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skelet666 [1.2K]
3 years ago
12

A hiker starting at point P on a straight road wants to reach a forest cabin that is 2 km from a point Q, 3 km down the road fro

m P . She can walk 8 km/hr along the road but only 3 km/hr through the forest. She wants to minimize the time required to reach the cabin. How far down the road should she walk before setting off through the forest straight for the cabin?

Mathematics
1 answer:
pantera1 [17]3 years ago
7 0

Answer:

2.19 km

Step-by-step explanation:

If x is the distance she walks down the road before turning, then the total time is:

t = x/8 + √((3 − x)² + 2²) / 3

t = x/8 + √(9 − 6x + x² + 4) / 3

24t = 3x + 8√(13 − 6x + x²)

24t = 3x + 8(13 − 6x + x²)^½

Take derivative of both sides with respect to x.

24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

When t is a minimum, dt/dx = 0.

0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)

3 / (6 − 2x) = 4(13 − 6x + x²)^-½

3 / (24 − 8x) = (13 − 6x + x²)^-½

(24 − 8x) / 3 = (13 − 6x + x²)^½

(24 − 8x)² / 9 = 13 − 6x + x²

576 − 384x + 64x² = 117 − 54x + 9x²

459 − 330x + 55x² = 0

Solve with quadratic formula.

x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)

x = (330 ± √7920) / 110

x = 2.19 or 3.81

Since 0 < x < 3, x = 2.19.

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user100 [1]
Given:$75
25 hours

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Total Cost = 75 + 25(25) = 75 + 625 = 700

Upscale Home Painting: No Fixed Cost ; Variable Cost : $40x
Total Cost = 40(25) = 1,000

The most cost effective company will be Painting USA whose charge will amount to $700.
3 0
2 years ago
The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measure
Gnoma [55]

The best and most correct answer among the choices provided by your question is the second choice or letter B "20".

The current area is 120(80)=9600 and he want to expand it by 4400 so that the new area will be 9600+4400=14000 

14000=(120+x)(80+x) 

14000=9600+200x+x^2 

x^2+200x-4400=0 

x^2-20x+220x-4400=0 

x(x-20)+220(x-20)=0 

(x+220)(x-20)=0, since x is an increase it must be greater than zero so 

x=20ft 

(120+20)(80+20)=14000ft^2


I hope my answer has come to your help. Thank you for posting your question here in Brainly.

4 0
2 years ago
Read 2 more answers
How do I solve tan(62) = 12/x?
notsponge [240]

Answer:

x = 6/31 = 0.194

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (62)-(12/x)=0

Step by step solution :

Step  1  :

           12

Simplify   ——

           x

Equation at the end of step  1  :

       12

 62 -  ——  = 0

       x

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  x  as the denominator :

          62     62 • x

    62 =  ——  =  ——————

          1        x  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

62 • x - (12)     62x - 12

—————————————  =  ————————

      x              x    

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  62x - 12  =   2 • (31x - 6)

Equation at the end of step  3  :

 2 • (31x - 6)

 —————————————  = 0

       x      

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 2•(31x-6)

 ————————— • x = 0 • x

     x    

Now, on the left hand side, the  x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  2  •  (31x-6)  = 0

Equations which are never true :

4.2      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.3      Solve  :    31x-6 = 0

Add  6  to both sides of the equation :

                     31x = 6

Divide both sides of the equation by 31:

                    x = 6/31 = 0.194

Answer :

                  x = 6/31 = 0.194

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What information is shown on the horizontal axis of a bar chart?
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The information shown on the horizontal axis of a bar chart is the qualitative class labels.

<h3>What is a bar chart?</h3>

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To learn more about bar charts, please check: brainly.com/question/14473126

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2 years ago
Does this seem answer seem correct?
Blababa [14]
I mean I think so I’m not completely sure it’s a really hard question
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3 years ago
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