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fgiga [73]
4 years ago
6

Y = 7ex, y = 7e−x, x = 1; about the y-axis

Mathematics
1 answer:
atroni [7]4 years ago
3 0
A "typical" cylindrical shell of wall thickness dx at x=x will have the length (in the y-direction) L = (e^x – e^-x). 

<span>Rotating this shell about the y-axis generates a volume dV = 2.π.x.L = 2.π.x.(e^x – e^-x).dx </span>

<span>Total volume V of all such cylindrical shells in the given range = 2.π.∫x.(e^x – e^-x).dx </span>

<span>= 4.π.[x.cosh(x) – sinh(x)] from 0 to 1. Now insert the limits and we obtain: </span>

<span>= 4.π.[1.543 – 1.175] = 4.624 cubic units</span>
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A certain bacteria is growing at a rate of 4 percent each day. If the culture of bacteria has 5,000 bacteria today, how many bac
Virty [35]
This is the concept of exponential growth, To get the number of bacteria after 10 days we use the formula:
f(t)=ae^(kt)
where;
a=initial number=5000
k=constant of proportionality= 0.04
t=time=10 days
f(t)=future number
thus the number of bacteria in 10 days will be:
f(t)=5000e^(0.04*10)
f(t)=7,459.12
The answer is 7,459.12
8 0
3 years ago
What is the selling price of a $12,543 boat if a $758 discount is given?
Lelu [443]
Given:
Selling Price: 12,543
Discount: 758

We simply deduct the discount from the original price to get the discounted selling price.

12,543 - 758 = 11,785

The new selling price of the boat is $11,785.

Discount of $758 is 6% of the Original selling price.
758 / 12,543 = 0.06
0.06 x 100% = 6%

8 0
3 years ago
Do I need to put parentheses in this? Why it why not?
Oksana_A [137]

Answer:

Parentheses can change the result of the answer. If you want to add 4 and 0.95 first, then multiply that number by 3, then you need parentheses.

Step-by-step explanation:

When you are given the question 3 X 4 + 0.95, it has to types of operations. <u>People solve using the order PEDMAS</u>:

Parentheses,

Exponents,

Division and Multiplication,

Addition and Subtraction.

Since there are <u>no parentheses</u> or exponents, the solver will do multiplication first, then addition.

3 X 4 + 0.95     Multiply first

= 12 + 0.95       Now add

= 12.95         Answer without parentheses

If you add <u>parentheses around 4 + 0.95</u>, the answer would change. According to PEDMAS, the parentheses must be solved before anything else.

3 X (4 + 0.95)       Add inside parentheses

= 3 X (4.95)       Now multiply

= 14.85           Answer with parentheses

If you added <u>parentheses around 3 X 4</u>, the answer would not change, because you still multiply first.

(3 X 4) + 0.95      Solving parentheses first

= 12 + 0.95       Add

= 12.95          Answer same as original

3 0
3 years ago
The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base
boyakko [2]

The circumference equal to 25 units

<h3>What is perimeter of square?</h3>

The perimeter of square is 4 times the side.

P= 4* side

The perimeter of the square,

4x = P

Now P is =  32 units then,

32 units = 4(x)

x = 8 inches

So,  the diameter of the cylinder formed by the rotation of 8 inches  

Now, the circumference of the base is

C = 2πr = πD

If r =8  inches

                           

C = π(8 units) = 8π units

C = 8(3.14) = 25.12 units

Hence, the circumference equal to 25 units

Learn more about perimeter of square here:

brainly.com/question/11495285

#SPJ1

6 0
2 years ago
Two coins
Romashka [77]

Answer:  There is a 50% chance one will land on heads.

Step-by-step explanation:

8 0
3 years ago
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