MATHEMATICS HIGH SCHOOL

Mauritius island is 2 km due south of its closest point along a straight coastline. Gibril is staying at a private room on the shore that is 6 km east of that point. Gibril is planning to go from the room to the island. Suppose Gibril runs at a rate of 8 kmph and swims at a rate of 3 kmph. How far should Gibril run before swimming to minimize the time it takes to reach the island?

Answers

Answer 1
Answer:

Answer:

5.19 Km

Step-by-step explanation:

According To the Question,

Suppose he Runs Xkm before swimming to minimize the time it takes to reach the island .

So, he should swim \sqrt{2^(2)+(6-X)^(2) } Km .

Now The Total Time is t = (X)/(8) + \frac{\sqrt{2^(2)+(6-X)^(2) } }{3} .

t = (X)/(8) + \frac{\sqrt{X^(2)-12X+40 } }{3}

(dt)/(dX)=1/8 + 1/3 * 1/2 * \frac{2X-12}{\sqrt{X^(2)-12X+40 } }

(dt)/(dX)=1/8 + (1)/(3) * \frac{X-6}{\sqrt{X^(2)-12X+40 } }

Now Put (dt)/(dX) = 0 , we get

1/8 + (1)/(3) * \frac{X-6}{\sqrt{X^(2)-12X+40 } } = 0

(1)/(3) * \frac{X-6}{\sqrt{X^(2)-12X+40 } } = - (1)/(8)

8(X-6)= -3 × {\sqrt{X^(2)-12X+40 }

square on both side,We get

64(X²-12X+36) = 9X² - 108X +360

55X² -660X + 1944 = 0

Apply Shri Dharacharya formula, To Find The Value of 'X'

X =[ - (-660) ±\sqrt{(-660)^(2)-4*55*1944 }  ] ÷ 2×55

X = (660±√7920) / 110

X= (660 - 89 ) / 110  ⇒ (Neglect '+' because it give 749/110 = 6.8 km Which is not possible )

X=571/110 ⇔ 5.19km he Should Run before swimming to minimize the time .

(For Diagram,Please Find In Attachment)

Related Questions

I had ⅖ of my chips and gave my dad ⅔ are they equivalent?
Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum distances that the dog may be from the house can be found using the equation |x – 500| = 8. What are the minimum and maximum distances that Morgan’s dog may be from the house?
John Gray bought a basic car for $32,750.00, with options that cost $375.00. There's a 6% sales tax in his state and a combined $50.00 license and registration fee. What was John's total cost?A. $35,165.50 B. $33,175.00 C. $35,140.00 D. $35,162.50
Simplify the expressions by combining like terms1. 6n^2 - 2n - 3 + 5n^2 - 9n - 62. 8c^2 - c + 3 + 2c^2-c + 2
What is the equation of this line graph?A. y = 2x + 1 B. y = 2x + 2C. y = -2x + 1 D. y = -1x + 1E. y = -3x + 1

(-8ab-8a+5) - (-3ab+8)

Answers

(-8ab - 8a + 5) - (-3ab + 8)
-8ab - 8a + 5 + 3ab - 8 (distrubute (-1))
-5ab - 8a - 3 (combine like terms)

understand?

Simplify completely quantity 4 x squared minus 32 x plus 48 all over quantity 3 x squared minus 17 x minus 6.

Answers

4x^2-32x+48
__________
3x^2-17x-6
⬇
4(x^2-8x+12)
__________
3x^2-17x-6

Answer:

(4(x-2))/(3x+1)

Step-by-step explanation:

i got it right on the test but I don't know the steps of solving it sorry

Which phrase best defines a square? A.
a quadrilateral with exactly one pair of parallel sides

B.
a quadrilateral with no congruent sides

C.
a rectangle with four congruent sides

D.
a parallelogram with four congruent angles
I think its D?

Answers

the answer is D a parallelogram with four congruent angles
 

Let 3 × 3 × 3 × 3 = n. Which choice also equals n? A) 3 × 4 B) 34 C) 4 ÷ 3 D) 43

Answers

none because 3x3x3x3=81 so n=81 and none of those answers equal 81
The answer is 81, but non of your choices has 81.

What is the circumference of a circle with a 72 centimeter radius

Answers

Answer:

452.39cm^2

Step-by-step explanation:

Answer:

  • c=452.39cm

-XxanimexX

What is the value of this expression?

(9^2+79)/2^2

(its a fraction)

Answers

Hey there!

Answer: \boxed{40}

Explanation:

Simplify to solve.

\boxed{40}\text{ is your answer.}

Hope this helps!

\text{-TestedHyperr}

Answer:

40

Step-by-step explanation:

(9^2 +79) /2^2

(81 +79) /4

160/4

40

Other Questions
A parabola opens upward. The parabola goes through the point (3,-1),and the vertex is at (2,-2).Find the value of A for the parabola. Show your work. Use Part 1 and 2 to write the equation of the parabola.
In which quadrants is the ordinate positive? I and II II and III I and IV
Which decimal number is 17/22 equal to?
Luke’s parents started a savings account to help him pay for college or a technology school when he turned 11 years old. Each month they put $125 into the savings account, and they continued this until he was 18 years old. The savings account did not accumulate any interest. Luke figured out that the first year of a technology school that he wanted to attend would cost him $12,480. If he had one year to save the rest of the money, how much would he need to save each month? A. 165B.40C.1980D.1040