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Nadusha1986 [10]

3 years ago

11

What is the sum of all the integers between the square root of 19 and the square root of 77?

1 answer:

Artist 52 [7]3 years ago

4 0

Since we are only dealing with integers, we do not need to worry about decimals. Therefore, finding the exact values of sqrt(19) and sqrt(77) is not important. We can just estimate.

19 is between 16 and 25 (which are 4^2 and 5^2), so the square root of 18 is some number between 4 and 5.

77 is between 64 and 81 (which are 8^2 and 9^2), so the square root of 77 is some number between 8 and 9.

So the integers (whole numbers) that are between our two sqaure roots are 5, 6, 7, and 8.

Add them up and we have our answer.

5+6+7+8 = 26

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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

2 years ago

Convert to a fraction in simplest terms: .45

photoshop1234 [79]

Answer:

9/20

Step-by-step explanation:

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2 years ago

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– 6 x + 4 < 29 answer?

svlad2 [7]

Answer:

its 847>×+18 enjoy hope it work

4 0

3 years ago

178 rounded to the nearest hundred

Reika [66]

In order to round to the nearest 100 you look at the 10s place.

It's 7 which means we round up. So 178 rounded to the nearest 100 is 200.<span />

6 0

2 years ago

Read 2 more answers

Jake is going to the store to buy candles. Small candles cost $3.50 and

Tanzania [10]

Answer:

Let

S= #small candles

L= #Large candles

S+ L =>20

3.50S + 5.00L < 80

Step-by-step explanation:

3 0

2 years ago