(a) 4
(b) y = sqrt(9 - (9/16)x^2)
The best guess to the formula using knowledge of the general formula for an ellipse is:
x^2/16 + y^2/9 = 1
(a). An ellipse is reflectively symmetrical across both the major and minor axis. So if you can get the area of the ellipse in a quadrant, then multiplying that area by 4 would give the total area of the ellipse. So the factor of 4 is correct.
(b). The general equation for an ellipse is not suitable for a general function since it returns 2 y values for every x value. But if we restrict ourselves to just the positive value of a square root, that problem is easy to solve. So let's do so:
x^2/16 + y^2/9 = 1
x^2/16 + y^2/9 - 1 = 0
x^2/16 - 1 = - y^2/9
-(9/16)x^2 + 9 = y^2
9 - (9/16)x^2 = y^2
sqrt(9 - (9/16)x^2) = y
y = sqrt(9 - (9/16)x^2)
Independent variable is 5 means x = 5
solve for f(x) when x = 5
f(5) = -2(5) +1
f(5) = -10 + 1
f(5) = -9
Solution (5,-9)
Answer
B. (5,-9)
Answer:
D
Step-by-step explanation:
According to remainder theorem, you can know the remainder of these polynomials if you plug in x = -6 into them.
<em>So we will plug in -6 into x of all the polynomials ( A through D) and see which one equals -3.</em>
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<em>For A:</em>
For B:
For C:
For D:
The only function that has a remainder of -3 when divided by x + 6 is the fourth one, answer choice D.
First, a bit of housekeeping:
<span>The meaning of four consecutive even numbers is 15. Wouldn't that be "mean," not meaning? Very different concepts!
The greatest of these numbers is _______ a^1
"a^1" means "a to the first power. There are no powers in this problem statement. Perhaps you meant just "a" or "a_1" or a(1).
The least of these numbers is ______a^2.
No powers in this problem statement. Perhaps you meant a_2 or a(2)
In this problem you have four numbers. All are even, and there's a spacing of 2 units between each pair of numbers (consecutive even).
The mean, or arithmetic average, of these numbers is (a+b+c+d) / 4, where a, b, c and d represent the four consecutive even numbers. Here this mean is 15. The mean is most likely positioned between b anc c.
So here's what we have: a+b+c+d
------------- = 15
4
This is equivalent to a+b+c+d = 60.
Since the numbers a, b, c and d are consecutive even integers, let's try this:
a + (a+2) + (a+4) + (a+6) = 60. Then 4a+2+4+6=60, or 4a = 48, or a=12.
Then a=12, b=14, c=16 and d=18. Note how (12+14+16+18) / 4 = 15, which is the given mean.
We could also type, "a(1)=12, a(2)=14, a(3) = 16, and a(4) = 18.
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