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timurjin [86]
3 years ago
9

Brainliest answer guaranteed URGENT

Mathematics
1 answer:
UNO [17]3 years ago
7 0

Answer:

y=-6.6 and y=10.6

Step-by-step explanation:

The given ellipse has equation:

\frac{(y-2)^2}{64}+\frac{x^2}{9}=1.

The center of this ellipse is (h,k)=(0,2)

We use the equation: a^2-b^2=c^2 to determine the foci.

\implies 64-9=c^2

\implies 55=c^2

\implies c=\pm \sqrt{55}

The directrices are given by y=k\pm\frac{a^2}{c}

y=2\pm\frac{64}{\sqrt{55}}

y=2\pm8.6

y=2-8.6 and y=2+8.6

The equation of the directrices are:

y=-6.6 and y=10.6

The correct answer is D

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3 0
2 years ago
A lidless box is to be made using 2m^2 of cardboard find the dimensions of the box that requires the least amount of cardboard
Jlenok [28]
1.8, Problem 37: A lidless cardboard box is to be made with a volume of 4 m3 . Find the dimensions of the box that requires the least amount of cardboard. Solution: If the dimensions of our box are x, y, and z, then we’re seeking to minimize A(x, y, z) = xy + 2xz + 2yz subject to the constraint that xyz = 4. Our first step is to make the first function a function of just 2 variables. From xyz = 4, we see z = 4/xy, and if we substitute this into A(x, y, z), we obtain a new function A(x, y) = xy + 8/y + 8/x. Since we’re optimizing something, we want to calculate the critical points, which occur when Ax = Ay = 0 or either Ax or Ay is undefined. If Ax or Ay is undefined, then x = 0 or y = 0, which means xyz = 4 can’t hold. So, we calculate when Ax = 0 = Ay. Ax = y − 8/x2 = 0 and Ay = x − 8/y2 = 0. From these, we obtain x 2y = 8 = xy2 . This forces x = y = 2, which forces z = 1. Calculating second derivatives and applying the second derivative test, we see that (x, y) = (2, 2) is a local minimum for A(x, y). To show it’s an absolute minimum, first notice that A(x, y) is defined for all choices of x and y that are positive (if x and y are arbitrarily large, you can still make z REALLY small so that xyz = 4 still). Therefore, the domain is NOT a closed and bounded region (it’s neither closed nor bounded), so you can’t apply the Extreme Value Theorem. However, you can salvage something: observe what happens to A(x, y) as x → 0, as y → 0, as x → ∞, and y → ∞. In each of these cases, at least one of the variables must go to ∞, meaning that A(x, y) goes to ∞. Thus, moving away from (2, 2) forces A(x, y) to increase, and so (2, 2) is an absolute minimum for A(x, y).
5 0
3 years ago
A jar holds 128 fluid ounces of juice. The label says the jar has 16 servings. How many fluid ounces are needed for 80 servings?
Bumek [7]
There are 16 servings for each 128 fluid ounces of juice. 

Divide 80 servings by 16 servings, and 5 should be the quotient. Therefore, there are 5 jars of juice. Multiply 128 by 5 since 128 fluid ounces are in one jar. The answer should be 640 fluid ounces. 
8 0
3 years ago
Read 2 more answers
Divide 3500 in the ratio 2: 2 : 3
BlackZzzverrR [31]

Answer:

1000 : 1000 : 1500

Step-by-step explanation:

2 + 2 + 3 = 7

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2 × 500 = 1000

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3 × 500 = 1500

1000 : 1000 : 1500

5 0
2 years ago
Read 2 more answers
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