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:
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 [tex]\sqrt{2^{2}+(6-X)^{2} } Km[/tex] .
Now The Total Time is t = [tex]\frac{X}{8} + \frac{\sqrt{2^{2}+(6-X)^{2} } }{3}[/tex] .
t = [tex]\frac{X}{8} + \frac{\sqrt{X^{2}-12X+40 } }{3}[/tex]
[tex]\frac{dt}{dX}=1/8 + 1/3 * 1/2 * \frac{2X-12}{\sqrt{X^{2}-12X+40 } }[/tex]
[tex]\frac{dt}{dX}=1/8 + \frac{1}{3} * \frac{X-6}{\sqrt{X^{2}-12X+40 } }[/tex]
Now Put [tex]\frac{dt}{dX} = 0[/tex] , we get
[tex]1/8 + \frac{1}{3} * \frac{X-6}{\sqrt{X^{2}-12X+40 } } = 0[/tex]
[tex]\frac{1}{3} * \frac{X-6}{\sqrt{X^{2}-12X+40 } } = - \frac{1}{8}[/tex]
8(X-6)= -3 × [tex]{\sqrt{X^{2}-12X+40 }[/tex]
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) ±[tex]\sqrt{(-660)^{2}-4*55*1944 }[/tex] ] ÷ 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
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Answers
Answer:
Elimination (multiplication and subtraction)
There is 1 solution
Step-by-step explanation:
The only way to solve this system of equations is by elimination (multiplication). Let's say that we want to cancel out the x. You multiply the first equation by 5 and you multiply the second equation by 2.
Your equations now are:
10x-5y=55 and 10x+6y=-22
You can subtract these equations to get -11y = 77.
Now that we know that y = -7, we can substitute y in to solve x.
10x-5(-7) = 55
10x=20
x=2
Final answer (2,-7)
Simplify 6(x + 3).
6x + 3
x + 18
6x + 18
6x + 9
Answers
Answer:
the answer of this question is = 6x + 18
Help plz..And No links!! I repeat No links!!
Answers
Answer:
5 more wheelbarrows
Step-by-step explanation:
10-5
5) Michelle and Autumn are at a gift shop. They each buy magnets and postcards. Michelle
buys 4 magnets and 6 postcards and spends $24. Autumn buys 2 magnets and 1 postcard and
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(4x + 6y = 24
a)
2x + y = 8
(4x + 6y = 8
b)
(2x + y = 24
c)
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y+by = 8
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Answer:it has to be A
Step-by-step explanation:
Which equation represents the formula for the general term, gn , of the geometric sequence 3 , 1 , 1/3 , 1/9 . . .?
Answers
Answer:
Explicit
gn = 3(1/3)^(n-1)
Recursive
gn =1/3gn-1
Step-by-step explanation:
3 , 1 , 1/3 , 1/9 . . .
gn = ar^(n-1)
Where,
a = first term = 3
r = common ratio = 1/3
Check:
g2 = ar^(n-1)
= 3(1/3)^(2-1)
= 3/3^(1)
= 1^1
= 1
The explicit formula is
gn = ar^(n-1)
gn = 3(1/3)^(n-1)
The recursive form for a geometric sequence is gn = rgn-1
recursive form for our sequence gn =1/3gn-1
Where,
gn = 3
Teresa tiene 12 años , su hermano pere tiene 7 y su padre 44. QUANTOS AÑOS TIENE Q PASAR PARA Q LA SUMA DE LAS EDADES DE TERESA Y SPERE SEAN IGUALES
Answers
Answer:
Tienen que pasar 25 años para que la suma de las edades de Teresa y Pere sean iguales a la edad de su padre.
Step-by-step explanation:
Dado que Teresa tiene 12 años, su hermano Pere tiene 7 y su padre 44, para determinar cuántos años tienen que pasar para que la suma de las edades de Teresa y Pere sean iguales a la edad de su padre se debe realizar el siguiente cálculo:
12 + 7 = 19
44 - 19 = 25
44 + 25 = 69
(12 + 25) + (7 + 25) = 37 + 32 = 69
Por lo tanto, tienen que pasar 25 años para que la suma de las edades de Teresa y Pere sean iguales a la edad de su padre.
You dont have to tell me the answers for those, just what x equals, please.
1) (2x - 1)3 = 9 commutative 2) 3(1x) = 9
3) 6x - 1 = 9 4) 6x - 3 = 9 distributive
5) 3*2x - 3*1 = 9 distributive 6) 3(1 - 2x) = 9
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Answers
Answer:
go to photo math
Step-by-step explanation:
You basically look at the bar graph on the right and see which statement is true. Brainliest and thank you!
Answers
Answer:
d. if graphed, the ordered pairs would form a straight line.
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Answers
Answer:
30000
Step-by-step explanation:
what is the value of x.
Answers
(3x-9)+30+24=180
3x-9+54=180
3x+45=180
-45 -45
3x=135
x=45
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Answers
Answer:
15
Step-by-step explanation:
Since, triangle ABC is the enlargement of triangle XYZ.
[tex] \therefore \triangle ABC \sim \triangle XYZ[/tex]
So, corresponding sides of both the triangles would be in proportion.
[tex] \therefore \frac{x}{6}=\frac{25}{10}[/tex]
[tex] \therefore x= \frac{6\times 25}{10}[/tex]
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What does (-3+ -2+ 5)2 equal to
Answers
-5 + 5 = 0
0 x 2 = 0
Hey there!
(-3+ -2 + 5)(2)
(-3 - 2 + 5)(2)
-3 - 2 = -5
(-5 + 5)(2)
-5 + 5 = 0
0(2) = 0
Possible answer #1: 0
(-3 + -2 + 5)^2
(-3 - 2 + 5)^2
-3 - 2 = -5
(-5 + 5)^2
-5 + 5 = 0
0^2 = 0 * 0 = 0
Possible answer #2: 0
Overall answer you’re probably looking for is: 0
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Franklin races bikes. In his city, there are 44 lengths of race tracks. The chart shows the race tracks and each track's length in miles. Race Track Length in Miles A \frac{1}{4} 4 1 B \frac{3}{2} 2 3 C 1\frac{3}{4}1 4 3 D \frac{4}{4} 4 4 Frankin races 33 laps in the same lane. The total distance he races is more than 4\frac{1}{2}4 2 1 miles. Which track does Franklin race on?
Answers
Answer:
51
Step-by-step explanation:
51 is elaginlent to 44 and 33 12 garde things
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20 ft
18 ft
15 ft
СА
B
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1, 320 ft
2, 700 ft
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OD
Answers
What can you tell about a triangle when given three side lengths?
What can you tell about the relationship between the angles of a triangle and its sides?
Answers
Answer:
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Step-by-step explanation:
What is the value of the expression 9 x 4 - (2 x 1/2)
Answers
Answer:
35x
Step-by-step explanation:
Start with parentheses, 2 x 1/2 = 1
9 x 4 = 36
36 - 1 = 35
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Answers
Answer:
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Step-by-step explanation:
Made this for twitch please answer this please
Answers
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a cylindrical container has a radius of 14 cm and I 20m high .it's curved surface is completely covered with a label . what is the area of the label in cm2 .take pie to be 22/7)
Answers
Answer:
The area of the label is 176,000 cm²
Step-by-step explanation:
The given parameters are;
The radius of the cylindrical container, r = 14 cm
The height of the cylinder, h = 20 m
The area covered with the label = The curved surface of the cylinder, A
The curved surface area of a cylinder, A = 2 × π × r × h
π = 22/7
∴ The curved surface area of the cylinder = A = 2 × 22/7 × 14 × 2000 = 176,000
A = 176,000 cm²
∴ The area of the label = The curved surface area of the cylinder = 176,000 cm².
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Answers
You want to find the positive square root of 1
Figure out which number squared (multiplied by itself) equals 1
The number 1 squared equals 1
1^2 = 1 × 1 = 1
So the positive square root of 1 is 1
[tex] \\ [/tex]
#CarryOnLearning!
A positive
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C none
D multiple
Answers
Answer:
postive
Step-by-step explanation:
positive collums so it's positive
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Answers
Answer:
Y = -1/2 - 2
Step-by-step explanation:
Y - intercept (b value in y = mx + b) equals -2.
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Answer:
the equation of the line in the following graph: y = -1/2x - 2
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Answers
Answer:
1. $40
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Step-by-step explanation:
1. Time between 12:00 and 2:00 is 2 hours, the difference in the money is $10, so the money earned per hour is $5. 5:00 is 3 hours from 2:00, so 25+5*3 is 40, or $40.
2. Time between 1:00 and 3:00 is 2 hours, and the difference in the numbers of computers fixed is 2, so the number of computers fixed per hour is 1. 6:00 is 3 hours from 3:00, so 7+3*1 is 10, or 10 computers.
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Answers
Answer:
The answer is 84 cubic feet.
Step-by-step explanation:
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Ridas father is 4 times old as rida. After 5 years father will be three times as old as rida.Find their present ages
Answers
Answer:
Rida is 10 years old and her father is 40 years old.
Step-by-step explanation:
Given:
Present age
Present age of Rida = x
Present age of Rida's father = 4x
Age after 5 years
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Age of Radi's father after 5 years = 3(x + 5)
What To Find:
The present age of Rida and Rida's father.
Solution:
According to the statement the equation will be,
⇒ 4x + 5 = 3(x + 5)
Remove and solve the brackets,
⇒ 4x + 5 = 3x + 15
Take numbers to RHS and variable to LHS,
⇒ 4x - 3x = 15 - 5
Subtract 3x from 4x and 5 from 15,
⇒ x = 10
Now substitute the values of Rida's age and Rida's father's age,
Rida's age = x = 10 years
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Please answer its fill in the blanks
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Answers
Answer:
1. Grassland
2. grass
3. Temperate grassland
4. prairies
5. steppe
6. tropical grassland
7. savanna
8. intermountain grassland
9. mixed prairie
10. tallgrass prairie
Step-by-step explanation:
Pls I just need the equation for this one
Answers
Answer:
y=1/3x
Step-by-step explanation:
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Answers
Answer:
b is 3 pythagorean theorem
Step-by-step explanation:
Answer:
your answer for B is 3
Step-by-step explanation:
this is easy its a Pythagorean Triple (with triples u dont have to do much work all u have to do is know ur Triples and its that easy)
so the Triples are
3,4,55,12,138,15,177,24,25p.s you might want to write these down for the future
so if we look at this picture of the triangle we can tell its a 3,4,5 triple
and there is one missing side which is 3.
Write an expression for the phrase.
A number increase by ten.
No links
Answers
Answer:
n + 10
Step-by-step explanation:
im pretty sure thats right, im sorry if not but have a great day!
Answer:
I'm not tryna be a but do u know how to ask questions in the app
Step-by-step explanation:
pls
You are going to design a deck or a dock for your cottage. Your deck/dock must be a composite shape made out of 3 shapes - 2 will be "glued” together and 1 will be "cut out” of the other(s). You must use 3 different geometric shapes. Design your deck/dock by including a diagram with
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