The distance to run to minimize the time needed to reach the island is
3.4 miles
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let x = distance to run.
Remaining distance to the point that is closest to the island = (4 - x) miles.
The distance d to the point x from the island is
using the Pythagorean theorem:
d² = 1² +(4 - x)²
d² = 1 + 16 -8x + x²
d² = 17 - 8x + x²
d = √(x² - 8x + 17)
Total travel time.
= Times running + Time swimming.
Speed = Distance / Time
Time = Distance/Speed
Total time:
T = x/6 + d/3
T = x/6 +√(x² - 8x + 17)/3
Minimized time is when T' is zero.
T' = 0
1/6 + 1/3 x 1/{2(√(x² - 8x + 17)} x (2x - 8) = 0
1/6 + (2x - 8)/6√(x² - 8x + 17) = 0
Multiply 6 on both sides.
1 + (2x - 8)/√(x² - 8x + 17) = 0
√(x² - 8x + 17) + 2x - 8 = 0
√(x² - 8x + 17) = 8 - 2x
Square both sides.
(x² - 8x + 17) = (-(2x - 8))²
(x² - 8x + 17) = (2x - 8)²
x² - 8x + 17 = 4x² - 32x + 64
4x² - x² - 32x + 8x + 64 - 17 = 0
3x² - 24x + 47 = 0
Finding the roots of the quadratic equation.
We get,
x = 3.4 and 4.6
Thus,
The distance to run to minimize the time needed to reach the island is
3.4 miles
Learn more about the Pythagorean theorem here:
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The sum is 14 you have 6 what is the other addend
Answer:
8
Step-by-step explanation:
6 + x = 14
Solve for x
Use Inverse operation
14 - 6 = 8
Meaning the answer would be 8.
PLEASE HELP
how i find b in y=mx+b
the coordinates are (4,2) and (11,18)
Please show your work
THANK YOU
Answer:
b=16/7
Step-by-step explanation:
b= y2-y1/x2-x1
b=18-2/11-4
b=16/7
PLEASE HELP!! NO LINKS
Answer:
Step-by-step explanation:
50 + 5x = 20 + 8x
20 + 8x = 50 + 5x
3x + 20 = 50
3x = 30
x = 10 students
50 + 5(10) = 50 + 50 = $100
answer is D
The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−3.
Find a possible formula for P(x). P(x)=,
In a parallelogram, opposite angles and opposite sides have the same measure. The sides of a parallelogram are 6 cm and 4 cm long, and the angles are 135 degree and 45 degree. What are the lengths of the diagonals?
Answer:
i dont know
Step-by-step explanation:
i dont know
SOMEONE PLEASE HELP ME
Answer:
∠1=55°
Step-by-step explanation:
Since all the angles in a triangle have to add up to 180° we can make an equation
80°+45°+∠1=180°
∠1=55°
Learning Task 2: Solve each proportion
1) 5/12 = 35/ n
2) n/ 52 = 180/ 120
3) 18/n = 21/28
4) n/4 = 24/6
5) 10/16 = n/56
Bonjour,
1) 5/12 = 35/ n
(5/12) /35 = n
5/12 * 1/35 = n
5/420 =n
1/84 =n
2) n/ 52 = 180/ 120
n= (180*52)/120
n=9 360/120 = 936/12 = 78
3) 18/n = 21/28
n = (21/28)/18
n = 21/28 * 1/18
n= 21/504 = 7/168= 1/24
4) n/4 = 24/6
n= 24/6 * 4
n= 96/6 =16
5) 10/16 = n/56
n= 10/16 * 56
n= 560/16
n= 35
epic gamer question i'll mark brainliest
answer this problem with the picutre
Answer:
75
Step-by-step explanation:
If we go from the bottom to the line that averages the sold cones by temperature (I forget its exact name), and then go to the left from that exact spot, it appears to be 75 cones.
work out angle x and y
Answer:
Angle y = 60°
Angle x = 65°
Write y - 3 = 1/3(x - 12) in standard form
Step-by-step explanation:
y-3=1/3x -4
add add four
y+1=1/3x
divide 1/3 into 1
y+3=x
Answer:
x - 3y = 3
This is the answer in standard form.
It takes Rick, traveling 36mph, 40 minutes longer to go a certain distance than it takes Evelyn traveling at 84mph. Find the distance traveled
d = r · t and we know that the distance is the same.
Let x = time it takes Evelyn (in hours, since the rate is mph).
Evelyn's distance is 84x.
Rick's distance is 36·(x+2/3) since 40 minutes longer is 2/3 of an hour longer
84x = 36(x+2/3)
84x = 36x + 24
48x = 24
x = 1/2
So it takes Evelyn 1/2 an hour, meaning the distance is 84(1/2) = 42 miles
To confirm this, it would take Rick 42/36 hours or 1 and 1/6 hours. That's 70 minutes, which is 40 minutes longer than Evelyn's 1/2 hour trip.
The distance is 42 miles.
Tricia wants to install a decorative wall paper
border around the top of the wall in her master
bedroom. The room measures 13ft by 21ft.
How many feet of the border will will she
need?
Answer:
68 ft
Step-by-step explanation:
this problem is asking for perimeter so instead of LxW
you would do L+L+W+W
(13 + 13 + 21 + 21) = 68
solve for x and y then find the measurement of each angle
Answer:
x = 10
y = 40
Step-by-step explanation:
DE is a straight line so the sum of angles DBA and ABE is equal to 180
13x - 18 + 5x + 18 = 180 add like terms
18x = 180 divide both sides by 18
x = 10
Same rule applies when calculating value of y
3y - 52 + 2y + 32 = 180 add like terms
5y - 20 = 180 add 20 to both sides
5y = 200 divide both sides by 5
y = 40
How many ways can 7 students be selected from an organization of 30 to attend a national conference?
Determine the number of possibilities for selection. Express your solution in a complete sentence reflective of the scenario.
The number of possibilities for selection is 2,035,000 ways
This question has to do with the combination
Given the following parameters
Total number of students = 30 students
If 7 students are to be selected from a pool of 30 students, the number of ways this can be done is expressed as:
30C7 = 30!/(30-7)!7!
30C7 = 30*29*28*27*26*25*24*23!/23!*7!
30C7 = 30*29*28*27*26*25*24/7!
30C7 = 10,260,432,000/5040
30C7 = 2,035,800
This shows that the number of possibilities for selection is 2,035,000 ways
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no need for explanation
Answer:
Step-by-step explanation:
iii) ∠AOE + ∠DOE + ∠DOB = 180 {Straight line angles}
67 + ∠DOE + 100 = 180
∠DOE = 180 - 167
∠DOE = 13°
ii) ∠BOC = ∠AOD {Vertically opposite angles}
∠BOC = ∠AOE + ∠DOE
= 67 + 13
∠BOC = 80°
i) ∠AOC = ∠BOD
∠AOC = 100°
Which equation represents this statement?
23 times a number is 65
23=n+65
23n=65
23+n=65
23=65n
Answer:
The correct equation is 23n=65
Step-by-step explanation:
23n=65 means a number 'n' multiplied with 23 gives you the product 65.
What is a negative slope and passes through the
origin?
Answer:
A negative slope is for the line running in opposite ways (downwards). And it cannot pass through the origin.
[tex]{ \underline{ \mathfrak{ \green{Good \: grace}} \: \:⚜ \: \: { \blue{ \mathfrak{Good \: God}}}}}[/tex]
Which scenario provides the most direct application of the Hypotenuse-Leg congruence criteria?
A.) two isosceles triangles congruent bases and base angles
B.) two equilateral triangles, each of which has 60 angles and 3-inch sides
C.) two 45 degrees -45degrees-90degrees triangles with congruent sides opposite to the right angle
D.) two right angles, each of which has a 4-foot side opposite the right angle and a 3-foot leg
The Hypotenuse-Leg congruence criteria is (D) two right angles, each of which has a 4-foot side opposite the right angle and a 3-foot leg
Two triangles are said to be congruent if they have the same size and shape. Hence, corresponding sides and angle are congruent to each other.
The Hypotenuse-Leg congruence theorem states that two right triangles are congruent if the hypotenuse and leg of one triangle is equal to the hypotenuse and leg of another triangle.
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Someone help for #36 please
A new company president is said to have caused the company "to do a 180." Before the new president, the company was losing 10,000 per month .What is the company most likely doing under the new president?
Answer:
Earning 10,000 per month.
Step-by-step explanation:
Since a "180" usually refers to an opposite, the opposite of "losing 10,000 per month" would happen.
So, the company would be earning money instead of losing money.
7.) six hundred thousand forty nine and eleven thousandths how do I write in standard form
Answer: Un alambre de acero de 1.5 m se estira 2.0 mm con fuerza F. El diámetro del alambre de acero es 4.0 mm. El módulo de Young del acero es 2.0 x 1011 Nm-2. Determine la fuerza F aplicada sobre el alambre.
Step-by-step explanation:
Find (gxf) when f(x)=5x-7 and g(x)=2x+3
Answer:
10[tex]x^{2}[/tex]+x-21
Step-by-step explanation:
you just do (5x-7)(2x+3) and foil it out
Please answer
A=
B=
C=
Answer:
I can't see the file
Step-by-step explanation:
PLEASE HELP ME NO LINKS PLEASE
Answer:
Step-by-step explanation:Class 1 :
mean= 78.83(rounded) median=88 range= 55
Class 2:
mean= 79.42 (rounded) median=85.5 range= 60
Class 3:
mean= 79.42 (rounded) median=78 range =45
Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example 3(a). (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P (x) = 2x^4 - x^3 - 10x^2 + 3x +10
A sprinter finished a 100-meter race in a time of 12.63 seconds.
If the sprinter were able to keep the same rate of speed, how long
would it take him to complete the 10,000-meter race?
Answer:
1263 seconds
Step-by-step explanation:
100 meters = 12.63 seconds
multiply both sides by 100 since
100*100= 10,000 meters
12.63*100= 1263 seconds
26:
= α : 8
18:x= x:8
Answer:
,=your head
Step-by-step explanation:
thanks for the points bye bye
Here are fractions A) 2/5 B) 2/3 C) 1/4 D) 1/4
Answer:
0.5 can also be written as 1/2 so we can eleminate the ones that are greater than 1/2 and put them ahead of 0.5 on the number line.
Since 2/3 is approximately 0.666666666666 we can put that above 0.5
2/5=0.4
1/4=0.25
1/10=0.1
Knowing this... The answer is D,C,A,B
Hope this helps
Have a nice day!!
Please give brainliest :D
[tex]8 \frac{1}{9} - 6\frac{7}{8}[/tex]
let's firstly convert the mixed fractions to improper fractions, and then subtract.
[tex]\stackrel{mixed}{8\frac{1}{9}}\implies \cfrac{8\cdot 9+1}{9}\implies \stackrel{improper}{\cfrac{73}{9}}~\hfill \stackrel{mixed}{6\frac{7}{8}}\implies \cfrac{6\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{55}{8}}\\\\[-0.35em]~\dotfill\\\\\cfrac{73}{9}-\cfrac{55}{8}\implies \stackrel{\textit{using}\stackrel{LCD}{72}}{\cfrac{(8\cdot 73) - (9\cdot 55)}{72}}\implies \cfrac{584-495}{72}\implies \boxed{\cfrac{89}{72}\implies 1\frac{17}{72}}[/tex]
