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3 years ago

Derive the equation of the parabola with a focus at (_5, 5) and a directrix of y = -1.

2 answers:

5 0

The answer is f(x) = one twelfth (x + 5)2 + 2, that is found when <span>focus and directrix of a parabola's formula is applied. </span>

mars1129 [50]3 years ago

4 0

Answer: Option D is correct.

Step-by-step explanation:

Since we have given that

focus = (-5,5)

and a directrix y= -1

Since, equation of parabola in this case will be

$(x-h)^2=4.a(y-k)$

Now, here

$y=k-a=-1\\\\\text { focus =(h,k+a)}\\\\\text{So,} k+a=5\\\\\text{ by solving these two equation , we get }\\\\a=3\text{ and } k=2$

So equation will be

$(x+5)^2=4\times 3(y-2)\\\\(x+5)^2=12(y-3)\\\\y=\frac{1}{12}(x+5)^2+2$

So, option D is correct .

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A nightclub has approximated the demand for their Thursday night drink special by p^2+200q^2=177, where p is the price (in dol

Irina18 [472]

Answer:

Step-by-step explanation:

Given the approximate demand function of night drink expressed as;

p^2+200q^2=177,

p is the price (in dollars) and;

q is the quantity demanded (in thousands).

Given

p = $7

q = 800

Required

dq/dp

Differentiating the function implicitly with respect to p shown;

2p + 400d dq/dp = 0

400q dq/dp = -2p

200qdq/dp = -p

dq/dp = -p/100q

substitute p and q into the resulting equation;

dq/dp = -7/100(800)

dq/dp = -7/80000

dq/dp = -0.0000875

This means that the rate of change of quantity demanded with respect to the price is -0.0000875

8 0

3 years ago

How to find volume of a drawing of a piece of cake?

Ipatiy [6.2K]

Just find the volume of a triangular prism.

volume=1/2*length*width*height.

8 0

3 years ago

[10] In the following given system, determine a matrix A and vector b so that the system can be represented as a matrix equation

irina1246 [14]

Answer:

$y=-\frac{158}{579}$

Step-by-step explanation:

To find the matrix A, took all the numeric coefficient of the variables, the first column is for x, the second column for y, the third column for z and the last column for w:

$A=\left[\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right]$

And the vector B is formed with the solution of each equation of the system: $b=\left[\begin{array}{c}3\\-3\\6\\1\end{array}\right]$

To apply the Cramer's rule, take the matrix A and replace the column assigned to the variable that you need to solve with the vector b, in this case, that would be the second column. This new matrix is going to be called $A_{2}$ .

$A_{2}=\left[\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right]$

The value of y using Cramer's rule is:

$y=\frac{det(A_{2}) }{det(A)}$

Find the value of the determinant of each matrix, and divide:

$y==\frac{\left|\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right|}{\left|\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right|} =\frac{158}{-579}$

$y=-\frac{158}{579}$

7 0

3 years ago

4x + 5x + 12 = 6(x-2)<br> Math

Rashid [163]

Hi there! :)

$\large\boxed{x = -8}$

4x + 5x + 12 = 6(x - 2)

Combine like terms and distribute the coefficient outside of the parenthesis:

9x + 12 = 6(x) + 6(-2)

9x + 12 = 6x - 12

Subtract 6x from both sides:

9x - 6x + 12 = 6x - 6x - 12

3x + 12 = -12

Subtract 12 from both sides:

3x + 12 - 12 = -12 - 12

3x = -24

Divide both sides by 3:

3x/3 = -24/3

x = -8.

4 0

3 years ago

jake makes 9 loaves of olive bread. he uses 30 grams of olives in each loaf.he started with 1 kilogram of olives.how many grams

8090 [49]

Considering that 1 kilogram is equal to 1000 grams and he made 9 loaves of bread using 30 grams each time, that equates to 270 grams of olives. 1000 - 270 = 730. Your answer is 730 grams of olives remain. Hope this helped.

6 0

3 years ago