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Serhud [2]
2 years ago
7

State the domain and range of the following relation x^2+y^2=16

Mathematics
1 answer:
Vlada [557]2 years ago
8 0

The domain and range is  [-4, 4] and [0, 4]

<h3 /><h3>What is Domain and range?</h3>

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

x² + y² = 16

y = √16 - x²

For domain under root should not be negative quantity,

16 - x²≥0

16≥x²

So, x≤4 or x≥4

Thus, the domain is  [-4, 4]

Range:

y is maximum at x=0, y=4

y is minimum at x=4, y=0

Thus, range = [0, 4]

Learn more about domain and range here:

brainly.com/question/12751831

#SPJ1

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why write a quadratic function whose graph has the given characteristics vertex :(2,3) point on graph (0,-1)
GaryK [48]
<h3>Answer:</h3>

f(x) = -(x -2)² +3

<h3>Step-by-step explanation:</h3>

We can fill in the vertex (h, k) values immediately in the vertex form ...

... f(x) = a(x -h)² +k

To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:

... -1 = a(0 -2)² +3

... -4 = 4a . . . . . . . . . subtract 3, simplify

... -1 = a . . . . . . . . . . . divide by 4

Now, we know the function is ...

... f(x) = -(x -2)² +3

5 0
3 years ago
Find four consecutive integers such that the sum of the first and third is eight les than twice the sum of the second and fourth
lyudmila [28]
X, x+1, x+2, x+3 are 4 consecutive integers

2(x + x+2) = 5(x+3) - 26
2(2x+2) = 5(x+3) - 26
4x + 4 = 5x + 15 - 26
4x + 4 = 5x - 11
15 = x
15, 16, 17, 18

x, x+2, x+4 consecutive even integers
2(x+4)+11 = x + 9
2x + 8 + 11 = x + 9
2x + 19 = x + 9
x = -10
-10, -8, -6
5 0
3 years ago
Evaluate integral_S integral (x - 2y + z) dS. S: z = 16, x^2 + y^2 le 1
vovikov84 [41]

S is the disk of radius 1 parallel to the x,y-plane and lying in the plane z=16. Parameterize this surface by

\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+16\,\vec k

with 0\le u\le1 and 0\le v\le2\pi. Take the normal vector to S to be

\vec r_u\times\vec r_v=u\,\vec k

(the orientation doesn't matter because this is a scalar surface integral)

Then

\displaystyle\iint_S(x-2y+z)\,\mathrm dS=\iint_S(u\cos v-2u\sin v+16)\|u\,\vec k\|\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^1(u^2(\cos v-2\sin v)+16u)\,\mathrm du\,\mathrm dv=\boxed{16\pi}

5 0
3 years ago
What's substitution for y=4x-1, 2x+y=5
Dennis_Churaev [7]

Step-by-step explanation:

y = 4x-1

2x+y = 5

2x+(4x-1) = 5

6x - 1 = 5

6x = 6

x = 1

4 0
3 years ago
Read 2 more answers
Rectangle ABCD has vertices at coordinates (0,8), (4,12), (12,4), and D, respectively. Which of the following correctly identifi
antoniya [11.8K]

Answer:

Step-by-step explanation:

the last coordinate would be8,0 because i did it on graph paper and checked it a bunch of time even with my math teacher

3 0
3 years ago
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