All categories

3 years ago

Find the distance between a and b

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

6 0

Answer:I believe it is 2.4

Step-by-step explanation:

You might be interested in

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

3 years ago

Find the 20th, 40th, 60th, and 80th percentiles of the standard normal distribution. Round the answers to two decimal places.

Fed [463]

To answer the question above, we have to use the z-score percentile table for the standard normal distribution. It shows:
The 20th percentile = - 0.84
The 40th percentile = - 0.25
The 60th percentile = 0.25
The 80th percentile = 0.84

I hope my answer helped you. Have a nice day!

3 0

3 years ago

Pls help.................

Crank

The correct answer is u multiple it by 5 then u move it directions

7 0

3 years ago

Read 2 more answers

Put them in order from least to greatest:<br> 8.85 8.9 8.948 8.826 8.97 8.866

Ray Of Light [21]

Answer: 8.826, 8.85, 8.866, 8.9, 8.948, 8.97

Step-by-step explanation: