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3 years ago

Which equation is equivalent to the given equation?x^2 – 10x = 14

Mathematics

1 answer:

kumpel [21]3 years ago

8 0

Answer:

(x - 5^2) = 39

Step-by-step explanation:

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An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co

Blizzard [7]

Answer:

$(a)$ $C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ $x=82 \text{planes}$

$(c)$ $p=\$30.91 M\;\; \text{per plane}$

$(d)$ maximum profit $=\$ 15.90M$

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

$m(x)=20x-5x^{\frac{3}{4}}+0.01x^2$

$(a)$ Find the cost, demand (or price), and revenue functions.

$C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ Find the production level that maximizes profit.

$f=R(x)-C(x)$

$\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)$

$\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx$

$x=320-7.7p$

$p=\frac{320-x}{7.7}$

$\frac{dp}{dx} = \frac{-1}{7.7}$

$\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0$

$\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0$

$\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0$

$\Rightarrow x=82 \text{planes}$

$(c)$ Find the associated selling price of the aircraft that maximizes profit.

$p=\frac{320-82}{7.7}$

$\Rightarrow p=\$30.91 M\;\; \text{per plane}$

$(d)$ Find the maximum profit.

Manufacturing cost of one plane is:

$m(1)=20-5+0.01$

$=\$15.01 M$

maximum profit $=\$(30.91-15.01)M$

$=\$15.90M$

3 0

3 years ago

★PLSSSSS HELPPPPPPPPP★

LiRa [457]

Answer:

i believe its C

Step-by-step explanation:

5 0

2 years ago

Tom, Mary and Bill are aged 10,12 and 15 years respectively. They share 259 euros in the same ratio as their ages. Find how much

tigry1 [53]

Answer:

70 , 84 , 105

Step-by-step explanation:

sum their ages , 10 + 12 + 15 = 37

divide the amount by this sum to find the value of one part of the ratio.

259 ÷ 37 = 7 ← value of 1 part of the ratio , then

10 parts = 10 × 7 = 70 euros ← Tom's share

12 parts = 12 × 7 = 84 euros ← Mary's share

15 parts = 15 × 7 = 105 euros ← Bill's share

7 0

2 years ago

Need help please and thank you

yulyashka [42]

Answer:

no thank you

Step-by-step explanation:

lol good day

6 0

2 years ago

Read 2 more answers

Morgan is arranging a bowling party for his friends. The party room at the bowling alley is $35. The bowling alley offers a part

vlada-n [284]

Your inequality is (x being number of people):
175≥35+10x+3x

First, combine like terms so your new inequality is:
175≥35+13x
Then subtract 35 from both sides which makes it:
140≥13x
then divide 140 by 13 making it:
<span>10.769≥x
</span>But because you can't have .769 of a person the actual answer is 10
then you have to subtract 1 because he isn't including himself and there is the answer!:
9≥x

7 0

3 years ago

Read 2 more answers

Which equation is equivalent to the given equation?x^2 – 10x = 14 ​

Which equation is equivalent to the given equation?x^2 – 10x = 14