -3,5 is bigger than -4.5, as there is a major distance from this negative number to cero.

5 0
4 years ago
Michael had 3 times as many mangoes as Junior. After eating 8 mangoes. Michael had
jolli1 [7]

Answer:

Michael: 24

Junior: 8

Step-by-step explanation:

8 is a multiple of 24, meaning if you ate 1/3 of 24 you get 16, which is doubled 8.

4 0
3 years ago
Who knows how to answer this. It's Dividing complex numbers.​
Elodia [21]

Answer:

answe is 1+i

<em><u>mark this as brainliest!!</u></em>

<em><u>mark this as brainliest!!follow me</u></em>!

4 0
3 years ago
Read 2 more answers
Brainliest to correct answer
jeyben [28]
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3 0
3 years ago
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The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served w
Oliga [24]

Answer:

(121.576 ; 273.424)

Step-by-step explanation:

Given the data:

175, 125, 180, 220, 240, 245

We can calculate the mean and standard deviation

Mean = Σx/ n = 1185 / 6 = 197.5

Standard deviation = 46.125 (calculator)

The confidence interval :

Mean ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Tcritical at 99%, df = n - 1 ; 6 - 1 = 5

Tcritical = 4.032

Margin of Error = 4.032 * 46.125/√6

Margin of error = 75.924

Confidence interval :

197.5 ± 75.924

Lower boundary = 197.5 - 75.924 = 121.576

Upper boundary = 197.5 + 75.924 = 273.424

(121.576 ; 273.424)

5 0
3 years ago
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