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Black_prince [1.1K]
3 years ago
8

Find the exact length of the curve. y2 = 4(x + 1)3, 0 ≤ x ≤ 1, y > 0

Mathematics
1 answer:
mylen [45]3 years ago
6 0
We can find this using the formula: L= ∫√1+ (y')² dx

First we want to solve for y by taking the 1/2 power of both sides:

y=(4(x+1)³)^1/2
y=2(x+1)^3/2

Now, we can take the derivative using the chain rule:

y'=3(x+1)^1/2

We can then square this, so it can be plugged directly into the formula:

(y')²=(3√x+1)²
<span>(y')²=9(x+1)
</span>(y')²=9x+9

We can then plug this into the formula:

L= ∫√1+9x+9 dx *I can't type in the bounds directly on the integral, but the upper bound is 1 and the lower bound is 0
L= ∫(9x+10)^1/2 dx *use u-substitution to solve
L= ∫u^1/2 (du/9)
L= 1/9 ∫u^1/2 du
L= 1/9[(2/3)u^3/2]
L= 2/27 [(9x+10)^3/2] *upper bound is 1 and lower bound is 0
L= 2/27 [19^3/2-10^3/2]
L= 2/27 [√6859 - √1000]
L=3.792318765

The length of the curve is 2/27 [√6859 - √1000] or <span>3.792318765 </span>units.
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8.6 x10^-9 in standard form
katen-ka-za [31]

-9 in power means that the value is in fractional and the 10 base is multipied 9 times and put it on denominator.

8.6 = 86 x 10^-1

Let's multiply :

86 x 10^-1 x 10^-9

= 86 x 10^-10

= 86/10000000000

=0,0000000086

Note : if you don't know about how 10^-1 x 10^-9 returns 10^-10, it's because of exponential rules. If the base are same wuth each other, then just do the addition operation in the exponent like this :

10^(-1+(-9))

= 10^(-1-9)

=10^-10

Hope it helps :)

4 0
3 years ago
The formula for converting degrees Celsius (C) to degrees Fahrenheit (F) is: F= 9C/5 + 32. Rearrange the formula so you could ch
pentagon [3]

Answer:

45F+800=C

Step-by-step explanation:

F+32=9C/5

5F+160=9C

45F+800=C

4 0
3 years ago
Which of the following is an arithmetic sequence with common difference 2
Marta_Voda [28]

Answer:

D

Step-by-step explanation:

4 0
3 years ago
The Bayer family just left the local pet store with Rover, their new family dog. The pet store owner told the Bayer family that
anyanavicka [17]

Answer:

A. Complete table below

B. Graph is attached below

C. y = 7x - 10

D. 60 pounds.

Step-by-step explanation:

We are given that, Bayer would grow at an average rate of 7 pounds per month.

So, in order to complete the table, <em>we will add 7 to the weights column</em>.

Part A: Thus, we get the following table.

Age, in months           2,      3,      4,       5,       6,        7,        8

Weight, in pounds      4,      11,      18,      25,    32,      39,     46.

Part B: Since, we have the ordered pairs (x,y) given by,

(2,4), (3,11), (4,18), (5,25), (6,32), (7,39) and (8,46).

The graph is shown below.

Part C: Taking any two pairs say (2,4) and (3,11).

We get the slope is, \frac{11-4}{3-2} i.e. slope is 7.

Then, y = mx + b gives, 4 = 7×2 + b i.e. b = 4-14 i.e. b = -10.

Hence, the linear model is given by 'y=7x-10', where x is the age(in months) and y is the weight(in pounds).

Part D: Now, we want to find the weight when Bayer is one year old.

Since, we have that, Bayer is already two months old.

So, we need to find weight when Bayer is 10 months old.

i.e. y=7x-10 ⇒ y = 7×10-10 ⇒ y = 70-10 ⇒ y=60

Hence, Bayer will be 60 pounds when he is one year orld.

4 0
3 years ago
Move (not take away) ONE stick to make the equation true
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Move the middle line of the +
3 0
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