The answer is 5 problems a student.
Step-by-step explanation:
180 = 55 + 41 + y (Angles in a triangle)
y = 180-(55+41)
y = 84
y+ z = 180 (Angles on a line)
z = 180 - y
z = 180 - 84
z = 96
The lines are parallel.
The angle opposite x is 109 because the are corresponding.
x is 109 (vertically opposite angles)
The remainder theorem says that dividing a polynomial <em>f(x)</em> by a 1st-degree polynomial <em>g(x)</em> = <em>x</em> - <em>c</em> leaves a remainder of exactly <em>f(c)</em>.
(a) With <em>f(x)</em> = <em>px</em> ³ + 4<em>x</em> - 10 and <em>d(x)</em> = <em>x</em> + 3, we have a remainder of 5, so
<em>f</em> (-3) = <em>p</em> (-3)³ + 4(-3) - 10 = 5
Solve for <em>p</em> :
-27<em>p</em> - 12 - 10 = 5
-27<em>p</em> = 27
<em>p</em> = -1
(b) With <em>f(x)</em> = <em>x</em> + 3<em>x</em> ² - <em>px</em> + 4 and <em>d(x)</em> = <em>x</em> - 2, we have remainder 8, so
<em>f</em> (2) = 2 + 3(2)² - 2<em>p</em> + 4 = 8
-2<em>p</em> = -10
<em>p</em> = 5
(you should make sure that <em>f(x)</em> was written correctly, it's a bit odd that there are two <em>x</em> terms)
(c) <em>f(x)</em> = 2<em>x</em> ³ - 4<em>x</em> ² + 6<em>x</em> - <em>p</em>, <em>d(x)</em> = <em>x</em> - 2, <em>R</em> = <em>f</em> (2) = 18
<em>f</em> (2) = 2(2)³ - 4(2)² + 6(2) - <em>p</em> = 18
12 - <em>p</em> = 18
<em>p</em> = -6
The others are done in the same fashion. You would find
(d) <em>p</em> = 14
(e) <em>p</em> = -4359
(f) <em>p</em> = 10
(g) <em>p</em> = -13/2 … … assuming you meant <em>f(x)</em> = <em>x</em> ⁴ + <em>x</em> ³ + <em>px</em> ² + <em>x</em> + 20
Answer:
The fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500
Step-by-step explanation:
Let
Cost per refrigerator (marginal cost) = r
Fixed costs per day for the factory = f
Total cost = variable cost + fixed cost
Monday
25,000 = 30r + f
Tuesday
30,000 = 40r + f
Using Monday,
f = 25000 -30r
Substitute f = 25000 - 30r into Tuesday
30,000 = 40r + f
30,000 = 40r + (25,000 -30r)
30,000 = 40r + 25,000 - 30r
Collect like terms
30,000 - 25,000 = 40r - 30r
5,000 = 10r
Divide both sides by 10
r = 5,000 / 10
= 500
r = $500
Substitute r= 500 into Monday equation
f = 25,000 -30r
= 25,000 - 30(500)
= 25,000 - 15,000
= 10,000
f = $10,000
Therefore, the fixed costs per day for the factory is $10,000 and marginal cost of one refrigerator for $500
