Answer:
100-89/100=11/100
=0.11
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?
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)
HURRYYY
Which expression is equivalent to E
1 (3),
n=10
15
15
3
Ση + Σ
=10 η = 10
31
O
15
15
15
Ση + Σ3 - Ση
h=10
h=10
η=10
15
3
Ο η Σ
η
η =10
Σ
8
15
3
Ση
η
η=10
Answer:
the first one
Step-by-step explanation:
it is really easy to see in this case.
the main formula is just a sum of a sum.
anything you just add you can split in its parts and then sum it all up - it is still the same.
so, the sum of (n + 3/n) can be split without any additional tricks into the sum of n and the sum of 3/n, and then add both results together.
the second option is wrong, because a division cannot be split like an addition. just try the first two elements (n=10 and n=11) for the simplified formula of the sum of (3/n). 3/10 + 3/11 is definitely not the same as (3 + 3) / (10 + 11).
the third and fourth option are already disqualified, because "n" assists outside of the sum operation (but "n" is only defined inside of it).
What is the image of (-9,9) after a dilation by a scale factor of 2 centered at the origin? (Will mark correct answer brainliest)
Answer:
Is this a line on a graph with point for x,y.
Step-by-step explanation:
-9 is x and 9 is y
HII GUYS DON'T WORRY I ONLY HAVE 3 MORE QUESTIONS LEFT I'M SO SORRY FOR BOTHERING YOU GUYS I'M SORRY THANK YOU FOR THE PEOPLE WHO HELP ME. <3
Answer:
Hello! answer: 96
Step-by-step explanation:
I will find the area of each face separately and add them up so... for the triangles those would both be 6. the rectangle on the bottom would be 28 and the rectangle standing up would be 21 now for the triangle on top that would be 35. now we would just add these up so...
6 + 6 + 28 + 21 + 35 = 96 Therefore the surface area is 96 Hope that helps!
0.1 X 4 is the same as 1 tenth of 4 Write this expression with a fraction instead of a decimals and then solve it.
Answer:
2/5
Step-by-step explanation:
0.1 × 4
= 1/10 × 4 = 4/10
= 2/5
I need help finding the slope G and J
Answer:
[tex]-\frac{5}{2}[/tex]
Step-by-step explanation:
G(-6 , 2) = (x1 , y1)
J(-4 , -3) = (x2 , y2)
slope = y2 - y1/x2 - x1
=-3-2/-4-(-6)
=-5/-4+6
=-5/2
Write an exponential function in the form y=ab^x that goes through the point (0,17) and (6,1088)
Answer:
y = 17(2)^x
Step-by-step explanation:
If the graph of y = ab^x goes through (0, 17), then
17 = ab*0, or a = 17
Then the function is y = ab^x with a = 17, or
y = 17*b^x and we must find b.
If the graph of y = 17*b^x also goes through (6, 1088), then the following must be true: 1088 = 17*b^6
which reduces to 64 = b^6
Taking the sixth root of both sides, we get 64^(1/6) = b, and so b = 2
Then the desired exponential function is
y = 17(2)^x
can you guys help me fill the right angle measures
Answer:
3 = 20
5 = 20
8= 160
Step-by-step explanation:
angle 2 and 3 are on the same line, so 180 - 160 is 20 degrees
rule of alternate interior angles: angle 5 is equal to 3
rule of alternate exterior angles: angle 8 is equal to 2
Se ha determinado que la población P (t) de una colonia de bacterias, t horas después de iniciar la observación, tiene una razón de cambio de P'(t) = 350 e0.18t + 220 e-0.3t. Si la población era de 250,000 bacterias cuando se inició la observación, ¿Cuál será la población20 horas después?
Answer:
La población 20 horas después será de 321,161 bacterias.
Step-by-step explanation:
t horas después de iniciar la observación, tiene una razón de cambio de P'(t) = 350 e0.18t + 220 e-0.3t.
Esto implica que la población después de t horas viene dada por:
[tex]P(t) = \int P^{\prime}(t) dt[/tex]
[tex]P(t) = \int (350e^{0.18t} + 220e^{-0.3t}) dt[/tex]
Teniendo en cuenta que
[tex]\int e^{at} dt = \frac{1}{a}e^{at}[/tex]
[tex]P(t) = \int (350e^{0.18t} + 220e^{-0.3t}) dt[/tex]
[tex]P(t) = \frac{350}{0.18}e^{0.18t} - \frac{220}{0.3}e^{-0.3t} + K[/tex]
En que k es la población inicial, o sea, [tex]K = 250000[/tex]. Entonces
[tex]P(t) = 1944.44e^{0.18t} -733.33e^{-0.3t} + 250000[/tex]
¿Cuál será la población 20 horas después?
Esto eres P(20). Entonces:
[tex]P(20) = 1944.44e^{0.18*20} -733.33e^{-0.3*20} + 250000 = 321161[/tex]
La población 20 horas después será de 321,161 bacterias.
How many solutions exist for the system of equations graphed below?
Help please !
Answer:
none (0) ...
think of two lines (or chop sticks places on a table) ...
there are three (3) possible orientations that they can be in.
1) they cross each other at one point
2) they are on top of each other (they touch everywhere)
3) they are side by side (parallel)
in situation one we say we have a solution
in situation two we say there is an infinite solutions (the same line)
in situation three (your problem) we say there is no solution (parallel lines)
Step-by-step explanation:
Answer:
none
Step-by-step explanation:
Write 120 as a product of primes.
Use index notation
Answer:
2³×3×5
Step-by-step explanation:
_______________
pls help me i don't know what to do
Answer:
C
Step-by-step explanation:
the size of the steps gives you the number before x
and the -1 , +4 is just what left when x equals zero, so in the two tables we find it in row two
Que sucede al estudiar el comportamiento del coseno (en triangulos no rectangulos) de la misma forma que estudamos el seno?
Answer:
En contraste con el seno, el coseno permite diferenciar triángulos obtusángulos de triángulos acutángulos.
Step-by-step explanation:
Por Geometría Euclideana sabemos que la suma de todos los ángulos internos de un triángulo es igual a 180°, si el triángulo no es rectángulo, entonces acutángulo o obtusángulo.
Un triángulo es acutángulo cuando todos sus ángulos son agudos, es decir, cuyas medidas sean mayores que 0° y menores que 90°, mientras que un triángulo es obtusángulo cuando uno de sus ángulos es mayor que 90° y menor que 180° y los dos ángulos restantes son agudos.
El seno es una función periódica y acotada entre -1 y 1, que es positiva entre 0° y 180°, significando que esta función trigonométrica es demasiado "débil" para diferenciar a un triángulo obtusángulo de uno acutángulo. En cambio, el coseno es una función periódica y acotada entre -1 y 1, que es positiva entre 0° y 90°, y negativa entre 90° y 180°, convirtiéndola en un criterio "fuerte" para diferenciar triángulos obtusángulos de triángulos acutángulos.
given an = -4 + (n - 1)7. what is arithmetic sequence
Answer:
Step-by-step explanation:
The given an = -4 + (n - 1)7 is already an arithmetic sequence with first term -4 and common difference 7. A more proper form would be an = -4 + 7(n - 1).
The first five terms of this sequence are {-4, 3, 10, 17, 24}
a right cone with base circumference 14 pi ft
and slant height 3 times the radius. Give answer in terms of pi
the answer is a batty fish with a Somali forehead
Which type of function best models the given data?
Answer:
3)
Step-by-step explanation:
Draw the graph and youll see
Answer:
Exponential growth function
Step-by-step explanation:
It multiplies by 3 each time
A total of 573 tickets were sold for the school play. They were either adult tickets or student tickets. There were 73 more student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
146 adult tickets were sold
Step-by-step explanation:
subtract 73 from 573 which = 500
then you'll take away 500 from 73 =427
then you will subtract 427 from 573= 146
One number is 9 times another. Their product is 27 times their sum. Find the numbers.
the answer is 3
.............. .......
Will mark brainly thanks
Answer:
The 8th term of the sequence is 255
Step-by-step explanation:
To find the 8th term of the sequence, we have to use the given sequence formula
All we have to do here is to make a substitution
We simply have to substitute the value 8 for n as follows;
a8 = 2^8 - 1
a8 =256-1
a8 = 255
2. A ramp is needed at the entrance of a supermarket. The ramp is to be 6.7 m long
and have a rise of 0.3 m. Calculate the angle of inclination of the ramp to the nearest
tenth of a degree.
Answer:
∅ = 2.6º
Step-by-step explanation:
sin = opp/hyp
sin∅ = 0.3/6.7
∅ = arcsin0.3/6.7
use calculator
∅ = 2.6º
you stand 25m from the base of a tree and the angle of elevation from the ground to the top of the tree is 48 degrees. How tall is the tree?
Answer:
The tree is about 27.77 meters tall
Step-by-step explanation:
I attached a helpful sheet that explains all my work visually.
13. You are going camping. The cost for renting a cabin at
Shady Knoll Campground at $65.00 plus $12.00 per person.
The cost in dollars is
I
C(n) = = 12n + 65, where n is the number of people.
Answer:
The function is correct, I just don't see a question.
Step-by-step explanation: 6 21 6 10
C(n) = 12n + 65
I will make up a question. How much will it cost 4 people each to rent the cabin?
C(n) = (12n + 65) / n n = 4
= (12 × 4 + 65) / 4
= (48 + 65) / 4
= 113 / 4
= $28.25
If your question is differnt just substitute the number of people into the question and solve for C(n)
The width of classroom is 4 meters less than the length, and the area is 192m^2. If the length is x m, find an equation in x and hence, find the dimensions of the classroom
Step-by-step explanation:
x(x-4) = 192
the Equation:
x²-4x -192 =0
=> (x-16) (x+12) =0
x= 16 or x= -12
since the x should be a possitive, so x = 16
the dimension :
the length = 16 m
the width = 12 m
Work out the area of the garden. HELP ASAP i’ll make u brainliest ♡︎
Answer: 120m2
Step-by-step explanation:8x11=88
19-11=8- length of triangle base. 1/2 base x height= 4x8=32
32+88=120m2
Step 4: Calculate the result:
63,756 60
miles / hour
70.5,280
Answer:
10.35miles/hour
Step-by-step explanation:
(63,756 x 60)/ (70 x 5,280) = (3,825,360/369,600) = 10.35
(Application of division)
Answer:
10.35 mph
Step-by-step explanation:
(63,756 times 60) / (70 times 5280) in calculator is equal to 10.35
please help!
For each sentence, drag a word that will make the statement true.
Words may be used once or more than once.
Equilateral triangles are ___
acute triangles.
Scalene triangles are ___
acute triangles.
Right triangles are ___
acute triangles.
Obtuse triangles are ___
isosceles triangles.
Answer:
Equilateral triangles are sometimes
acute triangles.
Scalene triangles are never
acute triangles.
Right triangles are never
acute triangles.
Obtuse triangles are always
isosceles triangles.
Does anyone know this???
Answer:
Step-by-step explanation:
a)
median= 25
interquartile range= 19
b)
On average The Braineys was the slowest at completing the test because they have a median time of 32 minutes whereas The Cleverites have a median time of 25 minutes.
check whether 7+3x is a factor of 3x^3+7x
Answer:
no
Step-by-step explanation:
refer to picture for solution
bank reduces the interest rate from 12% p.a. to 10% p.a to expand its business. By how much is the yearly interest on Rs. 8,400 decreased?
Answer:
$168
Step-by-step explanation:
yearly interest = principal x time x interest rate
interest when interest rate is 12% = 8400 x 0.12 = 1008
interest when interest rate is 10% = 8400 x 0.1 = 840
decrease in interest rate = 1008 - 840 = 168
solve it !!
[tex]\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed {\boxed {\boxed{ \boxed{ \sqrt{ \frac{8}{2} } }}}}}}}}}}}}}}}}}}}[/tex]
Simplify 8/2 :
8/2 = 4
Now you have sqrt(4)
Sqrt(4) = 2
The answer is 2