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Artist 52 [7]
3 years ago
5

A function f defined by f(x) = x² + px + q is such that f(3) = 6 and f¹(3) = 0. Find the value of q.

Mathematics
1 answer:
CaHeK987 [17]3 years ago
5 0

Answer:

q = 15

Step-by-step explanation:

Given

f(x) = x² + px + q , then

f(3) = 3² + 3p + q = 6 , that is

9 + 3p + q = 6 ( subtract 9 from both sides )

3p + q = - 3 → (1)

---------------------------------------

f'(x) = 2x + p , then

f'(3) = 2(3) + p = 0, that is

6 + p = 0 ( subtract 6 from both sides )

p = - 6

Substitute p = - 6 into (1)

3(- 6) + q = - 3

- 18 + q = - 3 ( add 18 to both sides )

q = 15

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the perimeter of a rectangular painting is 356 centimeters. if the length of the painting is 96 centimeters, what is its width.
sladkih [1.3K]
P = 2(l + w)
p = 356
l = 96

356 = 2(96 + w)
356 = 192 + 2w
356 - 192 = 2w
164 = 2w
164/2 = w
82 = w

check....
p = 2(l + w)
356 = 2(96 + 82)
356 = 2(178)
356 = 356 (correct)

so the width (w) = 82 cm

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Which expression is equivalent to the square root of 200?
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Answer:

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Step-by-step explanation:

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The following events took place at a manufacturing company for the current year: (1) Purchased $115,000 in direct materials. (2)
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The question was not written properly. Here is the appropriate form of question:

The following events took place at a manufacturing company for the current year:

(1) Purchased $115,000 in direct materials.

(2) Incurred labor costs as follows: (a) direct, $76,000 and (b) indirect, $33,600.

(3) Other manufacturing overhead was $127,000, excluding indirect labor.

(4) Transferred 75% of the materials to the manufacturing assembly line.

(5) Completed 60% of the Work-in-Process during the year.

(6) Sold 80% of the completed goods.

(7) There were no beginning inventories.

1- What is the company's Cost of Goods Sold?

Options:

a. $193,710

b. $154,968

c. $322,850

d. $258,280

Answer:

1- b. $154,968

Step-by-step explanation:

1- Cost of goods sold (COGS) is the is the expense of securing or assembling the items that an organization sells during a period, so the main costs remembered for the measure are those that are directly attached to the creation of the items, including the expense of work (labor cost), materials, and assembling overhead.

0.6*[$0 + 0.75*($115,000) + $76,000 + ($127,000 + $33,600)] <em>(because completed 60% of the Work-in-Process during the year)</em>

= $193,710

80% of $193,710 <em>(because sold 80% of the completed goods)</em>

0.8*$193,710

= $154,968

5 0
3 years ago
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