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3 years ago

Write an equation for a function that has vertical asymptotes at x=3 & x=-10

Mathematics

1 answer:

stepan [7]3 years ago

7 0

Answer:

$\frac{5}{ {x}^{2} + 7x - 30}$

Step-by-step explanation:

We can write a rational function.

We need to make sure our denominator both have zeroes at 3 and 10.

Set an equation equal to zero to find the function

$0 - x = 3$

$0 - x = - 10$

$0 - ( - 3) = = 3$

$0 - 10 = 10$

So we would represent that's as

$x - 3$

and

$x + 10$

Multiply the two binomial together.

$(x - 3)(x + 10) = {x}^{2} + 7x - 30$

Let our numbetator be any interger.

Use any equation as long as the quadratic is the denominator and the interger is the numerator.

$\frac{5}{ {x}^{2} + 7x - 30 }$

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3 years ago

Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least bui

Vesnalui [34]

<h3>The dimensions of the given rectangular box are:</h3><h3>L = 15.874 cm , B = 15.874 cm , H = 7.8937 cm</h3>

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box

= Area of the base + 4 x ( Area of the adjacent faces)

= S x S + 4 ( S x H) = S² + 4 SH ..... (1)

Also, Area of the box = S x S x H = S²H

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$\implies H = \frac{2000}{S^2}$

Substituting the value of H in (1), we get:

$A = S^2 + 4 SH = S^2 + 4 S(\frac{2000}{S^2}) = S^2 + (\frac{8000}{S})\\\implies A = S^2 + (\frac{8000}{S})$

Now, to minimize the area put :

$(\frac{dA}{dS} ) = 0 \implies 2S - \frac{8000}{S^2} = 0\\\implies S^3 = 4000\\\implies S = 15.874 \approx 16 cm$

Putting the value of S = 15.874 cm in the value of H , we get:

$\implies H = \frac{2000}{S^2} = \frac{2000}{(15.874)^2} = 7.8937 cm$

Hence, the dimensions of the given rectangular box are:

L = 15.874 cm

B = 15.874 cm

H = 7.8937 cm

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