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Gennadij [26K]
3 years ago
15

Find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)​

Mathematics
1 answer:
elena55 [62]3 years ago
3 0

Answer:

Hello

Step-by-step explanation:

The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1

and the disk ? (inside of a circle) of center (0,0) and radius 2

dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2}  \leq \ y  \leq \sqrt{4-x^2}\  ) \ \}\\

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Factor 60x−84 using the gcf
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Find the sum of all positive integers less than 200 that are divisible by 7.
Troyanec [42]

Step-by-step explanation:

the positive integer numbers that are divisible by 7 are an arithmetic sequence by always adding 7 :

a1 = 7

a2 = a1 + 7 = 7+7 = 14

a3 = a2 + 7 = a1 + 7 + 7 = 7 + 2×7 = 21

...

an = a1 + (n-1)×7 = 7 + (n-1)×7 = n×7

the sum of an arithmetic sequence is

n/2 × (2a1 + (n - 1)×d)

with a1 being the first term (in our case 7).

d being the common difference from term to term (in our case 7).

how many terms (what is n) do we need to add ?

we need to find n, where the sequence reaches 200.

200 = n×7

n = 200/7 = 28.57142857...

so, with n = 29 we would get a number higher than 200.

so, n=28 gives us the last number divisible by 7 that is smaller than 200 (28×7 = 196).

the sum of all positive integers below 200 that are divisible by 7 is then

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6 0
2 years ago
4 - 3x > 13 (Solve for x)
Fudgin [204]

Answer:

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4 - 3x > 13

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Now move the -3 over, divide on both sides.

When you multiply or divide by a negative, you have to reverse the sign.

-3x/-3 < 9/-3

X < -3

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3 years ago
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