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4 years ago

8

Determine the prime factorization of 64.

1 answer:

Morgarella [4.7K]4 years ago

8 0

You can draw a factor tree, until all leaves are primes:

64
2 * 32
2 * 2 * 16
2 * 2 * 2 * 8
2 * 2 * 2 * 2 * 4
2 * 2 * 2 * 2 * 2 * 2

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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

Could someone help please

Nataly_w [17]

Answer:

110 fence posts

Step-by-step explanation:

102÷6=17

multiply by 2 = 34

330÷6=55

multiply by 2=110

add together= 144 fence posts

3 0

4 years ago

joe boght 15 tolets. 1 was pure gold 2 were pure silver and the rest were wooden. how many wooden toilets were there?

borishaifa [10]

12.
It is easy all you have to do is 15-3 because 1+2=3

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3 years ago

Someone arranges three 24-karat gold squares (ofequalthickness)as shown below, and offers you a choice. You can

Katarina [22]

Answer:

idk

Step-by-step explanation:

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3 years ago

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iren2701 [21]

Answer:

y=4/3x-4

Step-by-step explanation:

put a point at 3 on x axis and -4 on y axis. then draw a line connecting then and you can see it goes up 4 and over 3 and it his the y intercept at -4

4 0

4 years ago