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posledela
2 years ago
10

Both circles have the same center. What is the area of the shaded region?

Mathematics
1 answer:
Nookie1986 [14]2 years ago
7 0

Answer:

21

Step-by-step explanation:

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What is the solution to the following system?<br> X+2y+z=9<br> X-y+3z=13<br> 2z=10
Vinvika [58]

Answer:  x = 0; y = 2; z = 5

Step-by-step explanation:

x+2y+z=9

x-y+3z=13

2z=10

==

Start with the last equation:  2z = 10, therefore z = 5 [easy]

Let's rewrite the second equation with 1) z=5, and 2) rearrange to find x:

x-y+3z = 13

x - y +3*5 = 13

x = y-2

Now use the values for x [(y-2)] and y [5] in the first equation:

X+2y+z=9

(y-2) +2y + 5 = 9

3y +3 = 9

3y = 6

y = 2

Now that we have y [2] and z [5], let's use the first equation to solve for x:

x+2y+z=9

x + 4 + 5 = 9

x + 9 = 9

x = 0

====

Try the three values (x=0, y=2, and z=5) in any of the formulas.  The result should/will equal the number shown.

5 0
3 years ago
Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).
Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>
  • The critical points of a function are the values of x for which:

f^{\prime}(x) = 0

In this problem, the function is:

f(x) = x^3 + ax^2 + b

Hence, the derivative is:

f^{\prime}(x) = 3x^2 + 2ax

Then:

f^{\prime}(x) = 0

3x^2 + 2ax = 0

x(3x + 2a) = 0

x = 0

3x + 2a = 0

3x = -2a

x = -\frac{2a}{3}

Since the critical point is at x = 2, we have that:

-\frac{2a}{3} = 2

-2a = 6

2a = -6

a = -3

Then:

f(x) = x^3 - 3x^2 + b

Critical point at (2,3) means that when x = 2, y = 3, then:

3 = 2^3 - 3(2)^2 + b

8 - 12 + b = 3

b = 7

You can learn more about the critical point concept at brainly.com/question/2256078

4 0
1 year ago
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