In the diagram below, assume that all points are given in rectangular coordinates. Determine the polar coordinates for each point using values of rr such that r≥0 and values of θ such that 0≤θ<2π. Visually check your answers to ensure they make sense.
(x,y)=(2,5) corresponds to (r,θ)=
(x,y)=(−3,3) corresponds to (r,θ)=
(x,y)=(−5,−3.5) corresponds to (r,θ)=
(x,y)=(0,−5.4)corresponds to (r,θ)=
Answers
Step-by-step explanation:
We have cartisean points. We are trying to find polar points.
We can find r by applying the pythagorean theorem to the x value and y values.
[tex]r {}^{2} = {x}^{2} + {y}^{2} [/tex]
And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.
[tex] \tan(x) = \frac{y}{x} [/tex]
Remeber since we are trying to find the angle measure, use inverse tan function
[tex] \tan {}^{ - 1} ( \frac{y}{x} ) = [/tex]
Answers For 2,5
[tex] {2}^{2} + {5}^{2} = \sqrt{29} = 5.4[/tex]
So r=sqr root of 29
[tex] \tan {}^{ - 1} ( \frac{5}{2} ) = 68[/tex]
So the answer is (sqr root of 29,68).
For -3,3
[tex] { -3 }^{2} + {3}^{2} = \sqrt{18} = 3 \sqrt{2} [/tex]
[tex] \tan {}^{ - 1} ( \frac{3}{ - 3} ) = - 45[/tex]
Use the identity
[tex] \tan(x) = \tan(x + \pi) [/tex]
So that means
[tex] \tan(x) = 135[/tex]
So our points are
(3 times sqr root of 2, 135)
For 5,-3.5
[tex] {5}^{2} + {3.5}^{2} = \sqrt{37.25} [/tex]
[tex] \tan {}^{ - 1} ( \frac{ - 3.5}{ - 5} ) = 35[/tex]
So our points are (sqr root of 37.25, 35)
For (0,-5.4)
[tex] {0}^{2} + { - 5.4}^{2} = \sqrt{} 29.16 = 5.4[/tex]
So r=5.4
[tex] \tan {}^{ - 1} (0) = undefined[/tex]
So our points are (5.4, undefined)
Related Questions
Please answer quickly! Will mark brainliest
Answers
Answer: C) 1/a^12•b^8
Step-by-step explanation:
A bag of potatoes weighs 15 pounds. How many kilograms is this?
Answers
Answer:
6.8 kg
Step-by-step explanation:
1 pound = 0.4536 kg
15(0.4536) = 6.804
in her kayak bunny can travel 70 miles downstream with the current in 5 hours. the return trip against the current takes 7 hours. find the speed of the kayak in Stillwater and the speed of the current
Answers
9514 1404 393
Answer:
kayak: 12 mphcurrent: 2 mphStep-by-step explanation:
Bunny's rate downstream is ...
(70 mi)/(5 h) = 14 mi/h = k + c
Bunny's rate upstream is ...
(70 mi)/(7 h) = 10 mi/h = k -c
The kayak speed is the average of these:
(14 mi/h +10 mi/h)/2 = ((k +c) +(k -c))/2
(24 mi/h)/2 = 2k/2
12 mi/h = k
Then the current speed is ...
c = k -10 = 12 -10 = 2 . . . . mi/h
The still-water speed of the kayak is 12 mi/h; the speed of the current is 2 mi/h.
_____
Additional comment
World-class kayak paddlers will not maintain a speed more than 8 mi/h for that distance and/or time (140 miles in 12 hours). Bunny is exceptional.
write an equation in point-slope form of the line that passes through the point (3, 5) and has a slope or -1
Answers
Answer:
y = -x + 8
Step-by-step explanation:
m = -1 ; x1 = 3 ; y1 = 5
Slope point form: y - y1 = m(x -x1)
y - 5 = -1(x - 3)
y - 5 = -1x - 3 *(-1)
y - 5 =-x + 3
y = -x + 3 + 5
y = -x + 8
Are 20,30, and 16 the sides of a right triangle? Please show workkk
Answers
Solve the following right triangle. Round to the nearest tenth.
Answers
I don’t know how to do this at all
Answers
9514 1404 393
Answer:
A) down
B) 25 m; 200 m/s
C) (20.41, 2065.82)
Step-by-step explanation:
When you are first introduced to equations for ballistic motion, you may be told that the formula is ...
h(t) = -4.9t² +v₀t +h₀ . . . . . height in meters at time t seconds
where v₀ is the initial upward velocity in meters per second, and h₀ is the initial height in meters.
When you are first introduced to quadratic equations, and the vertex form in particular, you may be told that the form is ...
f(x) = a(x -h)² +k . . . . . . . vertex (h, k) and vertical scale factor 'a'
When the scale factor (or leading coefficient) is negative the graph of the parabola opens downward. When it is positive, the graph opens upward.
Knowing these things, you are prepared to match the given equation to these patterns.
__
Part A: We observe that the leading coefficient of the function (-4.9) is negative, so the parabola opens down.
__
Part B: The constant in the first given equation is 25, so the initial height is 25 meters.
The coefficient of t in the first given equation is 200, so the initial velocity of the rocket is 200 m/s.
__
Part C: The vertex can be read from the second equation as ...
(h, k) = (20.41, 2065.82)
Using the commutative property, fill in the information necessary to make this a true statement. Solve: 5 × 8 = ×
Answers
Answer: 8*5
Step-by-step explanation: Because the comutative property says you can like, switch up the orders of the numbers in a thing and it is still trye. So 5*8=8*5.
The expression using the commutative property is
5 x 8 = 8 x 5.
What is an expression?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The commutative property states that,
a x b = b x a
Now,
Using the commutative property,
5 x 8 is equal to 8 x 5.
Thus,
5 x 8 = 8 x 5
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
evaluate the intergral2x(xsquared+3)exponent 4
Answers
Answer:
Step-by-step explanation:
I hope it helped you
Michael completed a race that is 7 kilometers long. Which distance is closest to the number of miles Michael ran? ( 1.609 kilometers = 1 mile)
Answers
Answer:
4.35 miles if rounded 4.5 miles
Step-by-step explanation:
7 divided by 1.609 sums up to 4.35052
Evaluate the expression: –5 + 280 + 62.
Answers
Answer:
the answer is 337
Step-by-step explanation:
-5 + 280 + 62
= 337
Answer:
337
Step-by-step explanation:
-5 plus 280 is 275
275 + 62 is...
337
Factor 7/10 out of 7/10z+21.
7/10z+21=
Answers
Answer:
1/100 (1471 z + 2100)
0.01 (1471 z + 2100) the result I got
and the Factorization over the splitting field:
14.71 z + 21
10. A tractor costs $13,650 and depreciates in value by 14% per year. How much will the tractor be worth after
10 years?
a $2,597.86 b. $13,510.00 c. $3,020.77 d. $50,603.57
Answers
question is in picture :) also pls explain (if u can)
Answers
The m’s would all be the same number.Another way of adding the same number to each other would be to multiply that number by the number of times you want to add it to each other.
With m + m + m you are adding it 3 times.
So instead multiply m by 3:
The answer is 3m
Answer:
Solution :-In the Question the concept used is the algebra
We know that
[tex] \sf \: x \times x = {x}^{2} [/tex]
and
[tex] \sf \: x + x = 2x[/tex]
Similarly
[tex] \sf \: m + m + m = 3m[/tex]
The method is also known as property of addition in algebra
is this a function? please explain if possible...
Answers
It is a function. Every x value is different.
A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth side is a wall that already exists. If the farmer has 148 feet of fencing, what is the largest area the farmer can enclose?
Answers
Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
The length of a rectangle is 4 inches less than its width and the area is 21 square inches. Find
the smallest dimension of the rectangle.
Answers
On an international exam; students are asked to respond to a variety of background questions. For the 41 nations that participated in the exam; the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.883. Does this suggest there is a linear relation between student task persistence and achievement score
Answers
Answer:
since r > 0.361
we reject H₀
Therefore, Yes, It does suggest that there is a linear relation between student task persistence and achievement score, since r [0.883 ] is greater than critical value for 30 [ 0.361 ]
Step-by-step explanation:
Given the data in the question;
n = 41
r = 0.883
H₀ : population correlation coefficient = 0 ( both are independent )
Hₐ : population correlation coefficient ≠ 0 ( there is a linear relation between student task persistence and achievement score )
critical value for n = 30 is 0.361
that means, for n = 41, critical value will be less than 362
now, since r > 0.361
we reject H₀
Therefore, Yes, It does suggest that there is a linear relation between student task persistence and achievement score, since r [0.883 ] is greater than critical value for 30 [ 0.361 ]
Simplify the variable expression below as much as possible.
(4.5)x+ 3x + 2
Answers
Answer:
23x +2
Step-by-step explanation:
20x + 3x + 2 = 23x + 2, also close ur curtains ouch
Based on the information given, the value of the expression is 23x + 2.
From the information given, the expression that was given is (4.5)x+ 3x + 2. This simply means that one has to multiply the values in the bracket first and solve it. This will be:
= (4 × 5)x + 3x + 2
= 20x + 3x + 2
= 23x + 2
Learn more about equations on:
https://brainly.com/question/13802812
Can someone solve for x? And maybe explain it in a simple way?
Answers
Answer:
x=10
Step-by-step explanation:
Because of the two parallel lines, the ratio between the sides must be the same. Since the bottom is 12 to 18 (a ration of two to three) we know that x and x+5 would have the same ratio. Logically, x would have to equal 10 so that x+5 would equal 15 and a ratio of two to three would exist there too. If you go to solve a problem and the answer isn’t obvious, jut set up a ratio.
12/18=x/(x+5)
then cross multiply and solve
12(x+5)=18x
12x+60=18x
60=18x-12x
60=6x
10=x
Answer:
x=10
Step-by-step explanation:
You can set it up as a proportion, since the lines are parallel, the sections are proportionate to each other.
[tex]\frac{x}{12} = \frac{x+5}{18} \\18x=12(x+5)\\18x=12x+60\\6x=60\\x=10[/tex]
1^12 multiplied by 3,268,584
Answers
Answer:
3,268,584
Step-by-step explanation:
1^12 is 1
According to a survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five. a. What is the probability of receiving no e-mails during an hour (to 4 decimals)
Answers
Answer:
the probability is 0.0067
Step-by-step explanation:
The computation of the probability of receiving no e-mails during an hour is shown below;
Let us assume x be the number of emails received during an hour
Now the probability of receiving no e-mails is
= e^-5 × 5^0÷ 0!
= e^-5 × 1 ÷ 1
= e^-5
= 0.00674
= 0.0067
Hence, the probability is 0.0067
−4x + 2y < 10 in slope intercept
Answers
Answer:
y < 2x + 5
Step-by-step explanation:
The format for slope intercept is y = mx + b. In this case, it is y < mx + b. Your equation is -4x + 2y < 10. First, start by adding 4x to -4x. This gets rid of that number on the left so it can just be 2y. Now, add that 4x to the right side of the equation. You are left with 2y < 4x + 10. The final step is to divide 2 from 2y. Since you are doing this step on the left side of the equation, you must now do it to the right. After also dividing 2 from 4x and 10, your final answer is y < x +5.
Are these ratios equivalent?
1 teacher to 9 students
5 teachers to 45 students
Answers
Answer: yes the ratios 1:9 and 5:45 are equivalent.
Step-by-step explanation:
1:9*5:5=5:45
U got any more math questions that I can answer? I’m really bored and I have to stay busy!
Simplify
8(10 m)
80 + m
18 m
80 m
810 m
Answers
80m, you kind of distribute so 8 times 10m is 80m
What is the total surface area of a rectangular prism whose net is shown 19 in. 17in. 6.in.
Answers
Answer:
1078in
Step-by-step explanation:
Surface area =2(wl+hl+hw)
2·(17·19+6·19+6·17)=1078in
A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were
defective. A store clerk generates random numbers to simulate a random sample of this shipment. The
clerk lets the numbers 1 through 300 represent defective MP3 players, and the numbers 301 through
5,000 represent working MP3 players. The results are given.
638 430 240 3,932 4,477 670 3,059 13 3,144 3,844
Based on this sample, how many of the MP3 players might the clerk predict would be defective?
The manager would expect
defective players in the shipment.
Answers
The sample was 10 numbers.
4 of the numbers are less than 301.
So 4 out of 10 would be defective.
4/10 = 0.4 x 100 = 40%
He would expect 40% to be defective.
Answer:
86 i think
Step-by-step explanation:
When calculating simple probability,
what goes in the numerator and what
goes in the denominator?
Please.
Answers
Answer:
The top number in a fraction. Shows how many parts we have. (The bottom number is the Denominator and shows how many equal parts the item is divided into.)
Step-by-step explanation:
ugriuhgi5ughoiruhr PLEASE HELP 10 POINTS!
Answers
Answer:
A = 6
B = 6
C = 7
D = 4
Step-by-step explanation:
What is the area of the parallelogram
shown above?
[?] square feet
Answers
Answer:
299 square feet
Step-by-step explanation:
Area of a parallelogram = base × height
Base = 23 ft
Height = 13 ft
Note: the other length, 15 ft is not needed in calculating area of the parallelogram. All we need is just the length of the base and the height.
Area of the parallelogram shown = 23 × 13
Area = 299 ft²