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2 years ago

Which condition must be satisfied in order to use the arc length formula L = the integral from a to b of sqrt(1 + f'(x)^2) dx?

Mathematics

1 answer:

ivanzaharov [21]2 years ago

6 0

Looking through my old calc notes, I am reading that f(x) needs to be continuous on [a,b] and f ' (x) also needs to be continuous on [a,b]. Both conditions are needed. If you had to pick just one, then I'd say f(x) being continuous is much more important. Though I'm not 100% sure on this one. My thinking is that if there was any discontinuities on f(x), then the arc length would be distorted and overblown. The arc length should not account for any piece that isn't on the curve.

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Estimate the difference 7 3/4-2/25 Show your work.

crimeas [40]

Answer: 7 3/4 - 2/25 = 767/100 = 7 67/100 = 7.67

Step-by-step explanation:

Conversion a mixed number 7 3/4

to a improper fraction: 7 3/4 = 7 3/4 = 7 · 4 + 3/4= 28 + 3/4 = 31/4

To find a new numerator:

a) Multiply the whole number 7 by the denominator 4. Whole number 7 equally 7 * 4/4 = 28/4

b) Add the answer from previous step 28 to the numerator 3. New numerator is 28 + 3 = 31

c) Write a previous answer (new numerator 31) over the denominator 4.

Seven and three quarters is thirty-one quarters

Subtract: 31/4 - 2/25= 31 · 25/4 · 25 - 2 · 4/25 · 4 = 775/100 - 8/100 = 775 - 8/

100 = 767/100

6 0

2 years ago

Read 2 more answers

Solve for x. x = 5° x = 18° x = 30° x = 36°

sergij07 [2.7K]

Answer:

x=36

Step-by-step explanation:

The 2 angles, ∠EAF and ∠FAB are on a straight line. This means they are supplementary, and add to 180 degrees.

So,

∠EAF +∠FAB =180

We know that ∠EAF is 3x and ∠FAB is 2x, so we can substitute them in

3x+2x=180

Combine like terms

5x=180

Divide by 5 on both sides

x=36

So, x=36 degrees, or the last choice

3 0

2 years ago

The cost price was $10000 she made a down payment of 2500 and agreed to pay the balance in 24 monthly installments of $350 how m

Airida [17]

Answer:

in total she spent 10900

Step-by-step explanation:

We know she made a down payment of 2500 dollars and she agreed to pay the balance in 24 monthly installments of 350 dollars. Thus we can do simple multiplying of 24 x 350 which gives us 8400. We also need to add in her down payment which is 2500 so in total we got 10900

5 0

2 years ago

What is the answer for 2x+y=2

beks73 [17]

Answer:

X=1 - y/2

Step-by-step explanation:

2x = 2 - y

divide both sides by 2

x = 1 - y/2

4 0

3 years ago

Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x

egoroff_w [7]

Answer:

$y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept.

Perpendicular lines always have slopes that are negative reciprocals (ex. 1/2 and -2, 3/4 and -4/3)

Determine the slope (m):

$y = 1 -2x$

Rearrange into slope-intercept form:

$y = -2x+1$

Now, we can identify clearly that the slope is -2. Because perpendicular lines always have slopes that are negative reciprocals, a perpendicular line would have a slope of $\displaystyle\frac{1}{2}$ . Plug this into $y=mx+b$ :

$y=\displaystyle\frac{1}{2} x+b$

Determine the y-intercept (b):

$y=\displaystyle\frac{1}{2} x+b$

Plug in the given point (1,3) and solve for b:

$3=\displaystyle\frac{1}{2} *1+b\\\\b=\displaystyle \frac{5}{2}$

Therefore, the y-intercept is $\displaystyle \frac{5}{2}$ . Plug this back into $y=\displaystyle\frac{1}{2} x+b$ :

$y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}$

I hope this helps!

8 0

2 years ago