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2 years ago

In the definition of fractional numbers, b ≠ 0. Why?

Mathematics

1 answer:

Nataliya [291]2 years ago

6 0

I have no idea. Just commenting to get the answer when someone else knows it

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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

2 years ago

The rate of change from 23 to 30 is

____ [38]

Answer:

Step-by-step explanation:

8 0

2 years ago

Divide 21 by g. Then, subtract 6.

IrinaVladis [17]

21/g - 6 = (21-6g)/g. G

8 0

3 years ago

Read 2 more answers

The mayor of Chicago is known for being a great host, and he puts a lot of time into preparing for events. For the mayor's next

LenaWriter [7]

Answer:

D) 3768 inches

Step-by-step explanation:

Given,

No. of plates = 100

Diameter of each plate = 12inches

So, radius of each plate = 12 / 2 = 6 inches

So, circumference of each plate

$= 2\pi \: r$

= 2 × 3.14 × 6 inches

= 37.68 inches

Hence, circumference of 100 plates = 100 × 37.68 inches

= 3768 inches

Hence, <u>3768 inches</u> of gold trim is required (Ans)

4 0

2 years ago

Rewrite the expression by combining like terms.<br> 3xy + 8x^2+ 4y + 2y - 5x^2

Lelu [443]

Answer:

3x^2 + 3xy + 6y

Step-by-step explanation:

7 0

2 years ago