1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artemon [7]
3 years ago
11

Use the arc length formula to find the length of the curve y = 5x − 4, −1 ≤ x ≤ 3. check your answer by noting that the curve is

a line segment and calculating its length by the distance formula
Mathematics
1 answer:
AnnZ [28]3 years ago
6 0
The given curve is y = 5x -4,  -1 ≤ x ≤ 3.

The length of the arc is computed from the formula
S= \int_{-1}^{3} \,\sqrt{1+ (\frac{dy}{dx} )^{2}} \, dx

The derivative is 
y' = 5

Therefore
S = \int_{-1}^{3} \sqrt{1+25} \, dx =\sqrt{26}*(3-(-1))=20.396

Note that 
x = -1 +> y = 5(-1) - 4 = -9
x = 3 => y = 5(3) - 4 = 11
The distance between the points (-1, -9) and (3, 11) from the distance formula is
D = √[(3-(-1))² + (11-(-9))²] = √(16+400) = 20.396
This answer agrees with that obtained by integration.

Answer: 20.396
Obtained by integration and verified by the distance formula.

You might be interested in
The amount in dollars an electrician charges in terms of the number of hours worked is represented by the function y=22x+42.
sasho [114]

Answer:

Step-by-step explanation:"

The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.

The equation is y=22x+42. The formula is y=mx+b.m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).

7 0
3 years ago
What are the intercepts of the graph of the equation, y=-7
goldenfox [79]

<u>Answer:</u>

y-7=0 is the same as y=7

The drawing of y=7 is a straight horizontal line intercepting the y axis at 7. So basically it's a horizontal line that passes through (0,7). Its slope is zero since it's a horizontal line.

<u>Step by step explanation:</u>

A line with no x in the equation is a horizontal line. In this case, y=7. All horizontal lines have a slope of 0, since there is never a change in the y coordinate (it is always 7) so the numerator of the fraction used to determine the slope is 0.

The y-intercept is, of course 7 (all y values on the line are 7). There is no x-intercept since it is a horizontal line through the point (0,7) so it will never intersect the x-axis.

7 0
2 years ago
Help!!!!!!!!!!!!!!!!!!!!!! I’m not good at math
Rufina [12.5K]
Multiply the 5 by both terms in the ()
5(y+3z) = 5y+15z
6 0
3 years ago
Read 2 more answers
2) 3=r+17<br> pls solve for r
Elan Coil [88]

Answer:

r = -14

Step-by-step explanation:

3 = r + 17

r + 17 = 3

r + 17 - 17 = 3 - 17

r = -14

6 0
3 years ago
Anyone know this one?
Shalnov [3]

Answer:

B) 2(3x^2+10x+15

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • A) Explain...
    9·1 answer
  • There are 10 sport balls in the equipment closet. Three or kick balls. Write the portion of the balls ever kick balls as a fract
    12·1 answer
  • Which is the best estimate for the productof 190.3003x198.7
    8·1 answer
  • If the total income generated from gasoline for aer was 408 million, how much would be the cost for a barrel of gasoline.
    5·2 answers
  • The value of a professional basketball player's autograph rose 40% in the last year. It is now worth $322.00. What was it worth
    13·1 answer
  • (GIVING BRAINLIEST) The Smith family is building a deck that is 200 square feet in area. What are the
    10·1 answer
  • What is the value of 5.4 <br> 54 tenths <br> 54 hundredths <br> 54 ones<br> 540 tenths
    8·2 answers
  • Simplify the expression to polynomial in standard form (3x+2)(3x-2)(2x-3)
    15·1 answer
  • A pair of slacks that sold for $17.75 is on sale for $14.91. What is the discount rate?
    9·1 answer
  • The Question is in the picture because I could not type it out correctly for some reason.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!