Trying to find the length of the robot arm given the xy point along with angle theta and angle theta r
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8a. The length of the robot arm, and the angle in radian and degrees are as follows
length of the robot arm = 30 unitsangle in radian = 7π/6 radian (anticlockwise)angle in degrees = 210 degrees (anticlockwise)8b. The length of the robot arm, and the angle in radian and degrees are as follows
length of the robot arm = 60 unitsangle in radian = π/6 radian (clockwise)angle in degrees = 210 degrees (clockwise)How to find the length of the robot arm and the angles8a
i. let the length of the robot arm be r
The length of the lever arm using the points is done by
r^2 = ( -26 )^2 + ( -15 )^2
r^2 = 676 + 225
r^2 = 900
r = √ 900
r = 30
ii. theta in radian
tan θ = opposite / adjacent
tan θ = y direction / x direction
tan θ = -15 / -26
tan θ = 15/26
θ = Arc tan ( 15/26 )
θ = 29.9816 degrees
θ ≈ 30 degrees
θ ≈ 30 degrees + 180 = 210 degrees
In radian
π = 180 degrees
? = 210 degrees
we cross multiply to get
? * 180 degrees = π * 210 degrees
? = π * 210 degrees / 180 degrees
= 7π/6 radian
8b
i. let the length of the lever arm be r
The length of the lever arm using the points is done by
r^2 = ( -30 )^2 + ( 52 )^2
r^2 = 900 + 2704
r^2 = 3604
r = √ 3604
r = 60.033
r ≈ 60
ii. theta in radian
tan θ = opposite / adjacent
tan θ = y direction / x direction
tan θ = -30 / 52
tan θ = -30/52
θ = Arc tan ( -30/52 )
θ = -29.9816 degrees
θ ≈ -30 degrees (clockwise direction)
In radian
π = 180 degrees
? = 30 degrees
we cross multiply to get
? * 180 degrees = π * 30 degrees
? = π * 30 degrees / 180 degrees
= π/6 radian
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Related Questions
Identify the domain and range of the function. y=x−−√−1
Answers
The domain of the function is [1, ∞) and the range of the function is [0,∞).
Domain and range:
The domain and range of a function are refers the set of all the inputs and outputs a function can give respectively.
Basically, domain takes all the possible input values from the set of real numbers whereas the range takes all the output values of the function.
Given,
Here we have the function
y = √x - 1
Now, here we need to find the domain and range of the function.
The given function is rewritten as,
√x - 1 > 0
Square both sides then we get,
x - 1 > 0
Add 1 on both sides then we get,
x > 1
Therefore, the domain is [1, ∞).
Similarly, let us consider, y ≥ 0
Therefore, the range is [0,∞).
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Divide 6.1 x 10^20 by 3.2 x 10^5. Express your answer in scientific notation.
PLEASE HELP!!!!
Answers
The division of the two numbers in scientific notation is equal to 1.91*10^15
Division of NumbersTo solve this problem, we have to divide the two numbers in scientific notation and to do this, we can simply apply division law of indices here;
We can first divide 6.1 by 3.2.
This will give us 1.90625 which is approximately 1.91.
Then applying the law of indices and subtract the power from one another. This becomes 20 - 5 = 15
The final value will be 1.91 * 10^15
The division of 6.1*10^20 by 3.2*10^5 is equal 1.91 *10^15
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(x ^ 2 + 11x + 18) / (x + 3) =
Answers
Answer:
x+8 - 6/x+3
Step-by-step explanation:
At 30 mph a trip from Town A to Town B takes 6 hours. If the speed were doubled, how many hours would the trip take?
Answers
The time taken by Town A to Town B will be 3 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance traveled by time. The unit of speed in miles per hour.
Given that at 30 mph a trip from Town A to Town B takes 6 hours.
The time taken will be calculated as,
Total distance = 30 x 6 = 180 meters
Speed = 30 x 2 = 60 mph
The time,
T = 180 / 60= 3 hours
Therefore, the time taken by Town A to Town B will be 3 hours.
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4505 x 219 standard algorithm
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After throughfall calculating the multiplication 4505 x 219 in standard algorithm, we have come to find that product is 986595
What is standard algorithm?In elementary math, a standard algorithm or method is a particular computation technique that is typically taught for resolving particular mathematical issues. In general, these techniques include exchanging, regrouping, long division, long multiplication using a standard notation, and standard formulas for average, area, and volume.
These techniques can vary somewhat by country and time, but they typically include these techniques. Similar techniques are also available for more complex functions like square roots, but they are no longer taught in general mathematics classes because calculators are more convenient.
4505 x 219 in standard algorithm is as follows:
⇒ 4 5 0 5
× 2 1 9
4 0 5 4 5
+ 4 5 0 5
+ 9 0 1 0
9 8 6 5 9 5
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You have one box that is 2 and 5 11 feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for 2 and 5 11. If you stack the boxes, about how tall will the stack be
Answers
You have one box that is 2 and 5/11
feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for
2 and 5/11. If you stack the boxes, about how tall will the stack be
we have that
[tex]2\frac{5}{11}=2+\frac{5}{11}=\frac{22+5}{11}=\frac{27}{11}=2.454545\ldots[/tex]If you stack the boxes,
we have
2.45+2.45=4.90 ft
Graph the equation using the slope and the y-interceptY=-8/5x-4
Answers
We got the linear equation:
[tex]y=\frac{-8}{5}x-4[/tex]The slope of this line will be -8/5 and the y-intercept will be -4.
To graph it, first find the intercept with x - axis.
We can find it if we equal the equation to zero.
[tex]\begin{gathered} \frac{-8}{5}x-4=0 \\ \\ -\frac{8}{5}x=4 \\ \\ x=-\frac{20}{8}=-\frac{10}{4}=-\frac{5}{2} \end{gathered}[/tex]Now, we got two points:
[tex](-\frac{5}{2},0),(0,-4)[/tex]To graph the function, we only join these points:
So that's the graph for the function.
A parking garage charges a flat fee of $3 to enter the garage and then an additional hourly
charge to park. The cost to park in the garage can be modeled by the equation: P = 3+c.h
where c is the hourly rate to park and h is the number of hours parked in the garage.
a) Write an equation to find the number of hours a person parked if we know P and c.
b) If c=$2.25, find P if the person parks for 6 hours.
c) If P=$25.50, find how many hours the person parked if the cost per hour is $2.25.
Answers
If the cost to park in garage can be modeled by the equation P = 3+ch
Part A
The equation to find the number of hours a person parked h = (P-3) / c
Part B
If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5
Part C
If P = $25.50, the person parked 10 hours if the cost per hour is $2.25
The flat fee of parking = $3
The cost to park in garage can be modeled by the equation
P = 3+ch
Where c is the hourly rate to park
h is the number of hours parked in the garage
Part A
The equation to find the number of hours a person parked is
P = 3+ch
c × h = P-3
h = (P-3) / c
Part B
c = $2.25
h = 6 hours
P = 3 + 2.25×6
= 3 + 13.5
= $16.5
Part C
P = $25.50
c = 2.25
h = (P-3)/c
= (25.50-3)/2.25
= 10 hours
Hence, if the cost to park in garage can be modeled by the equation P = 3+ch
Part A
The equation to find the number of hours a person parked h = (P-3) / c
Part B
If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5
Part C
If P = $25.50, the person parked 10 hours if the cost per hour is $2.25
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What are the dimensions, a, b, and c, of the net? 13 cm a = v cm b= cm cm 12 cm 15 cm 6 5 cm a с
Answers
Looking at the diagram of the triangular prism and its net, we can see that
a = width of the base = 5 cm
b = the slant height = 13 cm
c = length of the base = 15 cm
The admission fee to an amusement park is $18. It costs an additional "c" dollars to rent a locker to hold your belongings. The total cost for 9 people to
enter the amusement park and each rent a locker is $252. How much does it cost for one person to rent a
Answers
18 x 9=162
252-162=90
90 divided by 9 is 10
What is the slope of the line that contains these points? 9 X 17 13 21 -24 -21 -18 Y - -15 slope:
Answers
We have to use the slope formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (9,-24) and (13,-21). Where
[tex]\begin{gathered} x_1=9 \\ x_2=13 \\ y_1=-24 \\ y_2=-21 \end{gathered}[/tex][tex]m=\frac{-21-(-24)}{13-9}=\frac{-21+24}{4}=\frac{3}{4}[/tex]Hence, the slope is 3/4.Jordan wants to use the Starz princess hall, the Dynamic DJ's as his music And Roscoe's for his equipment. If Jordan has a total of $800 and wants the music to play for 4 hours, how many people can Jordan party?
Answers
The number of people that can attend Jordan's party is 50 people.
How many people can attend Jordan's party?The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.
The form of the linear equation would be:
Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)
$800 = $400 + ($50 x 4) + ($4 x p)
$800 = $400 + $200 + $4p
$800 = $600 + $4p
$800 - $600 = $4p
$200 = $4p
p = $200 / $4
p = 50 people
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Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
Answers
Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.
__________________________________
30 miles / 2 hours = 15 miles/hour
_________________________________________
Answer
15 miles/hour
Are the triangles congruent using AAS?
True
False
Answers
it would be SAS.
ANSWER ONLY A-Ca. what is the students speed from the 3rd to 5th minute?b. at what times during the bike ride did the student come to a stop?c. During what time intervals did the students speed increase?
Answers
SOLUTION:
Case: Distance time graph
Method:
a) the students speed from the 3rd to 5th minute
[tex]\begin{gathered} Speed,s \\ s=\frac{4-2.25}{5-3} \\ s=\frac{1.75}{2} \\ s=0.875miles\text{ }per\text{ }minute \end{gathered}[/tex]b) the times during the bike ride did the student come to a stop
d and h
8 minutes and 23 minutes
c) the students speed increase during.
b to c. 1 and 3 minutes
e to f. 11 and 15 minutes
f to g. 15 and 17 minutes
In AUVW, UW is extended through point W to point X, mZUVW = (3x + 16)°, mZWUV = (2x + 8), and mZVWX= (8x - 18). Find mZWUV.
Answers
Let's draw the figure to better understand the problem.
A print shop borrows $4200 from a credit union for 178 days. The credit union charges simple interest at an annual rate of 6.5% for this loan. Assume each day is 1/365 of a year.
round your final answers to the nearest cent.
A) Find the interest that will be owed after 178 days.
B) Assuming the print shop doesn't make any payments, find the amount owed after 178 days.
Answers
Using percentages, the answer to both the subparts are:
(A) Interest that will be owed after 178 days: $4,336.5(B) Interest after 178 days if sop doesn't repay: $4,473What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.So, since the interest is annual 6.5%:
(A) Interest that will be owed after 178 days:
Interest/2 ⇒ 6.5/2 ⇒ 3.25%Now, 3.25% of 4200:
4200/100 × 3.25 = 136.5$4,336.5(B) Interest after 178 days if sop doesn't repay:
Interest ⇒ 6.5%Now, 6.5% of 4200:
4200/100 × 6.5 = 273$4,473Therefore, using percentages, the answer to both the subparts are:
(A) Interest that will be owed after 178 days: $4,336.5(B) Interest after 178 days if sop doesn't repay: $4,473Know more about percentages here:
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Where ya got 12 from ?
Answers
Answer:
12 is the number that comes after 11 and before 13. 12 represents the number between 11 and 13. 12 is a composite number.
Step-by-step explanation:
12 is the number that comes after 11 and before 13.
12 represents the number between 11 and 13. 12 is a composite number.
however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation
Answers
Explanation:
For the given equation
[tex]50^x=17[/tex]For Erika to resolve the question
Step 1: We will take the logarithm of both sides
[tex]\log (50^x)=\log (17)[/tex]Step 2: Simplify the expression
Thus
[tex]x\log 50=\log 17[/tex]Step 3: Solve for x
[tex]x=\frac{\log 17}{\log 50}[/tex][tex]x=0.724[/tex]differentiate y = (x²-7x)^5 (3x^5-5x)
Answers
The given expression is
y = (x²-7x)^5 (3x^5-5x)
To differentiate, we would apply the product rule which is expressed as
(fg)' = f'g + fg'
Let f = (x²-7x)^5 and g = (3x^5-5x)
f' = 5(2x - 7)(x²-7x)^4
g' = 15x^4 - 5
By applying the product rule, it becomes
y' = 5(2x - 7)(3x^5-5x)(x²-7x)^4 + (15x^4 - 5)(x²-7x)^5
Use the drawing tool(s) to form the correct answer on the provided graph.The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.g(x) = -1/2f(x + 2)
Answers
Given:
The graph of the function f is given and the function g is as:
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]Required:
To graph the function g.
Explanation:
The graph of the function f(x+2), shift the graph f(x) left 2 units by subtracting 2 from the x-coordinates of the points on the graph of f.
The graph of the function
[tex]\frac{1}{2}f(x+2)[/tex]here
[tex]a=\frac{1}{2}[/tex]So the graph of g has undergone a vertical shrinking by a factor of
[tex]\frac{1}{2}[/tex]The graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]reflect the graph of
[tex]\frac{1}{2}f(x+2)[/tex]across the x-axis by multiplying the y coordinate of the points on the graph of
[tex]\frac{1}{2}f(x+2)[/tex]by -1.
Thus the graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]is as:
Final Answer:
The graph of the function g is attached in the explanation part.
Identify the segments that are skew to line EF. There are four answers.
Answers
The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.
The four lines that are skew to line EF are AB, GB, CH, and DC.
What are skew lines?The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.
We have,
A line EF on the given square figure.
We have the following lines on the given figure.
DG, CB, HA, FA, FG, GB, AB, EH, ED, DC,CH,
We see that,
FG, FA, EH, and ED are perpendicular and intersecting to line EF.
DG, CB, and HA are parallel to line EF.
So the remaining lines will be skew to line EF
i.e AB, GB, CH, and DC
Thus,
The four lines that are skew to line EF are AB, GB, CH, and DC.
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Question #36 Multiple-Choice Reduce -2 + b2 by 7 + b2. C5 0 2b2-7 C9
Answers
Answer:
[tex]-2+b^2-7-b^2=-9[/tex]Step-by-step explanation:
Reduce the following expressions:
[tex]-2+b^2-(7+b^2)[/tex]Operate like terms:
[tex]-2+b^2-7-b^2=-9[/tex]can you help please this is really important
Answers
The value of x is 10 and the length of SU is 50.
Here SU is the line and T is the mid-point of the line
So from this we have
SU = ST + TU
ST = TU
SU = 2ST = 2TU
ST = 3x - 5 and TU = 2x + 5
As ST = TU
3x - 5 = 2x + 5
x = 10
SU = 2ST
= 2( 3x - 5)
= 2( 3 × 10 - 5)
= 2( 30 - 5)
= 2× 25
= 50
Therefore the value of x is 10 and the length of SU is 50.
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What does it mean by non collinear points and another name for angle ABD?
Answers
a) Point = could be any point A to D = for example A
b) Line : AD
Could be any line named by the endpoints.
c) Segment: Fragment of a line
AB
d) Ray: part of a line that has a fixed star but no end:
BE
e) Angle : Could be any angle, the middle letter is where the angle rests.
f) 3 collinear points: A,B,C
3 points that are in the same line
g)Opposite rays: same end point but opposite directions
BE and BC
h) Plane: infinite set of points forming a connected flat surface.
ABDC
i) 3 non collinear points: AEC
Three points that aren't on the same line
j) another name for m
BE is the diameter of circle A. What's the measure of ∠BCE?Question 12 options:1) 90°2) 88°3) 180°4) 93°
Answers
Since BCE is an inscribed angle, it measures half the measure of the inscribed arc.
Angle BCE inscribes the arc BE of 180°, we have:
[tex]\begin{gathered} \text{BCE}=\frac{BE}{2} \\ BCE=\frac{180}{2} \\ \text{BCE}=90\degree \end{gathered}[/tex]Therefore the correct option is 1)
Given the function: f(x) = (x − 3)(x + 7)(x − 1)its f-intercept is:its x-intercepts are:
Answers
Given: Given the function: f(x) = (x − 3)(x + 7)(x − 1)
Required: its f-intercept and its x-intercepts.
Explanation:
[tex]f(x)=(x-3)(x+7)(x-1)[/tex]For f-intercept, put x = 0
[tex]\begin{gathered} f(0)=(0-3)(0+7)(0-1) \\ f(0)=21 \end{gathered}[/tex]So the f-intercept is (0,21).
For x-intercepts, put f(x) = 0
[tex]\begin{gathered} 0=(x-3)(x+7)(x-1) \\ x=3,-7,1 \end{gathered}[/tex]So x-intercepts are (3,0),(-7,0) and (1,0).
Final Answer:
f-intercept: (0,21)
x-intercept: (3,0),(-7,0),(1,0).
Given lines l, m and n are all parallel and cut by two transversal lines, find the value of 2. 2 12 6. т х 33 n
Answers
Answer:
66
Explanation:
By the Thales theorem, if we have the following figure:
Then, the following equation applies:
[tex]\frac{a}{c}=\frac{b}{d}[/tex]So, in this case, we can formulate the following equation:
[tex]\frac{6}{12}=\frac{33}{x}[/tex]Then, solving for x, we get:
[tex]\begin{gathered} 6\cdot x=33\cdot12 \\ 6x=396 \\ \frac{6x}{6}=\frac{396}{6} \\ x=66 \end{gathered}[/tex]Therefore, the value of x is 66.
The list price of a DVD player is $129. Sam found the player on sale for $90.30. What was the percent discount?
Answers
A percent discount of 30%
Explanation:
Since $129 represent 100% of the price, then the new price $90.30 represent 70 %
129 * 100 / 90.30 = 70 %
Since from the 100% of the price, it went to 70% of it, there was a discount of 30%
100 - 70 = 30%
The length of the smaller rectangle is 12 inches and the width is x inches. The length of the larger rectangle is 20 inches and the width is 15 inches. What is the area of the smaller rectangle?
Answers
The area of the smaller rectangle is 108 inches².
What is the Area of a Rectangle?The area of a rectangle is calculated to determine the area occupied by the rectangle within its boundary. A rectangle's area (A) is the product of its length 'a' and width or breadth 'b'. As a result, the Area of the Rectangle = (a × b) square units.
Given the dimensions of the smaller rectangle:
Length = 12 inches
Width = x inches
Given the dimensions of the larger rectangle:
Length = 20 inches
Width = 15 inches
To find the value of x we use proportion,
[tex]\frac{12}{x} = \frac{20}{15}[/tex]
Cross-multiplying, we get
12 × 15 = 20x
x = 180/20 = 9
Hence, the width of the smaller rectangle is 9 inches.
Area of the smaller rectangle = length × width
= 12 × 9
= 108 inches²
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