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weqwewe [10]
2 years ago
8

Given y = a(x - h)^2 + k, p = A. a B. 4a C. 1/4a

Mathematics
1 answer:
Flauer [41]2 years ago
8 0

9514 1404 393

Answer:

  C.  1/(4a)

Step-by-step explanation:

We assume you're comparing the vertex form ...

  y = a(x -h)^2 +k

to the form used to write the equation in terms of the focal distance p.

  y = 1/(4p)(x -h)^2 +k

That comparison tells you ...

  a = 1/(4p)

  p = 1/(4a) . . . . . . multiply by p/a; matches choice C

__

<em>Additional comment</em>

When using plain text to write a rational expression, parentheses are needed around any denominator that has is more than a single constant or variable. The order of operations requires 1/4a to be interpreted as (1/4)a. The value of p is 1/(4a).

When rational expressions are typeset, the fraction bar serves as a grouping symbol identifying the entire denominator:

  p=\dfrac{1}{4a}

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A store finds that its sales revenue changes at a rate given by S'(t) = −30t2 + 420t dollars per day where t is the number of da
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Step-by-step explanation:

Give the rate of change of sales revenue of a store modeled by the equation S'(t)= -30t^{2} + 420t. The Total sales revenue function S(t) can be gotten by integrating the function given as shown;

\int\limits {S'(t)} \, dt = \int\limits ({-30t^{2}+420t }) \, dt \\S(t) = \frac{-30t^{3} }{3}+\frac{420t^{2} }{2}\\  S(t)= -10t^{3} +210t^{2} \\

a) The total sales for the first week after the campaign ends (t = 0 to t = 7) is expressed as shown;

Given\ S(t) = -10t^{3} + 210t^{2}

S(0) = -10(0)^{3} + 210(0)^{2}\\S(0) = 0\\S(7) = -10(7)^{3} + 210(7)^{2}\\S(7) = -3430+10,290\\S(7) = 6,860

Total sales = S(7) - S(0)

= 6,860 - 0

Total sales for the first week = $6,860

b) The total sales for the secondweek after the campaign ends (t = 7 to t = 14) is expressed as shown;

Total sales for the second week = S(14)-S(7)

Given S(7) = 6,860

To get S(14);

S(14) = -10(14)^{3} + 210(14)^{2}\\S(14) = -27,440+41,160\\S(14) = 13,720

The total sales for the second week after campaign ends = 13,720 - 6,860

= $6,860

8 0
3 years ago
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