The time the boat is 0.5 m above the mean position during each cycle is (4n + 0.375) s
Since y = f(x) = 0.9sin(πx/2)
We want to determine the time, x at which the boat is 0.5 m above its mean position. This is the value of y at y = 0.5 m
So, y = f(x) = 0.9sin(πx/2)
0.5 = 0.9sin(πx/2)
Dividing through by 0.9, we have
0.5/0.9 = sin(πx/2)
5/9 = sin(πx/2)
Taking inverse sine of both sides, we have
sin⁻¹(5/9) = πx/2
sin⁻¹(0.5556) = πx/2
0.589 rad = πx/2
x = 2 × 0.589/π
x = 1.178/π
x = 0.375 s
Since the boat repeats its cycle every 4 seconds, the time the boat is 0.5 m above the mean position after n cycles is t = (4n + 0.375) swhere n is a positive integer. That is n = 0, 1, 2, 3...
So, the time the boat is 0.5 m above the mean position during each cycle is (4n + 0.375) s
Learn more about sine function here:
https://brainly.com/question/12102275
4. What are the last TWO DIGITS of 2^2017
a Explain how you found the last 2 digits of 2^2017
b. Show how you found the last 2 digits of 2^2017
Compute 2²⁰¹⁷ modulo 100.
From the given table,
2²² ≡ 2⁴² ≡ 2⁶² ≡ 4 (mod 100)
and we have
2017 = 32 • 62 + 33
62 = 1 • 42 + 20
Then
2²⁰¹⁷ ≡ (2⁶²)³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ 4³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ (2²)³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ 2⁶⁴ • 2³³ (mod 100)
2²⁰¹⁷ ≡ 2⁶² • 2²² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 4² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ (2²)² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 2⁴ • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 2¹⁷ (mod 100)
and from the table, we get
2²⁰¹⁷ ≡ 2¹⁷ ≡ 72 (mod 100)
the distance between town A and town B is 123 km. Two buses begin their journey and move directly toward each other. From town A, the bus is moving at a speed of 45 km/hr and from town B, the bus is moving at a speed of 67 km/hr. Assuming the buses started at the same time, find how far is their meeting point from town A?
Answer:
Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Step-by-step explanation:
Let speed of first bus be x mph
Then speed of second bus = x+10 mph.
Let A and B have a distance d.
Then given that faster bus reached in 3.5 hours.
i.e. ... i
THe other bus was away from B by 1/6 times d.
Distance travelled by slower bus = 1-1/6 = 5d/6
Time taken = 3.5 hours
i.e. ... ii
Divide i by ii to eliminate d.
ie Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Use ii equation
miles
If answered correct you will be MARKED BRAINLIEST
Answer:
a^18
Step-by-step explanation:
(a^2 x a^2 x a^2)^3
first, calculate the product inside the parentheses
(a^6)^3
simplify the expression
a^18
Gemma made 106 beaded necklaces . Leah made 145 beaded necklaces.
At a recent craft fair, Gemma sold each of her necklaces for $14. Leah sold each of her necklaces for $10 more. Who made more money at the craft fair? How much more? ( im using my brothers acc and he is 16)
Answer: Leah made more money by 1,996 dollars more than Gemma,
Step-by-step explanation: 1484 is how much Gemma made and 3480 is how much Leah made all you had to do is multiply the total amount of necklaces they sold and the price of each so Leah made more money by 1996 dollars
Given the value of cosine,
Cos 0=1/5
Find the value of sine
Sin(0)=
Answer:
25896
Step-by-step explanation:
Answer number eight please
Answer:
Obtuse triangleStep-by-step explanation:
#8If the square of one side is greater than the sum of squares of other sides, the angle opposite to this side is greater than 90°.
It means the triangle has an obtuse angle, so the triangle is an obtuse triangle.
Yall i need help asap! please help
Sorry, couldn't help in Q. 10
The question seems undefined or I haven't seen this question before.
Write the following phrase as an algebraic expression. Use k for the unknown.
"The product of 20 and a number"
Answer: 20k
Step-by-step explanation: product means to multiply. Use k for the unknown number. 20 times k can be written as 20k.
I will give BRAINLIEST please help
Answer:
-2.43 then -2 2/3 then 2.045 then 2 5/9 that is from least to greatest :) hope this helps
Step-by-step explanation:
i am positive :)
just to make sure you got it i put this in your comments too !
Need some help for Exponents.
1) Five squared
2) Eight to the 5th power
3) Nine cubed
4) 2 x 2 x 2 x 2
5) 7 x 7 x 7 x 7 x 7 x 7
6) 2.3 x 2.3
Find the value of each of the following:
7) 54
8) 132
9) (1.2)2
10) 180
11) 10002
12) 72 x 70
Critical Thinking Applications
13) Mali bought a new car. She drove 63 miles the first month and 64 miles the second month. How much further did she drive the second month? Explain each step.
14) Create an application problem similar to the one above. Solve your problem. Explain each step.
15) In your own words, write three or four sentences explaining what exponents are and how they are used in math.
16) Create and solve 5 problems using exponents.
Answer:
1) 25
2) 32,768
3) 729
4) 16 or 2^4
5) 117,649 or 7^6
6) 5.29 or 2.3^2
Not sure what 7-12 mean
13) 1 mile 64-63=1
14) Mali bought a new car. She drove 63 miles the first month and 100 the second month. How much further did she drive the second month? Explain each step. 37 miles 100-63=37
15) An exponet is a number raised to a power, which means that number times itself that many times. It is used because it's alot easier to go 7^6 than 7x7x7x7x7x7.
16) 8^5= 32,768 6^6= 46,656 5^7= 78,125 5^5= 3,125 4^10= 1,048,576
Step-by-step explanation:
Please help! It’s due today
Solve: 5|9 – 3x|– 7 = 38
Answer:
x = 0
Step-by-step explanation:
if i can get 3 snapple Iced tea. and its 3 for $6 How would it be if i get 2 snapple Iced tea?
explain
Answer:
4 dollars for 2 drinks (2 dollars for 1 drink)
Step-by-step explanation:
Okay, so you can get 3 snapple drinks from 6 dollars. and you want to know the cost of 2 snapple drinks.
3 ÷ 6 = 2
So 1 drink is 2 dollars, if you wanted to buy 2 drinks the cost would be 4 dollars! Have a great day friend! :D
Answer:
$4
Step-by-step explanation:
If 3 Snapple Iced teas cost $6, we can divide 6 by 3 to find the cost for one.
6/3 is 2 and 2 * 2 is 4, so 2 Snapple Iced teas would cost $4.
What is the y-intercept of the graph of the equation y =(2x−3)^2+7
Answer:
(0,16)
Step-by-step explanation:
Hi there!
The y intercept is the value in which the parabola passes through the y axis
Therefore, the value of x at the y intercept is 0
So to find the value of the y intercept, substitute x as 0 in the equation.
y=(2x-3)^2 + 7
If x=0, then:
y=(2(0)-3)^2 + 7
Multiply
y=(0-3)^2 + 7
Subtract 3 from 0
y=(-3)^2 + 7
Raise -3 to the second power
y= 9 + 7
Add 9 and 7 together
y = 16
So the y intercept is the point (0,16)
Hope this helps!
PLS HELPP!! The table shows the progress of Carson and Jayden as they each read books. Carson Jayden Pages Minutes Pages Minutes 8 6 6 97 16 11.5 12 18 20 20 30 What TWO statements are TRUE?
Answer:
Step-by-step explanation:
Help u guys plssss number 8
Answer:
27
Step-by-step explanation:
Note : -
That square like symbol at the intersection of two lines is 90°.
( 4x - 18 )° and 90° are corresponding angles.
Corresponding angles are equal since lines
a & b are parallel.
4x - 18 = 90
4x = 90 + 18
4x = 108
x = 108 / 4
x = 27
(6x + 4) - (3x - 2) simplify
Answer:
9x -2
Step-by-step explanation:
6x + 4 - 3x - 2
6x + 3x +4 - 2
9x -2
Answer:
3x + 4Step-by-step explanation:
(6x + 4) - (3x - 2) simplify
(6x + 4) - (3x - 2)=
6x + 4 - 3x + 2
3x + 6
answer and please show work.
If , a = x + 2y and b = x - 2y , find ( 2a + b ) - ( a - 2b ) , in terms of x and y .
don't give unwanted ans to get the points ~
stay away if u don't know the ans ( no spams and plagiarism )
well explained ans needed ~
Thanks !! ~
question ;
if , a = x + 2y and b = x - 2y , find ( 2a + b ) - ( a - 2b ) , in terms of x and y .
answer with explanation ;
by substituting the value of a and b 2a + b = 2 ( x + 2y ) + ( x - 2y ) = 2x + 4y + 1x - 2y = 2x + 1x + 4y - 2y = 3x + 2y a - 2b = ( x + 2y ) - 2 ( x - 2y ) = x + 2y - 2x + 4y = -1 + 6yi hope my answer helps !!
Answer:
4x - 4yStep-by-step explanation:
Simplify the expression:
( 2a + b ) - ( a - 2b ) =2a + b - a + 2b = a + 3bSubstitute values:
a + 3b = x + 2y + 3(x - 2y) = x + 2y + 3x - 6y = 4x - 4yexpess 756,000,000 in a scientific notation
Step-by-step explanation:
756000000 = 7.56×10⁸.
hope this helps you.
Answer:
7.56 x10^8
.......................................
What is the value of y?
Answer:
40°
Step-by-step explanation:
We know that a triangle is equal to 180°
Since one angle is 50° we can figure out that the rest of the angles are equal to 130° (180° - 50°)
If we use 40° then 2·(40°) = 80°
and the second angle is 40° + 10° = 50°
if we add all the angles (80° + 50° + 50°) we get 180° which is correct.
Find: (4x2y3 + 2xy2 – 2y) – (–7x2y3 + 6xy2 – 2y)
Place the correct coefficients in the difference.
x2y3 +
xy2 +
y
Answer:
final answer: 58xy
Step-by-step explanation:
24xy + 4xy - 2y + 42xy - 12xy + 2y
(24xy + 4xy + 42xy - 2xy) + ( - 2y + 2y)
(24 + 4 + 42 - 12)x xy + ( - 2 + 2)xy
58xy + ( - 2 + 2)xy
58xy + 0y
58xy
Answer:
1st one is 11
2nd one is -4
3rd one is 0
Step-by-step explanation:
no need
you can trust me :)
Hector watched
1
4
of a movie in the morning, and he watched some more at night. By the end of the day, he still had
2
3
of the movie left to watch. How much of the movie did Hector watch at night?
Answer:
how watched 3/4 of the movie
Step-by-step explanation:
I know this because 2 is more then half of 3 and 3 is more then half of 4 so you can come to a conclusion that he watched a total of 3/4 and 2/4 at night.
P.S when ever using a fraction when typing like 1/4 instead of doing
1
4
do 1/4
Drag the numbers to order them from least to greatest.
0.7
-4.5
0.3
-0.5
2.3
Answer:
-4.5, -0.5, 0.3, 0.7, 2.3
Step-by-step explanation:
The higher the negative number the lower it really is.
Answer:
-4.5, -.5, .3, .7,2.3
Step-by-step explanation:
how many teaspoons are in 15 milliliters? 1 tsp = 5 mL
Answer:
The number of teaspoons in 15 ml is 3 tsp.
Step-by-step explanation:
All you have to do is divide 15 by 5 and get 3. This is because for every 5 ml there is 1 tsp. So for the 15 ml, there is 3 tsp.
For each table, write the equation that represents the price per ticket.
Answer:
x=7.5y
Step-by-step explanation:
I took the test
Can some one help me
Answer:
Step-by-step explanation:
Line A:
Mark two points in line A.
(1,3) & ( 2 , 5)
[tex]Gradient =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{5-3}{2-1}=\dfrac{2}{1}\\\\\\= 2[/tex]
Line B:
(0,5) ; (5,0)
[tex]Gradient = \dfrac{0-5}{5-0}=\dfrac{-5}{5}=-1[/tex]
If a = 8 and b = 36 calculate the value of a^(1/3) b^(-3/2)
Answer:
[tex]\frac{1}{108}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^m}[/tex]
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^m}[/tex]
[tex]a^{\frac{1}{3} }[/tex] × [tex]b^{-\frac{3}{2} }[/tex] ← substitute a = 8 and b = 36
= [tex]8^{\frac{1}{3} }[/tex] × [tex]36^{-\frac{3}{2} }[/tex]
= [tex]\sqrt[3]{8}[/tex] × [tex]\frac{1}{36^{\frac{3}{2} } }[/tex]
= 2 × [tex]\frac{1}{(\sqrt{36})^3 }[/tex]
= 2 [tex]\frac{1}{6^3}[/tex]
= 2 × [tex]\frac{1}{216}[/tex]
= [tex]\frac{1}{108}[/tex]
Which table shows the values that would result from using the function machine?
Answer:
A
Step-by-step explanation:
Evaluate f(2). This gives you 2^2 + 1, which is 5. That eliminates C and D.
f(3) = 3^2 + 1 = 10. This must mean that A is the answer.
How many real solutions does the function shown on the graph have?
no real solutions
one real solution
two real solutions
cannot be determined
Answer:
you can find the answer in this link bit.3ckFc
Step-by-step explanation:
no real solution ig
Determine the solution and the reasoning that justifies the solution to the systems of equations.
O (2,7), because this point is true for both equations
O (4, -6), because this point lies only on one of the two lines
(4, -6), because this point makes both equations true
O (2,7), because the lines intersect the x-axis at these points
Answer:
A or CStep-by-step explanation:
The system is not given to give exact answer.
Possible solution is:
A. (2,7), because this point is true for both equations
Yes, same point lies on both lines, it is their intersectionB. (4, -6), because this point lies only on one of the two lines
No, this is not a solution to both equationsC. (4, -6), because this point makes both equations true
Yes, same point lies on both lines, it is their intersectionD. (2,7), because the lines intersect the x-axis at these points
No, this is not confirming any solution