5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.
Answers
9514 1404 393
Answer:
±√58 ≈ ±7.616
Step-by-step explanation:
The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.
|x| = √(3² +7²) = √58
The motion is bounded between positions ±√58.
_____
Here's a way to get to the relation used above.
The sine of the sum of angles is given by ...
sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)
If this is multiplied by some amplitude A, then we have ...
A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)
Comparing this to the given expression, we find ...
A·cos(c) = 3 and A·sin(c) = -7
We know that sin²+cos² = 1, so the sum of the squares of these values is ...
(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²
That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...
x = A·sin(θ +c) . . . . for some angle c
x = (√58)sin(θ +c)
This has the bounds ±√58.
Related Questions
The diagram shows a pyramid with a rectangular base. The volume of the pyramid is 108cm^3.
What is the length of the base edge labeled x?
1. 2cm
2. 6cm
3. 18cm
4. 30cm
Answers
Answer:
Solution given:
Volume of pyramid=108cm³
area of base*height=108cm²
6*x*3=108
x=108/18
x=6
option2:6cm
Alright another here we go, Please help!
Answers
Answer:
4x=y
Step-by-step explanation:
4x=y is your answer because if x is 5, like in the table, then 4(5) would equal 20, which is the y-value. It also works for every number in the table.
Hope this helps.
simplify the following expression
Answers
Answer:
10m^3+10m^2+100m these is the answer to your question
2,1,4,3,6,5,8,___
plz answer this question and solve
Answers
Answer:
2,1,4,3,6,5,8,7
Step-by-step explanation:
Given:
2,1,4,3,6,5,8,___
Pairing the sequence in twos
2,1
4,3
6,5
It can be seen that each pair of the sequence is arranged in descending order (from highest to lowest)
1, 2 is written as 2,1
3, 4 is written as 4,3
5, 6 is written as 6, 5
Then the next two numbers
7, 8 will be written as 8,7
2,1,4,3,6,5,8,7
This histogram represents a sampling of recent visitors to the mall on a Friday night, grouped by their ages.
In which interval is the median located?
40-49
30-39
20-29
10-19
Answers
Answer:
20 - 29
Step-by-step explanation:
Please find the complete question in the attached image
An histogram is a bar-like graph used to represent numerical data. On the y-axis is the frequency of the data and on the x-axis is the data
median is a measure of central tendency. It measures the middle number in a set of observation
there are 20 observations (visitors),
1, 2, 3,5,6, 7, 8, 9,| 10, 11, | 12,13,14,15,16,17,18,19,20
the median is 10 and 11 or 10.50
there are 9 numbers on either sides of 10 and 11
the 10th and 11th visitor would be found in the age group 20 - 29
Besties helpppp please FASTTT
Answers
Answer:
180
Step-by-step explanation:
area of a trapezoid = [tex]\frac{a+b}{2}h[/tex]
where a = base 1
b = base 2
and h = height
This is what we are given
base 1 = 23
base 2 = 37
and height = 6
That being said we plug in the given values into the formula
[tex]A=\frac{37+23}{2} 6\\23+37=60\\\frac{60}{2} =30\\30*6=180[/tex]
Hence the area of the trapezoid is 180 square feet
Use the equation ˆ y = 16.279 − 0.206 x to find the value of ˆ y given x = 48 . Round the result to the nearest tenth.
Answers
Answer:
[tex]y=6.391[/tex]
Step-by-step explanation:
Given
[tex]y=16.279 - 0.206x[/tex]
Required
Find y when [tex]x = 48[/tex]
Substitute [tex]48[/tex] for [tex]x[/tex] in [tex]y=16.279 - 0.206x[/tex]
[tex]y=16.279 - 0.206 * 48[/tex]
Multiply
[tex]y=16.279 - 9.888[/tex]
Subtract
[tex]y=6.391[/tex]
Which ratio is equivalent to 1 to 8?
7 to 14
7 to 9
6 to 41
6 to 48
Answers
6 to 48 simplified
it becomes 1 to 8
so the answer is 6 to 48
plz mark as brainliest
A 6-foot tall man has a 9-foot shadow. At the same time, a tree he is standing next to has a 30-foot shadow.
A. 20 ft
B. 27 ft
C. 45 ft
D. 21 ft
E. 24 ft
Answers
Answer:
A.20 ft
Step-by-step explanation:
the shadow is double the height of the object.
If you have an ant science workbook is increased to 605% as large as its actual size 16 mm what is the size of the ant in the photo
Answers
Answer:
yfguk
Step-by-step explanation:
How do I solve this?
Answers
Answer:
5a-30
Step-by-step explanation:
multiply 5 since its outside by the numbers inside the parethesis
I think it would be (5 × a) + (5 × -6)
A citys annual rainfall totals are normally distributed and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z < 1.5) = 0.0668. If the standard deviation of the city's yearly rainfall total is 1,8 inches, what is the city mean annual rainfall?
Answers
Answer: 40.5
Step-by-step explanation:
A rectangular box has a base measuring a by a meters and height of b meters.
Which of the following represents the surface area of the box?
Answers
Answer:
2a(a+2b) square metres
Step-by-step explanation:
surface area of a box = 2(lw+wh+lh)
l is the length = a metres
w is the width = a mtres
h is the height = b metres
Substitute into the formula
surface area of a box = 2(a*a+ab+ab)
surface area of a box = 2(a² + 2ab)
surface area of a box = 2a(a+2b) square metres
This give sthe surface area of the box
Carlos has $13 in his bank account and writes a check for $22. After the check has been cashed, what will the bank balance show?
Answers
Answer:
Step by step explanation:
13-22=-9
If Jaliya has 5 paintings and paints 6 more how much does she have now?
Answers
Answer:
11
Step-by-step explanation:
5+6
5 + 6= 11
if ur learning multiplication the answer is 30
6 x 5 = 30
what rule should be used to transform a table of a data to represent the reflection of f( x) over the line y = x
Answers
Answer:
according to the question
y=x
p(x,y) reflection p'(y,x)
6
For a movie scene, a stuntman will slide down a wire that is connected from the top of a building to the ground. The wire,
the side of the building, and the ground can be represented as the sides of a right triangle, as shown in the figure below.
Building
600
Wire
70 feet
x feet
The height of the building where the wire is attached is 70 feet. Based on the angle measure in the figure, which of the
following is closest to the value of x?
A-140.0
B-70.0
C-121.2
D-40.4
Answers
Answer:
my best guess would be B for sure
Hi could some PLEASE help me !!!!
Answers
Answer:
3x=78+x-2
Step-by-step explanation:
polynomial test
solve or simplify
-7x(11x+12)
i need help on these
Answers
Answer:
-77x^2 -84x
Step-by-step explanation:
[tex] - {77x}^{2} - 84x[/tex]
just multiply -7 by each number within the parentheses.
Which equation describes the circle
with center (5,-1) and radius 7?
A (x - 5)' + (y +1)* = 7
B (x - 5)* + (y + 1)* = 49
(x + 5) * + (y - 1) = 7
D(x + 5)' + (y - 1)' = 49
Answers
Answer:
B. (x-5)²+(y+1)² = 49
Step-by-step explanation:
An equation of a circle with center (h, k) and radius r is
[tex] \large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }[/tex]
We have all given information we need. Our h is 5 - Our k is -1 and our radius is 7
Substitute these values in
[tex] \large{ {(x - 5)}^{2} + {(y - ( - 1))}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = 49 }[/tex]
So the answer is B choice.
10.
C =
= ✓ [?]
11
С
Find the
missing length.
Pythagorean Theorem: a2 + b2 = c2
Answers
Answer:
Your answer is [tex]\sqrt 221[/tex]
Step-by-step explanation:
[tex]10^2+11^2=c^2\\100+121=221\\c=\sqrt{221}[/tex]
Hope this helps!
A square is split into four
similar squares, one of
the new squares is split
into fourths again, and
this process continues.
What kind of sequence
does this demonstrate?
Answers
Answer:
Geometric Sequence.
Step-by-step explanation:
We are told that the square is split into 4 similar squares. One of the new squares is now split into fourths again and this same sequence is repeated over again.
This means that there is a common ratio which is ¼.
Since there is a common ratio and not common difference, this sequence is said to be a geometric sequence.
Classify the pair of angles shown.
Answers
Answer:
complementary angles
Step-by-step explanation:
The two angles add to 90 degrees, which means they are complementary angles
Nurse Jackson examines immunization records for this past winter at the school where she works. Got flu Didn't get flu Total Vaccinated 120 380 500 Not vaccinated 160 140 300 Total 280 520 800 How many students were not vaccinated and did not get the flu? O A. 300 B. 380 O C. 160 D. 140
Answers
Answer:
140
Step-by-step explanation:
ap3x
Factor the expression completely.
15x2-5x - 10
15x2-5x - 10 =
Answers
Answer:
x=8
Step-by-step explanation:
30-5x-10
-5x+30-10
-5x+40
-5x= -40
divide both sides by -5
-5x/-5= -40/-5
x=8
Calculate the surface area of this cylinder. Use 3.14 for the value of pi.
Answers
Answer:
1884.96 cm squared
PLEASE HELP!!! Will Give Brainliest!! Calculate the limit, if it exists, of the following (pre-calculus problem, please show work)
Answers
What is the equation of the trend line in the scatter plot?
Use the two yellow points to write the equation in slope-intercept form. Write any coefficients
as integers, proper fractions, or improper fractions in simplest form.
Answers
Answer:
y = 5/8x + 9
Hope this helps!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x.
(6x + 1)(5x + 8)
Answers
Answer:
91
Step-by-step explanation:
you add the numbers that are in the () then you times those two numbers together and you will get the answer
If sin 0 = 1/2, find the degree measure of 0.
Answers
Answer:
30°
Step-by-step explanation:
[tex] \sin \theta = \frac{1}{2} \\ \\ \sin \theta = \sin 30\degree \\ \\ \theta = 30 \degree[/tex]