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:

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)

Mauritius Island Is 2 Km Due South Of Its Closest Point Along A Straight Coastline. Gibril Is Staying

Related Questions

Marcus wants to end the semester with at least an 85 test average in his math class. On his first 3 tests, he earned 83, 97, and 80. What will he have to earn on his fourth test to have at least an 85 average? Let g represent the grade needed on his fourth test. Write an inequality that models the situation.

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]\frac{83+97+80+g}{4} \geq 85[/tex]

»»————- ★ ————-««  

Here’s why:  

The average is found by dividing the sum of the values by the number of values.

⸻⸻⸻⸻

[tex]\frac{83+97+80+g}{4} \geq 85[/tex]

⸻⸻⸻⸻

The numerator would consist of the test grades and the unknown 'g' and the denominator would be the number of tests he taken.

"At least" indicates a greater than or equal to inequality.

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Andy £9500 Bevan £25000 Cheryl £13250 Deva £75000 Elliott £12750 Frankie £29500 Grace £11000 a) Work out the mean income to 2 DP. b) Deva was given a large bonus for 30 years service. Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?

Answers

Answer:

a. £25142.86

b. £16833.33

Step-by-step explanation:

According to the Question,

Given, The Salary Of 7 People in An Office are,

Andy ⇒ £9500

Bevan ⇒ £25000

Cheryl ⇒ £13250

Deva ⇒ £75000

Elliott ⇒ £12750  

Frankie ⇒ £29500

Grace ⇒ £11000

a. The mean income = Total Sum of Salaries ÷ Number of Workers

Mean = (9500+25000+13250+75000+12750+29500+11000) ÷ 7

Mean = 176000 / 7 ⇒ £25142.86

b. Now, The Mean income After Excluding Deva's Salary is,

Mean = (9500+25000+13250+12750+29500+11000) ÷ 6

Mean = 101000 / 6 ⇒ £16833.33

14. Evaluate the expression.
4!
24
28
20

Answers

Answer:

24.

Step-by-step explanation:

By definition,  factorial 4

= 4!

= 4*3*2*1

= 24.

the answer is 24!!!
it just is!

8 less than a number x is more than 5 times that same number.

Answers

Answer:

x < -1/2

Step-by-step explanation:

x - 8 > 5x

-8 > 5x -x

-8 > 4x

Divide through by 8

-1/2 > x or x < -1/2.

That is ofcourse if I interpreted the first part correctly.

You and your friends decide to go to the recreation center to play pickup basketball. You decide to play the game 21 where a layup equals 1 point and a jump shot equals two points. You made 11 layups and need to decide how many jump shots you need to make in order to win… Remember that you must not go over 21 points or you lose.​

Answers

Answer:

5 jump shots.

Step-by-step explanation:

Let l = number of layups and j = number of jump shots

l + 2j = 21

11 + 2j = 21

2j = 10

j = 5

5 jump shots are needed to win the game and not go over 21 points.

True or false question. In Standard form, the number 3.5 *10^4 is 3,500.

Answers

Answer: False

Step-by-step explanation:

10^4=10000. 10000*3,5=35000.

Answer:

No, you missed a zero.

Step-by-step explanation:

In the given case, as we have the number as  

3.5 × 10^4, we need to move decimal digit to the right by three points. For this, let us write 3.5 as 3.50000 and moving decimal point four points to right means  

35000.0

Hence in standard notation  

3.5 × 10^4=35,000

Find the slope of the line that passes through (10, 4) and (6, 3).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

The slope of the line that pass through the points (10, 4), and (6, 3) is 1/4

Step-by-step explanation:

The given points son the line are; (10, 4), and (6, 3)

The slope of a line is the rate of change of the y-values of the line relative to the x-values of the given line and the slope. 'm', can therefore be found by specifying two points on the line, (x₁, y₁), and (x₂, y₂), from which we get;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore, the slope of the found line is given as follows;

(x₁, y₁) = (10, 4) and (x₂, y₂) = (6, 3)

[tex]Slope \ of \ the \ line, \, m =\dfrac{3-4}{6-10} = \dfrac{-1}{-4} = \dfrac{1}{4}[/tex]

The slope of the line that pass through the points (10, 4), and (6, 3), m = 1/4

PLEASE HELP ME 50 PTS and i'll give brainliest please help me this is the video they game me to do this hw but I still don't understand it https://youtu.be/7Uos1ED3KHI

Answers

1.) 70x/100x^2 = 7/10x

2.) 16x^3/24x = 2x^2/3

3.) 7x(2x+1)/21(2x+1) = x/3

4.) 35x - 35/x^2 - 1 =  35/x + 1

5.) x + 7/x^2 + 4x - 21 = 1/x - 3

6.) x^2 - 6x + 5 = x - 5/5

7.) x^2 - 36/x^2 - 3x - 18 = x + 6/x + 3

8.) x^2 - 3x - 10/x^2 + x - 2 = x - 5/x - 1

please help find x!!

Answers

Answer:

X= 360- (180+35)

X= 145

Step-by-step explanation:

since angle at a point is same as angle in a circle =360°

And we've being given two values out of three that makes up the point. so we subtract the sum of the two values from the size of angle at a point

Evaluate expression- Which of these answer choices are correct answer to the question

Answers

Answer:

i=10^5

eq is 2^n*i

hence 2^3*10^5

8*100000

=800.000 bacteria

pls mark as brainliest

what additional information is needed to prove the triangles congruent by AAS

Answers

Answer:

pq=su

Step-by-step explanation:

its the only one that makes sense

What I Can Do
Construet an appropriate graph for the Charity donations of each grade level in a high school: ​

Answers

Answer:

You should have a graph that has the words on the y axis Grade 7 Grade 8 Grade 9 and Grade 10 on each differnt line. Than put the number corosponding to the grade on each line, making the graph rise up and down.

Step-by-step explanation:

Can't make one.

make q subject in formula
t=q/2 + 5

Answers

Answer:

[tex] q = 2(t - 5) [/tex]

Step-by-step explanation:

[tex]t = \frac{q}{2} + 5 \\ \\ t - 5 = \frac{q}{2} \\ 2(t - 5) = q[/tex]

hope this helps you.

Have a nice day!

Answer:

2 ( t - 5 ) = q

Step-by-step explanation:

t = q/2 + 5

subtract 5 from both side

t - 5 = q / 2 + 5 - 5t - 5 = q / 2

multiply each side by 2.

2 × ( t - 5 ) = q / 2 × 22 ( t - 5 ) = q

Which are correct representations of the inequality –3(2x-5) <5(2 - x)? Select two options.
u x<5
. -6x-5 < 10 - X
0 -6x + 15 <10 - 5x
-3
--2
-1
0
2
3
5
to
6
7
-7
1-6
-5
-3 -2 -1 0
2
3

Answers

Answer:

Step-by-step explanation:

-6 and up going left

Please help if you can!

Answers

Answer:

D: 78 ft2    

Step-by-step explanation:

6x13=78

Answer:

Rectangle

Result

Area = l × w

= 13 × 6

= 78 feet2

Step-by-step explanation:

#Brainliestbunch

round 0.982 to 2 decimal places

Answers

Answer:

0.98

Step-by-step explanation:

0.982,0.98()2 (round up if 5+ down 4-) 0.98

The number 0.982 rounded of to two decimal places will be 0.98.

What is rounding a number to some specific place?

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

The digit 5 acts as a limit.

if the right-sided digit to the digit where we've to round off is < 5, we keep it the same and make all right-sided values 0, and if the right-sided digit is > 5, then we make it increase by 1, and the rest of the right-sided digits become 0. If the digit on right is 5, and after it, there are only zeros or no value, then we round up (increase by 1, as we did in 347500 -> 34800 ) (Well there are many detailed rules of rounding)

Since the given number is 0.982, and in this number the thousandth place is taken by 2, therefore, the number when rounded off will be equal to 0.98.

Hence, the number 0.982 rounded of to two decimal places will be 0.98.

Learn more about Rounding Numbers here:

https://brainly.com/question/1285054

#SPJ2

Please help will give branliest

Answers

Answer:

ok

8^7*512/262144=4096

8^4=4096

?=4

Your Welcome

BIFFY OUT!!!

A cylinder has a radius of 6 and a height of 10 find the volume

Answers

Answer:

30cm

Step-by-step explanation:

Vn = Vc

1/3 X Pie x 6^2 x hn = Pie x 6^ x 10

hn = 30cm

Given: Radius=7cm,

Height=10cm

Volume of the cylinder=πr2h

=722×7×6×10=1540cm3

Given m || n, find the value of x and y

Answers

Step-by-step explanation:

5x-6+7x+18=180

12x=180+6-18

12x=168

168÷12=14

X=14

for y

3y+11=7x+18(7×14+18)

3y+11=116

3y=116-11

3y=105

y= 35

Answer this wuestion for me man

Answers

Answer:

The length of ribbon is [tex]\sqrt{32}[/tex].

Step-by-step explanation:

Length of the side of square = 4 inches

let the length of the diagonal is x.

By use of Pythagorean theorem

[tex]x^2 = 4^2 + 4^2 \\\\x =\sqrt {16 + 16}=\sqrt{32}[/tex]

someone help tysm will give brainliest !!

Answers

Answer:

11. A) x = 2 .    B) x=-1 .   C) x = 0

12. A) y = 20 . C) y = -3 . D) y = 0

Step-by-step explanation:

When the line is vertical, take the x coordinate

When the line is horizontal, take the y coordinate

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

[NO LINKS]
This is Jovan’s solution for the equation x^2-8x-9=0:

x2 – 8x – 9 = 0

x2 – 8x = 9

x2 – 8x + 16 = 9 + 16

(x – 4)2 = 25

x – 4 = 25 and x – 4 = - 25

x = 29 and x = -21

Is Jovan’s solution correct?

Answers

Answer:

No, it's wrong

[tex] {x}^{2} - 8x - 9 = 0 \\ (x - 9)(x + 1) = 0 \\ x = 9 \: and \: - 1[/tex]

Answer:

No

Step-by-step explanation:

x² – 8x – 9 = 0 x² – 8x = 9 x² – 8x + 16 = 9 + 16 (x – 4)² = 25 x – 4 = 25 and x – 4 = - 25 ⇒ Incorrect, should be x - 4 = 5 and x - 4 = -5 x = 29 and x = -21                ⇒ Incorrect, should be x = 9 and x = -1

help meee it's pythagorean theorem, just need answers plsssssss

Answers

Answer:

Hi, there your answer is C or D and the second page is C

Step-by-step explanation:

simplify an expression
(x^2y^4z)^5/(xy)^2
A) y10z5
B) x6y7z5
C) x7y9z5
D) x8y18z5

Answers

Answer:

d

Step-by-step explanation:

Pleaseee HELP ASAP !!!

Answers

Your answer is going to be b

Answer:

A: (x-5.5)^2 + (y-4)^2=12.25

Step-by-step explanation:

Find the area of a regular Heptagon with a side length of 7?

Answers

Answer:

[tex]seven \: sides \\ area = (7 \times 7) \\ = 49 \: sq \: units[/tex]

A diagonal of a cube goes from one of the cube's top corners to the opposite corner of the base of the cube, Find the length of a diagonal d in a cube that has an edge of length 10 meters. ​

Answers

d = 17.3 m

Step-by-step explanation:

We can extend Pythagorean theorem to 3 dimensions by writing

[tex] {d}^{2} = {x}^{2} + {y}^{2} + {z}^{2} [/tex]

or

[tex]d = \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } [/tex]

Since we are dealing with a cube of side 10 m, then

x = y = z = 10 m

so we get

[tex]d = \sqrt{ {10}^{2} + {10}^{2} + {10}^{2} } [/tex]

or

[tex]d = \sqrt{3 \times {10}^{2} } = 10 \sqrt{3} \: m[/tex]

This becomes

d = 17.3 m

Lacy got a $100 gift card to an online clothing store. She
uses the gift card to buy a pair of pants for $19.99. She
also wants to use the gift card to buy some shirts. Each
shirt costs $11.69.
Which of these inequalities describes this situation, where
n is the number of shirts Lacy wants to buy?

Answers

Answer:

80.01>11.69n

Explanation:

100-19.99=80.01

she has 80.01 dollars to spend on shirts. The shirts are 11.69 with n being the number of shirts. we have to take off 19.99 because she bought the pants so the total has to be less then 80.

Help, please. I really need help one this

Answers

Answer:

2#) 20f+15-2f

18f+15

2#) choose 1

3#)60-3h-9

51-3h —> 3(17-h)

3#)choose 1

4#) 4(5x+3y)

20x+12y

4#)choose 4

5#) r+3r+ _=6r

6r-4r= 2r

5#)choose 4

Only point (1 ) I didn't know I'm sorry

- Javid bought 3 pairs of Nike Jordan True Flight sneakers
for $127.59 each. He sold 2 pairs of the shoes at a 28%
markup and the third pair for a 52% increase. What did
he sell each pair of shoes for?

- Harris wanted to purchase a pair of Reebok Liquid Speed sneakers for
$190. The price of the sneakers decreased 10% in value each of the next 2 weeks. Harris said that the shoes were 20% less than their original value after 2
weeks. Is Harris correct?

Please help me with these two. I will mark you as brainly

Answers

I’m not surevhcxjjbvcvhhccc
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