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
Stella [2.4K]
3 years ago
14

How do you do this question?

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
5 0

Step-by-step explanation:

y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1

dy/dx = 12√x

Arc length is:

s = ∫ ds

s = ∫₀¹ √(1 + (dy/dx)²) dx

s = ∫₀¹ √(1 + (12√x)²) dx

s = ∫₀¹ √(1 + 144x) dx

If u = 1 + 144x, then du = 144 dx.

s = 1/144 ∫ √u du

s = 1/144 (⅔ u^(³/₂))

s = 1/216 u^(³/₂)

Substitute back:

s = 1/216 (1 + 144x)^(³/₂)

Evaluate between x=0 and x=1.

s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]

s = 1/216 (145)^(³/₂) − 1/216

s = (145√145 − 1) / 216

You might be interested in
True or False? Using the quadratic formula allows you to find the x-intercepts of a quadratic equation.
levacccp [35]
True using the formula allows you to find the x intercepts of the equation
5 0
3 years ago
Find Arc PR<br>Please help and give explanation ​
garri49 [273]
Arc PR is 156 degrees. Since both angles are are making the forming arc they should be congruent. You can put (5x+23)=(9x-21) which is x=11.
Then you plug in 11 into your equation; 5(11)+23=78.
Since the vertex is on the outside of the circle then the arc is forms is 2 times the value of the angle.
78(2)=156
8 0
3 years ago
Draw the image of a triangle with vertices (2, 1), (3, 3), and (5, 1). Then perform the
NARA [144]

Answer:

It would be B

Step-by-step explanation:

6 0
2 years ago
Sally is standing at one corner of a snowy rectangular field that measures 200 ft by 200 ft. She wishes toreach a warm cabin loc
pshichka [43]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The optimal point(i.e the position of  P) that will allow Sally to reach the cabin as quickly as possible is  d =  50 \ ft from the cabin.

Step-by-step explanation:

From the question we are told that

   The speed from the point Sally is standing to the point P is  u =  3 \  ft /s

   The speed from the point P to the cabin is v  =  5 \  ft /s

   

Let denote the distance from the bottom left corner to the  P  be  y  ft

 Generally according to Pythagoras theorem the distance from Sally's first position to point P is mathematically represented as

          s = \sqrt{y^2 + 200^2}

Generally the distance from that point P to the cabin is mathematically represented as

       d =  200 -y

Generally the time it takes Sally to cover that distance s is mathematically represented as

       t_1 =  \frac{s}{u}

=>     t_1 =  \frac{ \sqrt{y^2 + 200^2}}{3}

Generally the time it takes Sally to cover that distance d is mathematically represented as

       t_2 =  \frac{d}{v}

=>     t_2 =  \frac{ 200 - y }{5}

So the total time taken is  

        t= \frac{ \sqrt{y^2 + 200^2}}{3}  +  \frac{ 200 - y }{5}

Generally the minimum time taken with respect to the distance is mathematically evaluated by differentiating and equating the derivative to 0

So  

     \frac{dt}{dy} =\frac{1}{3} \frac{y}{ \sqrt{y^2 + 200^2} }  -  \frac{1}{5}  =0      

=> \frac{dt}{dy} = \frac{y^2 }{y^2 + 200 ^2} =\frac{9}{25}

=> 25y^2 = 9y^2 + 9 * 200^2        

=> 16y^2 = 360000          

=> y = 150

So the distance from point P to the cabin is  

           d =  200 -150

=>       d =  50 \ ft

So  the optimal point(i.e the position of  P) that will allow Sally to reach the cabin as quickly as possible is  d =  50 \ ft from the cabin

       

8 0
2 years ago
Find the height of a triangle with a base of 6.4 meters and an area of 22.4 square meters
nevsk [136]

Answer:

Its height would be 7 meters.

7 0
2 years ago
Other questions:
  • If 60% of people said that they like
    12·2 answers
  • It's in the attachment <br> URGENT
    8·1 answer
  • The store bought shoes for 40 dollars. They want to make a 20 percent markup. How many dollars did they raise the original prise
    6·2 answers
  • K=mv^2/2 solve for v
    11·1 answer
  • Express the following fraction in simplest form using only positive exponents.
    5·1 answer
  • One batch of walnut muffins uses 1 1/3 cup of walnuts.How many cups of walnuts are needed to make 3 3/4 batches of muffins?
    10·1 answer
  • What is the equation in point slope form of the line that passes through the point (–1, –3)(–1, –3) and has a slope of 4?
    5·1 answer
  • Triangle has side lengths of (9k – 4m) centimeters, (8k + 3n)
    7·1 answer
  • Which expression is equivalent to Cosine (StartFraction pi Over 12 EndFraction) cosine (StartFraction 5 pi Over 12 EndFraction)
    6·2 answers
  • How many eighths do you shade to equal 1 half?<br><br> 3<br><br> 4<br><br> 1<br><br> 2
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!