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Wittaler [7]
2 years ago
8

Could someone show me a step by step process on how to do this problem? Calculus 2

Mathematics
1 answer:
yuradex [85]2 years ago
3 0

The arc length is given by the definite integral

\displaystyle \int_1^3 \sqrt{1 + \left(y'\right)^2} \, dx = \int_1^3 \sqrt{1+9x} \, dx

since by the power rule for differentiation,

y = 2x^{3/2} \implies y' = \dfrac32 \cdot 2x^{3/2-1} = 3x^{1/2} \implies \left(y'\right)^2 = 9x

To compute the integral, substitute

u = 1+9x \implies du = 9\,dx

so that by the power rule for integration and the fundamental theorem of calculus,

\displaystyle \int_{x=1}^{x=3} \sqrt{1+9x} \, dx = \frac19 \int_{u=10}^{u=28} u^{1/2} \, du = \frac19\times\frac23 u^{1/2+1} \bigg|_{10}^{28} = \boxed{\frac2{27}\left(28^{3/2} - 10^{3/2}\right)}

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When the expression $-2x^2-20x-53$ is written in the form $a(x+d)^2+e$, where $a$, $d$, and $e$ are constants, then what is the
Sladkaya [172]
We start with 2 x^{2} -20x-53 and wish to write it as a(x+d) ^{2} +e

First, pull 2 out from the first two terms: 2( x^{2} -10x)-53

Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have x^{2} -10x and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square: x^{2} -10x+25=(x-5) ^{2}

The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have 2( x-5) ^{2}-53 and when we multiply that out it does not give us what we started with. It gives us 2 x^{2} -20x+50-53=2 x^{2} -20x-3

So you see our expression is not right. It should have a -53 but instead has a -3. So to correct it we need to subtract another 50.

We do this as follows: 2(x-5) ^{2}-53-50 which gives us the final expression we seek:

2(x-5) ^{2}-103

If you multiply this out you will get the exact expression we were given. This means that:
a = 2
d = -5
e =  -103

We are asked for the sum of a, d and e which is 2 + (-5) + (-103) = -106


7 0
3 years ago
What is 12% of 18? Show work
tatuchka [14]

Answer:

2.16

Step-by-step explanation:

12/100=0.12

18 · 0.12=2.16

7 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bx%20%2B%202%20%7D%20%20%3D%209%20%5Ctimes%28%20%20%7B2%7D%5E%7Bx%7D%20%29%20-%
nataly862011 [7]

Hello, please consider the following.

{2}^{x + 2 } = 9 \times( {2}^{x} ) - 2\\\\2^x \cdot 2^2=9\cdot 2^x-2\\\\(9-4)2^x = 2\\\\2^x=\dfrac{2}{5}\\\\\text{We take the ln.}\\\\xln(2)=ln(2)-ln(5)\\\\x=\dfrac{ln(2)-ln(5)}{ln(2)}=-1.32193...

Let me know if you need further explanation.

Thank you

7 0
3 years ago
Perry and Jacob each improved their yards by planting hostas and ivy. They bought their supplies from the same store. Perry spen
marissa [1.9K]

Answer:

hosta=11 ivy=9

Step-by-step explanation:

Logically thinking... $20 for 1 h and 1 i

So I would say $11 H and $9 I

3 0
3 years ago
2) When we divide ______ by 8 gives a quotient of 75 and a remainder of 3
Pani-rosa [81]

Answer:

603

Step-by-step explanation:

603/8

600/8 + 3/8 = 75, 3/8

4 0
3 years ago
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