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Vladimir79 [104]
3 years ago
13

If the mass of a proton is 2.34 × 10–14 grams, what is the mass of 1,000 protons?

Mathematics
1 answer:
Alex17521 [72]3 years ago
8 0
Masse of 1 proton: = 2.34 x 10⁻¹⁴

masse of 1000 protons = 2.34 x 10⁻¹⁴ x 1000 or 2.34 x 10 ⁻¹⁴ x 10³ =2.34 x 10⁻¹¹
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Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive
Ivan

Answer:

(a) The average cost function is \bar{C}(x)=95+\frac{230000}{x}

(b) The marginal average cost function is \bar{C}'(x)=-\frac{230000}{x^2}

(c) The average cost approaches to 95 if the production level is very high.

Step-by-step explanation:

(a) Suppose C(x) is a total cost function. Then the average cost function, denoted by \bar{C}(x), is

\frac{C(x)}{x}

We know that the total cost for making x units of their Senior Executive model is given by the function

C(x) = 95x + 230000

The average cost function is

\bar{C}(x)=\frac{C(x)}{x}=\frac{95x + 230000}{x} \\\bar{C}(x)=95+\frac{230000}{x}

(b) The derivative \bar{C}'(x) of the average cost function, called the marginal average cost function, measures the rate of change of the average cost function with respect to the number of units produced.

The marginal average cost function is

\bar{C}'(x)=\frac{d}{dx}\left(95+\frac{230000}{x}\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g\\\\\frac{d}{dx}\left(95\right)+\frac{d}{dx}\left(\frac{230000}{x}\right)\\\\\bar{C}'(x)=-\frac{230000}{x^2}

(c) The average cost approaches to 95 if the production level is very high.

\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})\\\\\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)\\\\=\lim _{x\to \infty \:}\left(95\right)+\lim _{x\to \infty \:}\left(\frac{230000}{x}\right)\\\\\lim _{x\to a}c=c\\\lim _{x\to \infty \:}\left(95\right)=95\\\\\mathrm{Apply\:Infinity\:Property:}\:\lim _{x\to \infty }\left(\frac{c}{x^a}\right)=0\\\lim_{x \to \infty} (\frac{230000}{x} )=0

\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})= 95

6 0
3 years ago
Find the surface area of the composite figure​
Gnoma [55]

Answer:

=280 in^2

Step-by-step explanation:

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

Let's find the surface area of the pink rectangular prism first.

2*10=20+20=40

4*10=40+40=80

4*2=8+8=16

40+80+16=136

The surface area for the pink rectangular prism is 136 in^2.

-------------------->>>>>

Now, let's find the surface area of the green rectangular prism.

4*7=28+28=56

4*7=28+28=56

4*4=16+16=32

56+56+32=144

The surface area for the green rectangular prism is 144 in^2.

-------------------->>>>>

Now let's add the surface area of both rectangular prisms to find the surface area of the composite figure.

136+144=

=280 in^2

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

Hope this is helpful.

6 0
3 years ago
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I Believe that it's -120
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3 years ago
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Mark is baking cookies he needs 2/3 cup of flour for each batch of cookies if each batch represents 1/4 of the total numbers of
Lera25 [3.4K]

Answer: 2 2/3 cups of flour

Step-by-step explanation: If one batch represents 1/4 of the total number of cookies he needs, then it can be deduced that he needs four total batches. If it requires 2/3 cups of flour for each batch and he needs 4 batches, you would multiply 2/3 by 4 to get the answer.

2/3 × 4 = 2 2/3

3 0
3 years ago
Simplify -6 x (-5) x 3 x (-2) x 4
aksik [14]

Answer:

-720

Step-by-step explanation:

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3 years ago
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