Drag the tiles to the correct boxes to complete the pairs. Match the polar equations to their rectangular forms.
Answers
Answer:
C, A, E, B, D
Step-by-step explanation:
The conversion relations between rectangular and polar coordinates can be used to find the polar coordinate equivalents. Those relations are ...
x = r·cos(θ)y = r·sin(θ)x² +y² = r²__
x = 2Using the expression for x, this is ...
r·cos(θ) = 2
r = 2/cos(θ) . . . . divide by cos(θ)
r = 2·sec(θ) . . . . use the trig identity
__
x²+y²=36From above, this becomes ...
r² = 36
r = 6 . . . . . . take the square root
__
x²+y²=2yFrom above, this becomes ...
r² = 2·r·sin(θ)
r = 2·sin(θ) . . . . . . divide by r
__
x=√3yUsing the above relations, this is ...
r·cos(θ) = √3·r·sin(θ)
1/√3 = sin(θ)/cos(θ) . . . . . . divide by √3·r·cos(θ)
tan(θ) = 1/√3 ⇒ θ = arctan(1/√3)
θ = π/6
__
x=yFrom above, this is ...
r·cos(θ) = r·sin(θ)
1 = sin(θ)/cos(θ) = tan(θ) . . . . divide by r·cos(θ)
θ = arctan(1)
θ = π/4
_____
Additional comment
An equation of the form y = kx defines a line through the origin and through opposite quadrants of the Cartesian plane. Above, we found the equivalent polar equation to be θ = arctan(k). Using the principal branch of the arctangent function, this is the equation of a ray.
However, the tangent function is periodic with period π, so θ = arctan(k)+π is also an equivalent to the rectangular equation. It is the opposite ray, so forms the complete line when joined with the first ray.
The correct answer for the polar coordinates will be C, A, E, B, D
What is a polar coordinate system?
The polar coordinate system is a two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane. The pole is the reference point, and the polar axis is the ray from the pole in the reference direction.
The conversion relations between rectangular and polar coordinates can be used to find the polar coordinate equivalents. Those relations are ...
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
x = 2
Using the expression for x, this is ...
r·cos(θ) = 2
r = 2/cos(θ) . . . . divide by cos(θ)
r = 2·sec(θ) . . . . use the trig identity
x²+y²=36
From above, this becomes ...
r² = 36
r = 6 . . . . . . take the square root
x²+y²=2y
From above, this becomes ...
r² = 2·r·sin(θ)
r = 2·sin(θ) . . . . . . divide by r
x=√3y
Using the above relations, this is ...
r·cos(θ) = √3·r·sin(θ)
1/√3 = sin(θ)/cos(θ) . . . . . . divide by √3·r·cos(θ)
tan(θ) = 1/√3 ⇒ θ = arctan(1/√3)
θ = π/6
x=y
From above, this is ...
r·cos(θ) = r·sin(θ)
1 = sin(θ)/cos(θ) = tan(θ) . . . . divide by r·cos(θ)
θ = arctan(1)
θ = π/4
However, the tangent function is periodic with period π, so θ = arctan(k)+π is also equivalent to the rectangular equation. It is the opposite ray, so forms the complete line when joined with the first ray.
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Related Questions
Each student in Ms. Garai's class is either a junior or a senior. Ms. Garai has 30 students in her class, 24 of whom are juniors. Recently, she took some of the students from her class on a field trip. Of the 24 juniors in the class, 2/3 went on the trip.
Use this information to answer the questions below.
If not enough information is given to answer a question, click on "Not enough information."
(a) How many seniors are in the class?
(b) How many seniors from the class went on the field trip?
(c) How many juniors from the class went on the field trip?
Answers
Seniors in the class = total number of students - total number of juniors
30 - 24 = 6
Juniors that went on the field trip = 2/3 x 24 = 16 students
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Find the volume of the right circular cone with radius 6 cm, height 7 cm
[tex]( \pi = \frac{22}{7} )[/tex]
Answers
Answer:
Volume = 264 cm³Step-by-step explanation:
Formula:
Let b be the base (circle) of the cone
and h be the height of the cone
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
……………………………………………
→ b = π × r²
= π × 6²
= (22÷7) × 36
= 113.142857142857 cm²
→ h = 7
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
The volume = (1÷3)×(113,142857142857)×(7)
= 264 cm³
===================
METHOD 2 :
Volume = (1÷3)×(22÷7)×36×7
= (1÷3)×22×36
= 22×12
= 264
in a Table
Which statements comparing the functions are true?
Check all that apply.
f(x) and h(x) have x-intercepts.
Of(x), g(x), and h(x) have y-intercepts.
The domain of g(x) includes more values than the
domains of f(x) and h(x).
The range of g(x) includes more values than the
ranges of f(x) and h(x).
Og(x) has the greatest maximum.
h(x) has the lowest minimum.
Answers
The true statement about the functions is (d) the range of g(x) includes more values than the ranges of f(x) and h(x).
How to compare the three functions?The attached image represents the missing part of the question
From the attached image, we have the following properties:
All three functions have the same domain values (-4 to 1)The function g(x) includes more range values than othersh(x) has the greatest maximum of 2g(x) has the lowest minimum of -19The property 2 above is calculated as follows:
Range of g(x) =|-4 + 19| = 15
Range of f(x) =|1 + 2| = 3
Range of h(x) =|2 + 8| = 10
Hence, the true statement about the functions is (d) the range of g(x) includes more values than the ranges of f(x) and h(x).
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1. La asistencia a un juego de béisbol profesional fue de 4500 personas y el dinero
recaudado en la entrada fue de CS 49500. Si cada persona compró un boleto de
C$10 o un boleto de C$15 ¿Cuántos boletos de cada tipo se vendieron?
Answers
Resolviendo un sistema de ecuaciones veremos que se vendieron 900 boletos de $15 y 3600 boletos de $10.
¿Cuántos boletos de cada tipo se vendieron?
Primero definamos las variables:
x = número de bolteos de $10 vendidos.y = número de bolteos de $15 vendidos.Sabemos que se vendieron 4500 boletos, entonces:
x + y = 4500
Y se recaudo un total de $49,500, entonces:
x*$10 + y*$15 = $49,500
Entonces tenemos un sistema de ecuaciones:
Para resolver esto, primero debemos aislar una de las variables en la primer ecuación, voy a aislar x:
x = 4500 - y
Ahora reemplazamos esto en la otra ecuación:
(4,500 - y)*$10 + y*$15 = $49,500
Ahora debemos resolver estoy para y.
$45,000 - y*$10 + y*$15 = $49,500
y*$5 = $49,500 - $45,000 = $4,500
y = ( $4,500)/$5 = 900
Entonces:
x = 4500 - 900 = 3600
Se vendieron 900 boletos de $15 y 3600 boletos de $10.
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A school has 100 windows. On a cool day, 95 of the windows were closed. Which decimal represents how many of the windows were open? *
Answers
Answer: 0.05
Step-by-step explanation:
Since 95 out of 100 were closed, the closed window is 95% = 0.95.
5 open windows = 5% = 0.05
An expression is given.
(3x - 1) - 2.75 (x + 2)
Which expression is equivalent to the given expression?
A. 0.25x - 6.50
B. 0.25x + 1.00
C. 0.25x + 4.50
D. 0.25x - 3.00
Answers
A. 0.25x - 6.50
Explanation:
(3x - 1) - 2.75 (x + 2)
= 3x - 1 - 2.75x - 5.5
=0.25x -6.5
Hence A is equivalent to 0.24x -6.5
Give a non-zero counterexample to the following statement:
Every multiple of 10 is also a multiple of 30.
Answers
Answer:
20 or 40 or 50
(there are many others)
Step-by-step explanation:
A counterexample is an example that shows the statement is not true. The statement in this question is that if a number is a multiple of 10 (10, 20, 30, 40, 50, 60...) then it is a multiple of 30. Some numbers are, like 60 and 90, but not all numbers. So for example (counterexample) 20 is a multiple of 10 but NOT a multiple of 30.
40 is a multiple of 10, but NOT a multople of 30.
50 is a multiple of 10, but NOT a multiple of 30.
r
2 cm
x = [?] cm
3 cm
Enter a decimal rounded to the nearest tenth.
Enter
Done
Answers
Answer:
x = 3.6
Step-by-step explanation:
By the property of intersecting chords, we have:5*x = 6*3-> 5x = 18-> x = 18/5-> x = 3.6question about college I have straight a’s in all my classes and this year I might be getting a C or lower in one of my classes will that affect my chances into getting accepted into colleges? (average colleges no Ivy League)
Answers
Keiko surveyed people with cell phones. Ages in years = a Texts they send per day = t He drew a best-fit line and determined its equation. Evaluate how many texts a 15 year old would send each day according to Keiko's trend line.
Answers
Answer:
68 texts per day
Step-by-step explanation:
The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).
__
Substitute the number (15) for the variable (a) and do the arithmetic:
t = -1.63a +92.14
t = -1.63(15) +92.14 = -24.45 +92.14
t = 67.69
Keiko's trend line estimates a 15-year-old would send about 68 texts per day.
Keiko bought 13 pounds of sugar for $6. How many dollars did she pay per pound of sugar?
Answers
Step-by-step explanation:
13 pounds of sugar for $6.
for a single pound of sugar we need to divide everything by 13 to keep the same ratio (relationship).
1 pound cost then 6/13 = 0.461538462... ≈ $0.46
A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.64 years and the standard deviation is 9.39 years.
a) Construct a 80% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the interval have been met.
b) How large is the margin of error?
a) What is the confidence interval?
b) What is the margin of error?
The margin of error is
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.
The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]
Thus, we can compute the confidence interval:
[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]
Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.
Part B
The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]
5b 2 −6b−2 is prime TURE OR FALSE!! 100 POINTS PLEASE HELP!!!!
Answers
The given quadratic expression; 5b² -6b -2 is prime because the discriminant is not a perfect square.
What is the discriminant of the expression?According to the task content; it is required to identify if the expression is prime.
On this note, it follows that the discriminant of the expression can be evaluated as follows;
= 36 -(4× 5 × -2)
= 76.
Hence, the expression is prime since 76 is not a perfect square.
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I need help asap !! I will mark Brainly!
Answers
Answer: x-axis
Explanation:
x-axis: it is the horizonzontal axisx-coordinates: it is the x-value of a point in reference to the x-axisy-axis: it is the vertical axisy-coordinates: it is the y-value of a point in reference to the y-axisHope that helps!
what is its first derivative
Answers
Answer:
2ax + b + C
where C is a constant.
Find the slope of the line passing through the points (5,8) and (6,12).
Answers
Answer:
Calculator soup can help just search for whatever your learning and add a calculator at the end
AB BG, AC GC, ZABC LGBC ZBACZBGC
A
B
#
C
G
1. What rigid transformation will take triangle GBC onto triangle ABC?
2. Explain why G' will coincide with A
3. Is triangle GBC congruent to triangle ABC? Explain your reasoning, and be sure to list any sides/angles you compared.
CAN SOMEONE HELP ME PLS, YOU’LL EARN FREE EASY POINTS IF IT’S THE RIGHT ANSWER, NO RANDOM ANSWERS BC YA’LL BE GIVING ME THE WRONG ANSWER SOMETIMES :(
Answers
Answer:
Step-by-step explanation:
1) Reflection over [tex]\overline{BC}[/tex]
2) The triangles are congruent by SAS, so when [tex]\triangle GBC[/tex] is mapped onto [tex]\triangle ABC[/tex], because points [tex]G[/tex] and [tex]A[/tex] are corresponding, [tex]G'[/tex] will correspond with [tex]A[/tex].
3) Yes, because [tex]\overline{BG} \cong \overline{AB}, \overline{GC} \cong \overline{AC}, \angle BAC \cong \angle BGC[/tex], so the triangles are congruent by SAS.
Please help me please tell me the answer AND explain why it's the answer
Answers
Answer:
NOStep-by-step explanation:
If x = 3
then
5x² = 5×(3)² = 5 × 9 = 45
and 45 > 40
Therefore
3 is not a solution to the inequality 5x² < 40.
Hi Student!
This question is fairly simply and the main goal of this question is to determine whether x = 3 is a solution of the expression that was provided or not. The first step that we take is to plug in all of the values or in this case we input the value 3 for everywhere we see x in the equation. The next step is to simplify the expression on both sides and finally compare the expression to see if it evaluates to true. If it evaluates to true then x = 3 is a solution but if it evaluates to false then x = 3 isn't a solution.
Plug in the values
[tex]5x^2 < 40[/tex][tex]5(3)^2 < 40[/tex]Simplify the expression
[tex]5(3*3) < 40[/tex][tex]5(9) < 40[/tex][tex]45 < 40[/tex]Looking at the final expression that was simplified, we can see that it states that 45 is less than 40 when we know that is not the case. Therefore, this would evaluate to the expression being false and x = 3 not being a solution of the expression that was given in the problem statement.
what equation is equivalent to 2^3^x =10
Answers
Answer:
[tex]log_2(10)[/tex]
how to findSimplify the equation using logarithms.
part 1[tex]2^3x=10[/tex]
[tex]log_1_0(2^3x)=log_1_0(10)[/tex]
log rule ⇩
[tex]log_a(x^y)=y*log_a(x)[/tex]
move exponent out of log.
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
part 2isolate variable further
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]
formula for combining logs. ⇩
[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]
the result ⇩
[tex]x=log_2(10)[/tex]
A bacteria population has been doubling each day for the past 5 days. It is currently
100000. What was the population 5 days ago?
Answers
Which line on the graph could represent this scenario?
a(x)
f(x)
g(x)
h(x)
Answers
Answer: g(x)
Step-by-step explanation:
A family has a monthly income of $3912. Their monthly expenditures are as shown in the graph below.
Rent 21%
Food 24%
Transportation 11%
Other Expenses 18%
Savings 26%
How much money does the family save in a month?
Answers
Answer: The save $1134.48
Step-by-step explanation:
3912 x 0.29 = 1134.48
The amount of money that the family saves in a month will be $1,017.12.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
A family has a month-to-month payment of $3912. Their month-to-month uses are displayed in the diagram underneath.
Rent 21%
Food 24%
Transportation 11%
Other Expenses 18%
Savings 26%
Then the amount of money that the family saves in a month is calculated as,
⇒ $3,912 x 0.26
⇒ $1,017.12
The amount of money that the family saves in a month will be $1,017.12.
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qualities?
x + 4y > 12
3y > x + 6
Answers
The solution to the given system of inequality is (-12, 6).
System of equationsThese are equations that contains unknown variables.
Given the equations
x + 4y > 12
3y > x + 6
__________
x + 4y > 12
3y - x > 6
Subtract
4y - 3y > 12 - 6
y > 6
Substitute y = 6 into the equation
x + 4y >12
x + 4(6) > 12
x > -12
Hence the solution to the given system of inequality is (-12, 6)
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Maxwell wants to know how much space his globe occupies. Should he find its surface area or volume? Explain your answer
Answers
Since, Maxwell wants to know how much space his globes occupies he has to find its volume.
What is a volume?
Volume is the amount of space an object or substance occupies.
Every three dimensional object occupies a space.
Volume is measured in cubic units.
Therefore, the three dimensional object that has a width, length and height will have its volume as follows;
volume = lwh
where
l = lengthw = widthh = heightTherefore, the space occupied by the globe is the volume of the globe.
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Question 8: The equation of motion of a particle is
s = t^3 4t^2 + 2t + 8
Where s is in meters
and t is in seconds
Find the acceleration after t=5 seconds.
Answers
Answer:
D) [tex]22\:\text{m/s}^2[/tex]
Step-by-step explanation:
Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:
Position of Particle: [tex]s(t)=t^3-4t^2+2t+8[/tex]
Velocity of Particle: [tex]v(t)=3t^2-8t+2[/tex]
Acceleration of Particle: [tex]a(t)=6t-8[/tex]
After [tex]t=5[/tex] seconds, the acceleration of the particle is [tex]a(5)=6(5)-8=30-8=22\:\text{m/s}^2[/tex]
The acceleration of the particle after 5 seconds is 38 m/s².
What is acceleration?Acceleration is the rate of change of velocity or the slope of velocity.
We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.
∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.
Now, s = t³ + 4t² + 2t + 8 meters.
ds/dt = 3t² + 8t + 2 m/s.
d²s/dt² = 6t + 8m/s²
Now, at t = 5 seconds d²s/dt² = 6t + 8 is,
d²s/dt² = 6(5) + 8 m/s².
d²s/dt² = 38 m/s².
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Which expression represents the perimeter of the triangle?
8x + 2
18x
8x
Answers
Answer:
8x
Step-by-step explanation:
(3x+1)+(3x-1), the 1's cross out, so it is 3x+3x=6x. 6x+2x=8x.
Answer:
8x
Step-by-step explanation:
got it right!!!
The endpoints of one diagonal of a rhombus are (-7, -2) and (-1, -4). If the coordinates of the 3rd vertex are (-6, -9), what are the coordinates of the 4th vertex? (-8, 13) (-2, 3) (-6, 13) (7, -8)
Answers
The coordinates of the 4th vertex of the rhombus are (-2,3)
How to determine the coordinates of the 4th vertex?The diagonals are given as:
(-7, -2) and (-1, -4)
The 3rd vertex is given as: (-6,-9)
Calculate the distance between the vertices of the diagonals and the 3rd vertex using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]d_1 = \sqrt{(-7 + 6)^2 + (-2 + 9)^2} =\sqrt{50[/tex]
[tex]d_2 = \sqrt{(-1 + 6)^2 + (-4 + 9)^2} =\sqrt{50[/tex]
Let the 4th vertex be (x,y)
So, we have:
[tex]d_3 = \sqrt{(-7 - x)^2 + (-2 - y)^2} =\sqrt{50[/tex]
[tex]d_4 = \sqrt{(-1 - x)^2 + (-4 - y)^2} =\sqrt{50[/tex]
Equate d3 and d4
[tex]\sqrt{(-1 - x)^2 + (-4 - y)^2} = \sqrt{(-7 - x)^2 + (-2 - y)^2}[/tex]
Take the square of both sides
[tex](-1 - x)^2 + (-4 - y)^2 = (-7 - x)^2 + (-2 - y)^2[/tex]
Expand
[tex]1 + 2x + x^2 + 16 + 8y + y^2 = 49 + 14x + x^2 + 4 + 4y + y^2[/tex]
Evaluate the like terms
1 + 2x + 16 + 8y = 49 + 14x + 4 + 4y
Collect like terms
14x - 2x + 4y - 8y = 1 + 16 - 49 - 4
12x - 4y = -36
Divide through by 4
3x - y = -9
Next, we test the options in the above equation
Point (-8,13) means x = -8 and y = 13
So, we have:
3x - y = -9
3(-8) - 13 = -9
-37 = -9 --- this is false
Point (-2, 3) means x = -2 and y = 3
So, we have:
3x - y = -9
3(-2) - 3 = -9
-9 = -9 --- this is true.
Hence, the coordinates of the 4th vertex are (-2,3)
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150pounds = what in kilograms
Answers
this is your answer.
Answer: 68.0389
Answer:
68.04 is the correct answer
I looked it up
9.8765 plus what has a 10 in the front
Answers
Answer:
0.1235
Step-by-step explanation:
I'm not exactly sure what you mean, but I'm guessing that it's how much is needed to get 10 as the whole number. In that case, you just do 10-9.8765 to get 0.1235. So, 9.8765+0.1235=10. Hope this helped!
The radius of a semicircle is 3 kilometres. What is the semicircle's perimeter?
Answers
Answer:
In terms of Pi: [tex]3\pi + 6[/tex] km
Exact value (rounded): 15.42477 km
Approximated (3.14): 15.42 km
Step-by-step explanation:
Hello!
A semicircle's perimeter can be found using the formula: [tex]P = \pi r + 2r[/tex]
We can plug in the values to solve for the perimeter.
Solve[tex]P = \pi r + 2r[/tex][tex]P = \pi(3)+ 2(3)[/tex][tex]P = 3\pi + 6[/tex]In terms of Pi, it is [tex]3\pi + 6[/tex],
Exact value of Pi, it is 15.42477
Approximation of Pi (3.14), it is = 15.42