Find the vertices and foci of the hyperbola with equation x squared over nine minus y squared over sixteen = 1.

1 answer:

7 0

<em>Standard equation of hyperbola is </em> $\frac{x^{2} }{ a^{2} } - \frac{ y^{2} }{ b^{2} } = 1$ .

<em>Comparing given info with standard equation, we get
</em>a(vertices)= +3 and -3
foci = $\sqrt{ a^{2} + b^{2} } = \sqrt{9+16} = \sqrt{25} =5$ .

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You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.

RUDIKE [14]

Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

$xy = 288 \\ \\ \\ \\ \Rightarrow y= \frac{288}{x}$

Substituting for y into the equation for the length of fencing needed, we have

$P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}$

For the amount of fencing to be minimum, then

$\frac{dP}{dx} =0 \\ \\ \Rightarrow1- \frac{576}{x^2} =0 \\ \\ \Rightarrow \frac{576}{x^2} =1 \\ \\ \Rightarrow x^2=576 \\ \\ \Rightarrow x=\sqrt{576}=24$

Now, recall that

$y= \frac{288}{x} = \frac{288}{24} =12$

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.

8 0

3 years ago

Find the volume of a right circular cone that has a height of 7.4 in and a base with a diameter of 5.4 in. Round your answer to

JulijaS [17]

Answer:

approximately 56.51 cubic inches

Step-by-step explanation:

volume of a cone = 1 / 3 × pi × radius^2 × height

= 1/3 × 22/7 × 7.29 × 7.4

= 56.5148 cubic inches

8 0

2 years ago