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Stella [2.4K]
3 years ago
9

Answer the following questions about the sphere whose equation is given by x2+y2+z2−8x+4y=−4. 1. Find the radius of the sphere.

Radius: ????= 2. Find the center of the sphere. Write the center as a point (????,????,c) where ????, ????, and c are numbers. Center:
Mathematics
1 answer:
Anna [14]3 years ago
8 0

Answer:

we have (a,b,c)=(4,-2,0) and R=4 (radius)

Step-by-step explanation:

since

x²+y²+z²−8x+4y=−4

we have to complete the squares to finish with a equation of the form

(x-a)²+(y-b)²+(z-c)²=R²

that is the equation of a sphere of radius R and centre in (a,b,c)

thus

x²+y²+z²−8x+4y=−4

x²+y²+z²−8x+4y +4 = 0

x²+y²+z²−8x+4y +4 +16-16 =0

(x²−8x + 16) + (y² + 4y + 4 ) + (z²) -16 = 0

(x-4)² + (y+2)² + z² = 16

(x-4)² + (y-(-2))² + (z-0)² = 4²

thus we have a=4 , b= -2 , c= 0 and R=4

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Ben works for software company in Cleveland. To train new employees, Ben travels to their two other locations, Buffalo and Phila
Andru [333]

Answer:

Explanation:we will solve this question with help of linear programming.

Now,  let Ben goes x times in buffalo trip and goes y times in Philadelphia trip. Thus, according to the question, Min Z= 180x+300y

And s.t.r. 2x+3y≤105, where x≥5, y≥15.

since at (0,0) 0≤105(true), so area of 2x+3y≤105 will cover the origin.

But, 0≥5 and 0≥15 are false, so their area will not cover the origin.

Thus, after drawing the graph of these three lines we will get a feasible reason of triangle ABC, where point A≡(5,31.667), B≡(5,15), and C≡(30,15)

Z at A- 180×5+300×31.667=10,400.1

at B-180×5+300×15=1350( which is minimum.)

at C- 180×30+300×15=5,850

Thus, Ben should go 5 times to buffalo trip and 15 times to Philadelphia to minimize his cost which is $1350.




3 0
3 years ago
What is the area?Please i need help
antiseptic1488 [7]

Answer:

65

Step-by-step explanation:

Base by High

then divided by 2

4 0
3 years ago
What symbol do I use and number line help plzz​​
Ghella [55]
For all three boxes?
6 0
2 years ago
15/3 + (6,5 + 4,2) - 0,6 <br><br> Please show your work, thank you :)
kifflom [539]

Answer:

15/3 + (6.5 + 4.2) - 0.6 = 15.1

Step-by-step explanation:

You can first reduce the fraction to 5 when you multiply by 3, then calculate what's in the parenthesis. So now you have 5 + 10.7 - 0.6, then just solve from left to right. Hope this helps

3 0
2 years ago
(-3 - 5i)(-3 + 5i) =
Black_prince [1.1K]
Hello,
You don't know (a-b)(a+b)=a²-b²?

(-3)²=9
(5i)²=-25
Answer 9 +25=34


6 0
3 years ago
Read 2 more answers
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