Answer:
a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex]
b) Hence the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a meter is 5.5 meters
Step-by-step explanation:
a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :
[tex]x^2 + (y-yc)^2 = R^2[/tex] ,
where
R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)
= 14 m / 2
= 7 m (radius of the circle)
Also, center of the circle will be at (0, 2 + R) i.e (0,9)
So, is the trajectory path equation to the circle
Let [tex]x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi)[/tex] be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t
At t= 10s, y = 16 m so we have,
[tex]9 + 7 * sin(10* w + \phi) = 16[/tex] ---------------(1)
Also, at t= 25s, y =2 m so we have,
[tex]9 + 7* sin(25 * w +\phi) = 2[/tex]--------------(2)
Solving we have, [tex]10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2[/tex]
[tex]15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6[/tex]
Therefore [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex] is the instantaneous height of the pink short at time t ( in seconds)
b) At t= 10minutes = 10 * 60 s = 600s, we have,
[tex]y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)[/tex]
= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)
A textbook store sold a combined total of 331 physics and sociology textbooks in a week. The number of sociology textbooks sold was 45 less than the number
of physics textbooks sold. How many textbooks of each type were sold?
Answer: Number of sociology books sold = 143 books
Number of physics books sold = 143 + 45 = 188 books
Step-by-step explanation:
Let us take the number of sociology books sold = x
Number of physics books sold = x+45
So now we can form an equation
x+x+45 = 331
2x+45 = 331
2x = 331-45
2x = 286
x = 286 ÷ 2
x = 143
In XYZ, what is the cosine ratio of X?
Answer:
c) 12/15 = 4/5
Step-by-step explanation:
imagine we mirror the triangle up, so that Z is on top.
then you can clearly see that 6 is cos(X) times r (and r is then 7.5).
XY is sin(X)×7.5
and again, 7.5 is r (the line making the X angle).
so, the cosine ratio of X is
6 = cos(X)×7.5
cos(X) = 6/7.5 or then 12/15. or simplified 4/5.
Vanessa and her friends are watching three movies consecutively. The first movie is 2 hours and 17 minutes long. The second movie is 84 minutes long, and the last movie is 99 minutes long. How much time will they spend watching the movies?
Answer:
320 minutes (5 hours and 20 minutes).
Step-by-step explanation:
2 hours and 17 minutes = 137 minutes
137 + 84 + 99 = 320
Therefore, they will spend 320 minutes (5 hours and 20 minutes) watching movies.
Which expression is equivalent to the expression 10.5 - 7.5 + 12?
�� 10.5 + 7.5 + 12
�� 7.5 - 10.5 + 12
�� 10.5 + (-7.5) + 12
�� 10.5 + (-12) + 7.5
Answer:
The 3rd one, 10.5+(-7.5)+12
Step-by-step explanation:
If something is +(-), the answer is minus.
So therefore 10.5-7.5+12 would be our answer
Which is equivalent to the original expression
Hope this helps!
urgent help needed
help me with the question of o.math
That's the solution to that question
Find the accumulated value of an investment of $10,000 for 7 years at an interest rate of 5.5% if the money is a. Compounded semiannually;b. Compounded quarterly; c. Compounded monthly; d. Compounded continuously
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Annual interest rate (i)= 0.055
Initial investment (PV)= $10,000
Number of years (n)= 7
To calculate the future value (FV), we need to use the following formula (except in d):
FV= PV*(1+i)^n
a.
Semiannual interest rate= 0.055/2= 0.0275
Number of semesters= 7*2= 14
FV= 10,000*(1.0275^14)
FV= $14,619.94
b.
Quarterly rate= 0.055/4= 0.01375
Number of quarters= 7*4= 28
FV= 10,000*(1.01375^28)
FV= $14,657.65
c.
Monthly interest rate= 0.055/12= 0.0045833
Number of months= 7*12= 84
FV= 10,000*(1.0045833^84)
FV= $14,683.18
d.
To calculate the future value using continuous compounding, we need to use the following formula:
FV= PV*e^(n*i)
FV= 10,000*e^(7*0.055)
FV= $14,696.14
Match the stem and leaf plot
to the correct set of data.
Franco made a dozen muffins for his party upon taking them out he noticed two of the muffins were badly burned Franco served 7/
10 of the remaining muffins which Equation shows the fraction of the non-burned muffins that remain.
Total muffins = 12
Burned muffins = 2
not burned = 10
Total served = 7/10
= 7 muffins
So
10 - 7/10
3 unburned muffins left
Fraction = 3/10
Must click thanks and mark brainliest
Its awpicture please help if you can
8tbsp. 2tsp.
x 15
_________
Solve this system of equations with matrices. x – 5y – 4z = 15 -3x +2y + 3z = -6 4x + 8y – 2z = 3
Answer:
x = 59/10, z = 237/70, and y = -121/70
Step-by-step explanation:
How much of a circle does a 100-degree angle turn through?
A.1
B.100/180
C.50/360
D.100/360
Answer:
100/360
Step-by-step explanation:
A circle is 360 degrees
100/360
10/36
5/18
(6 1/4)^4
Answer fast or i will report you
Answer:6
Step-by-step explanation: The rules of exponential says (a^x)^y=a^xy.
Therefore you will multiply 1/4 with 4 to get an exponent of 1. So the answer is 6^1 which is also written as 6
What is the product of 2x and 4x2−3xy+y2?
A.6x3−x2y+xy2
B.8x3−6x2y+2xy2
C.2x3−x2y−xy2
D.6x3−5x2y+2xy2
E.−8x3+6x2y−2xy2
Please help
[tex]\bf \large \rightarrow \: \:2x \: \: ( \: 4 {x}^{2} \: - \: 3xy \: + \: {y}^{2} \: )[/tex]
[tex]\bf \large \rightarrow \: \: 8 {x}^{3} \: - \: 6 {x}^{2}y \: + \: 2x {y}^{2} [/tex]
Option ( B) is the correct answer
Help fast!
Describe at least two ways to find or
estimate the year the population of the town
will be 40 thousand. (You don't have to
actually find the value.)
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞
Answer:
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Step-by-step explanation:
The minimum value of the curve = (1.9, -5.7),
The maximum value = (0, 2)
The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)
The point the function crosses the y-axis (the y-intercept) = (0, 2)
The given points can be plotted using MS Excel, from which we have;
F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5
The correct option is therefore, F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)
Answer:
A. F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
Step-by-step explanation:
Write 0.2 repeating as a fraction in simplest form (The 0.2 is repeating, so the 2 has the repeating bar above it, just need someone to solve this, it would help a lot thanks.)
If x is the number 0.222…, then 10x = 2.222…. Subtracting x from 10x eliminates the fractional part, so that
10x - x = 2.222… - 0.222…
==> 9x = 2
and solving for x gives x = 2/9.
(ii) Differentiate x2 + 3x -4.
Answer:
2x +3
Step-by-step explanation:
d/dx(x2 + 3x -4)
d/dx (x^2) + d/dx(3x)- d/dx(4)
2x +3 -0
2x +3
what must be added to a + b to get a
Answer:
we have to add (-b) to get (a)
Step-by-step explanation:
a+b+(-b)=a
a+b-b=a
a=a
Hence verified.
Hope this helps you. Have a nice day^_^
which equations have a leading coefficient of 3 and a constant term of -2?
Answer: the answer to this is 3x-2
Step-by-step explanation:
Find the missing value.
Hint: Use the number line to find the missing value.
-5 = -8-
H
-15
-10
-5
0
5
10
15
Stuck? Review related articles/videos or use a hint.
Answer:
-3
Step-by-step explanation:
-8 - x =-5
I hope this helped! :)Plssss help me with this question!!!!
[tex]\\ \sf\longmapsto x+14+x=32[/tex]
[tex]\\ \sf\longmapsto 2x+14=32[/tex]
[tex]\\ \sf\longmapsto 2x=32-14[/tex]
[tex]\\ \sf\longmapsto 2x=18[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{18}{2}[/tex]
[tex]\\ \sf\longmapsto x=9[/tex]
help me, thank you!!!
Answer:
Step-by-step explanation:
i don't understand this language but i think you want to simplify it.
[tex]\frac{3x-3\sqrt{x} -3}{x+\sqrt{x} -2} -\frac{\sqrt{x} +1}{\sqrt{x} +2} +\frac{\sqrt{x} -2}{1-\sqrt{x} } \\=\frac{3x-3\sqrt{x} -3}{x+2\sqrt{x} -\sqrt{x} -2} -\frac{\sqrt{x} +1}{\sqrt{x} +2} -\frac{\sqrt{x} -2}{\sqrt{x} -1} \\=\frac{3x-3\sqrt{x} -3}{\sqrt{x} (\sqrt{x} +2)-1(\sqrt{x} +2)} -\frac{(\sqrt{x} +1)(\sqrt{x} -1)+(\sqrt{x} +2)(\sqrt{x} -2)}{(\sqrt{x} +2)(\sqrt{x} -1)} \\=\frac{3x-3\sqrt{x} -3}{(\sqrt{x} +2)(\sqrt{x} -1)} -\frac{(x-1)+(x-2)}{(\sqrt{x} +2)(\sqrt{x} -1)} \\[/tex]
[tex]=\frac{3x-3\sqrt{x} -3-2x+3}{(\sqrt{x} +2)(\sqrt{x} -1)} \\=\frac{x-3\sqrt{x} }{(\sqrt{x} +2)(\sqrt{x} -1)}[/tex]
Mr. Johnston needs a shelf to hold a set of textbooks, each 1 3/4 in. Wide. How many books will fit on a 35-in.-long shelf?
Answer:
20 books
Step-by-step explanation:
35/1.75
20
FIND THE AREA OF THE SHADED REGION.
This problem can be a bit confusing, so let's break it down:
First, let's take the area of the square (A = b · h):
A = 15 · 15
A = 225 cm²
Now comes the confusing part:
We can tell that the non-shaded area is 1/4 of a circle, so, if we take 1/4 of the area of a circle, we can subtract its area from the area of the square:
A = πr²
A = 15²π
A = 225π
1/4 A = 225π / 4
New Area = 56.25π
Or... about 176.7
Since we have both of the areas, all we have to do is subtract:
225 - 176.7 =
48.3.
Your final answer is 48.3 cm²
This is a scale drawing of a house where 1 centimeter represents 0.6 meters. What is the height of the house at its highest point? Round to one decimal point, if necessary.
Answer:
Height of the house = 3 meter (Approx.)
Step-by-step explanation:
Given:
Scale model;
1 centimeter = 0.6 meter
According to graph
Height of cube = 5 cube = 5 centimeter
Find:
Height of the house
Computation:
Height of the house = height of the house in scale model x Scale model
Height of the house = 5 x 0.6
Height of the house = 3
Height of the house = 3 meter (Approx.)
Justin is saving money to buy a stereo. He has $25 saved in the bank right now. He earns $40 each week delivering newspapers.
Let y = the total amount of money Justin has, and x is in weeks.
Slope -1/4, passes through (12,-4)
Answer:
y = - [tex]\frac{1}{4}[/tex] x - 1
Step-by-step explanation:
Assuming you require the equation of the line
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
To find c substitute (12, - 4) into the partial equation
- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1
y = - [tex]\frac{1}{4}[/tex] x - 1 ← equation of line
Solve for y, given that b=22(Round your answer to 1 decimal place, if necessary.)
Answer:
37.7
Step-by-step explanation:
First, we have to divde 22/7 to find the scale factor. I chose 22 and 7 because those two sides are ocngruent. We get 3.14. We then have to multiply 12 by 3.14 beacuse that is the side that is congruent with the side y. When you multiply you should get 37.68. Since we have to round we get 37.7.
find the supplement of 3/4 of a right angle
Answer:
Step-by-step explanation:
¾*90=67.5
180-67.5=112.5°
Answer:
60°
Step-by-step explanation:
You can see the explanation in the picture
