Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 - 3 sin θ
Answers
Answer:
Symmetry about y-axis
Step-by-step explanation:
We are given that
[tex]r=4-3sin\theta[/tex]
When the graph is symmetric about x- axis then the point (x,y) change in to (x,-y) and the function remain same.
The point[tex] (r,\theta,)[/tex] is replaced by [tex]( r,-\theta)[/tex]
Substitute the value then we get
[tex]r=4-3 sin(-\theta) [/tex]
[tex]r=4+3sin\theta[/tex] ([tex]sin(-\theta)=-sin\theta)[/tex]
The value of function changes .Hence , the function is not symmetric about x- axis.
When the function is symmetric about y-axis then the point [tex](r,\theta) [/tex] change into point [tex](r,\pi-\theta)[/tex] and function remain same
Substitute the value
[tex]r=4-3sin(\pi-\theta)[/tex]
[tex]r=4-3 sin\theta[/tex] ([tex]sin(\pi-\theta)=sin\theta[/tex])
The value of function does not change when point change ,Hence, the function is symmetric about y- axis.
When the graph is symmetric about origin then the point [tex](\theta,r)[/tex] change into point[tex](r,\pi+\theta)[/tex] and the value of function remain same.
Substitute the value then we get
[tex]r=4-3sin(\pi+\theta)[/tex]
[tex]r=4+3sin\theta [/tex]
[tex]r=4+3sin\theta [/tex]
Hence, the graph has symmetry about y-axis .
Related Questions
can someone help me with this question
Answers
First: 2x*3x=6x^2
Outwr: 2x*4=8x
Inner: 5*3x=15x
Last: 5*4=20
Put it together and simplify.
6x^2+8x+15x+20
6x^2+23x+20
Final answer: D
Solve for F. Let m=5, a=3 F=ma
Answers
State how many imaginary and real zeros the function has. f(x) = x^5+7x^4+2x^3+14x^2+x+7
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Since the degree of the equation is 5, then the number of zeros is also equal to 5. We can find for the 1st value of the root by trial and error. To do this, we find for the value of x which makes the equation equal to zero, that is:
x^5 + 7x^4 + 2x^3 + 14x^2 + x + 7 = 0 (find x)
By trial and error I made (which I will not show anymore), the possible root is -7. This is equivalent to x + 7.
To find more roots, we divide x^5 + 7x^4 + 2x^3 + 14x^2 + x + 7 by x + 7. The answer of the division results in x^4 + 2x^2 + 1 which is a perfect square trinomial in the form of:
(x^2 + 1)^2
Therefore the other 4 roots are:
x^2 + 1 = 0 ---> i, -i
and
x^2 + 1 = 0 ---> i, -i
Therefore the answer is:
1 real and 4 imaginary zeros
Given cos A = .29 find the angle A in radians. Round your answer to the nearest hundredth.Answer 1.19 radians 1.28 radians 1.34 radians 1.46 radians
Answers
Answer: The correct option is (B) 1.28 radians.
Step-by-step explanation: We are given that for an angle A :
[tex]\cos A=0.29.[/tex]
We are to find the measure of angle A in radians.
We know that the relation between degree and radians is given by
[tex]80^\circ=\pi~\textup{radians}\\\\\\\Rightarrow 180^\circ=\dfrac{22}{7}~\textup{radians}.[/tex]
Now, we have
[tex]\cos A=0.29\\\\\Rightarrow A=\cos^{-1}(0.29)\\\\\\\Rightarrow A=73.14^\circ.[/tex]
Again,
[tex]180^\circ=\dfrac{22}{7}\\\\\Rightarrow 1^\circ=\dfrac{22}{7\times180}\\\\\Rightarrow 73.14^\circ=\dfrac{22}{1260}\times73.14=1.277=1.28~\textup{radians}.[/tex]
Thus, the measure of angle A in radians is 1.28 radians.
Option (B) is CORRECT.
What's four minus (-2)
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Because [tex]Four [/tex]became a negative
remember (neg = negative ; pos = positive)
[tex]neg. + neg. = pos. [/tex]
[tex]pos. + pos. = pos.[/tex]
[tex]neg. + pos = neg.[/tex]
[tex]pos. + neg. =neg.[/tex]
Negatives goes on the [tex]LEFT [/tex]side of the number-line
Positives goes on the [tex]RIGHT [/tex]side of the number-line
Tom has deposited $500 in an account which earns 2% interest each year. Which expression correctly shows the total value of his account after 3 years?
A) 500 + 0.02 + 0.02 + 0.02
B) 500 + 0.02[500 + 0.02(500 + 0.02*500)]
C) 500 + 0.02*0.02*0.02(500)
D) 500 + 3(0.02)500
Answers
500+3×0.02×500=530
find the arc length of a central angle of 90° in a circle whose radius is 4 inches
Answers
Circumference = 2 * pi * 4 = 8pi
arc length = 1/4 * 8pi = 2pi or 6.28 ins to nearest hundredth.
Answer:
2 pie in
source: Trust me bro
STVU is an isosceles trapezoid. If SV = 3x - 11 and TU = x + 13, find the value of x
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
SV = TU
3x - 11 = x + 13
Transpose the terms with x and the constants in each sides of the equation.
3x - x = 13 + 11
2x = 24
x = 12
Thus, the value of x from the equation is 12.
In how many different ways can a group of 9 people be divided into 3 groups, with each group containing 3 people?
Answers
The second three can be selected in 6c3 ways which equals 20.
Then the third set of three can be selected in 3c3 which equals 1 way.
Now we want three things to happen, so multiply 84 and 20 and you get 1680.
The order of this does not matter so divide 1680 by 3 and you have 280!!
Find the indicated critical z value. Find zα/2 for α = 0.08
Answers
The value of z that yields the expected central area takes into account the excluded areas at both tails.
Half the tail area is α/2 = 0.08/2 = 0.04.
The central area is 1 - 0.04 - 0.04 = 0.92.
From standard normal tables, obtain
z(α/2) = 1.75
Answer: 1.75
To find the critical z value for α = 0.08, we first divide α by 2 to get 0.04. This value corresponds to the tail regions in a two-tailed test. We then lookup or calculate the z value associated with a cumulative probability of 0.04, which gives us a z value of approximately 1.75.
Explanation:The question is about finding the indicated critical z value. In statistics, critical values are used to make decisions about the null hypothesis in hypothesis testing. When α = 0.08, α/2 = 0.04 which refers to the tail regions in a two-tailed test.
First, we find the z value associated with α/2=0.04. This is found by looking at a standard z-table, or using a statistical calculator or a software tool that can calculate the inverse of the standard normal cumulative distribution function. For α/2=0.04, the z value is approximately 1.75.
Therefore, the critical z value (zα/2) is approximately 1.75.
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If 2+2=4 why is the answer fish
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suppose you buy a CD for $500 that's earns 3% APR and is compounded quarterly. The CD matures in 3 years. Assume that if funds are with drawn before the CD matures, the early withdrawal fee is 3 months interest. what is the early withdrawal fee on this account?
Answers
Or 4 times a year
So the early withdrawal fee on this accoun is
500×0.03×(1÷4)=3.75
Answer:
The answer is $3.75
Step-by-step explanation:
P = $500
r = 3% = 0.03
n = 4
t =[tex]3/12=1/4[/tex]
Now compound interest formula is :
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting the values in formula we get,
[tex]A=500(1+\frac{0.03}{4})^{4*1/4}[/tex]
[tex]A=500(1.0075})^{1}[/tex]
= $503.75
Now, withdrawal fee = amount paid - principle
=> [tex]503.75-500=3.75[/tex] dollars.
So, the answer is $3.75.
Which of the following is equivalent to 5√13^3?
A) 13^2
B) 13^15
C) 13^5/3
D) 13^3/5
Answers
(13^3)^(1/5) rule: (a^b)^c=a^(b*c)
13^(3*1/5)
13^(3/5)
Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.
(x): 0, 1, 2, 3, 4
f(x): 14, 12.6, 11.34, 10.206, 9.185
A) Exponential; y=14(0.10)^x
B) Linear; y= -1.2024x + 13.871
C) Exponential; y= 14(0.90)^x
D) Linear; 18.871x - 1.2024
Please explain you answer. Please someone help me, I'm in need of some help.
Answers
PROOF
Give to x the respective values of x & calculate y, using y = 14(0.9)ˣ
x | y
---------|---------
0 | 14(0.9)⁰ = 14
1 | 14(0.9)¹ = 12.6
2 | 14(0.9)² = 11.34
3 | 14(0.9)³ = 10.206
4 | 14(09)⁴ = 9.1845
Answer:
simplified answer: its letter c
Step-by-step explanation:
A 3 kg toy car rests st the top of a 0.45 meter ramp. What is its gravitational potential energy?
Answers
Gravity : g
Mass : m
height : h
P = mgh = 3 x 9.8 x 0.45 = 13.23 Joule
Potential energy is work , from the known formula
W = Fd ( work = force x distance )
W = P ( in case of potential energy height change)
F is the force acting on the body in case of ideal ramp , the only force acting is the weight of the body
F = mg ( not just <m> as the force is mg (Newton) gravity effect)
d is the displacement in direction of force, as we have considered the force to be the weight not it's component in direction of the ramp , the change in displacement is the change in height so
d = h
W = Fd = (F = mg) x (d = h) = mgh
W = mgh = P
The gravitational potential energy of a 3 kg toy car resting at the top of a 0.45-meter ramp is calculated using the formula PE = mgh, giving us a result of 13.2385 Joules.
The calculation of gravitational potential energy for a 3 kg toy car at the top of a 0.45-meter ramp. Gravitational potential energy (PE) is calculated using the formula PE = mgh, where m stands for mass, g is the acceleration due to gravity (usually 9.81 m/s² on Earth's surface), and h is the height above the reference point. In this case, PE = 3 kg × 9.81 m/s² × 0.45 m, which gives us a gravitational potential energy of 13.2385 Joules. As the car is at rest on the top of the ramp and has not yet moved, its potential energy is at its maximum at that point.
Which statement is correct when a scatterplot is constructed? A.The independent variable is the input variable and should be represented by the x-axis. B.The independent variable is the input variable and should be represented by the y-axis. C.The dependent variable is the input variable and should be represented by the x-axis. D.The dependent variable is the input variable and should be represented by the y-axis.
Answers
Answer:- A.The independent variable is the input variable and should be represented by the x-axis.
Explanation:-
A. Correct.
B. Not correct.
Reason:- The independent variable is the input variable and should be represented by the x-axis.
C. Not correct.
Reason:- The dependent variable is the output variable and should be represented by y-axis.
D. Not correct.
Reason:-The dependent variable is the output variable and should be represented by y-axis.
Answer:
A.The independent variable is the input variable and should be represented by the x-axis.
Step-by-step explanation:
It was right on the test.
Twelve employees were sick. If the company has 360 employees, what percent of the employees were sick on Monday? Round to the nearest tenth.
Answers
Number that were sick = 12
Therefore,
Percentage of employees that were sick = [tex] \frac{12}{360} * 100 = \frac{1}{3} * 10 [/tex] = 3.3 %
The price of a new pair of shoes is $52.00. If you order them directly from the company on the internet, you can save money and the price is only $42.64. What is the percent change?
Answers
Answer:
It will be 18% decrease, Because they said they lowered the price.
Step-by-step explanation:
The percentage decrease in buying shoes on the internet with respect to shop is 18%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction of 100.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
Price in shop = $52.00
Prince in online = $42.64
The percentage decrease with respect to price in the shop ⇒
(Price in shop - Prince in online)/(Price in the shop) × 100
⇒ (52 - 42.64)/52 × 100
⇒ (9.36/52) × 100
⇒ 18%
Hence "The percentage decrease in buying shoes on the internet with respect to shop is 18%".
For more about the percentage,
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Which value must be added to the expression x2 + 12x to make it a perfect-square trinomial?
Answers
answer
36
(ax^2+bx)=0
(b/2)^2=(12/2)^2=(6)^2=36
x^2+12x+36=(x+6)^2
how can the properties of exponents help solve exponential equations?
Answers
The properties of exponents and logarithms allow for simplifying and solving exponential equations by manipulating exponents, such as multiplying and dividing quantities, raising a power to another power, and using the inverse relationship between exponents and logarithms.
Explanation:The properties of exponents are essential for solving exponential equations because they allow for the manipulation of the equations into forms that are easier to solve. The exponential and natural logarithm are inverse functions, meaning ln (e^x) = x and e^(ln x) = x. By using this relationship, any base number b can be expressed as e^(ln b), making complex calculations more manageable.
When multiplying exponential quantities, we can apply the rule where the exponents are added together, such as in (a^m) × (a^n) = a^(m + n). If we raise an exponent to another power, we multiply the exponents, which is depicted in the example of (5^3)^4 = 5^(3×4) = 5^12. Similarly, dividing exponential quantities involves subtracting exponents, and an exponential raised to a negative exponent signifies an inversion.
The logarithmic properties also come into play when working with exponents. The logarithm of a product is the sum of the logarithms: log(xy) = log(x) + log(y). This is useful when solving exponential equations since logarithms can help linearize them, making it easier to isolate the variable and find the solution.
The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 120, 0. The vertex is at 60, 35.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?
Part B: What is an approximate average rate of change of the graph from x = 20 to x = 35, and what does this rate represent?
Answers
Vertex is at (60, 35).
Part A: What do the x-intercepts and maximum value of the graph represent?
The x-intercepts represent the points at the ground, so with that you have the width of the tunnel at ground level is 120 ft - 0 ft = 120 ft..
The vertex represents the maximum height, which is at the center of the tunnel. So, you know that the maximum height is at x = 60 ft and it is 35 ft
What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height?
The increasing interval is (0,60), and the decreasing interval is (60,120).
That represents that the height increase from the left border (x = 0) until the center of the tunnel (x = 60 ft), reaching a height of 35 ft, and starts to decrease toward the right border until the ground level (x = 120).
Part B: What is an approximate average rate of change of the graph from x = 20 to x = 35, and what does this rate represent?
Find the y -coordinate for x = 20 and for x = 35. Supposse they are (I do not have the figure, because you did not include it) y = 15 and y = 45.
Then the average rate of change is equal to [change in height] / [change in x] = [45 - 15] / [35 - 20] = 30 / 15 = 2.
Remember that you have to use the real approximate values for the height that you can read in the figure. If the number is positive means that the height is increasing in that interval.
Answer:
i have the image of the tunnel and here is my work
Part B: x=20 y=20 x=35 y=60 so {60-20}/{35-20}=40/15=2.6
hope this helps
WILL GIVE BRAINLIEST PLEASE HELP!!!
Which of the following equals 1/16 when evaluating f (–2)?
A.
f(x)=2^(x-2)
B.
f(x)=-2^(x-6)
C.
f(x)=-2^(n-2)
D.
f(x)=2^(n-8)
Answers
f(x)=2^(x-2) = 2^(-4) = 1/2^4 = 1/16
answer
A.
f(x)=2^(x-2)
To win a state "A" lottery, one must correctly select 5 numbers from a collection of 50 numbers (1 through 50). The order in which the selection is made does not matter. The neighboring state "B" has a lottery where one must correctly select 6 numbers from a collection of 60. Which lottery would you rather play? Support your choice with mathematical calculations.
Answers
The graph of a function is shown: scatterplot of the following points: negative 3 and 2, negative 2 and negative 1, 2 and negative 1, and 3 and 3 Which of the following correctly identifies the set of outputs?
Answers
First, you need to plot the points in a cartesian plane as what is shown at the top of the attached picture. Then, you make a matrix wherein the x coordinates are placed in the first row, and the y coordinates in the second row (shown as the black box in the picture). Make sure that you arrange the points in order (whether clockwise or counterclockwise).
Once you create the matrix, you find its determinant. This is done by multiplying the numbers diagonally. The equation will be: arrow down - arrow up. The solution is as follows:
Determinant = [(-3×-1) + (-2×-1) + (2×3)] - [(2×-2) + (-1×2) + (-1×3)] = 20
Then, we use the equation for area of any polygon: A = 1/2*determinant
A = 1/2*20 = 10 square units
Thus, the output of the point plotted together creates a quadrilateral with an area of 10 square units.
Answer:
{–2, 1, 2, 5}
Step-by-step explanation:
i got it right on the test lol
Solve for number 9 please:)
Answers
Matt is five years older than twice his cousin andy’s age. the sum of their ages is less than 35. what is the greatest age that andy could be?
Answers
x = 5 + 2y
The second independent equation would be the sum of their ages:
x + y ≤ 35
As you can observe, I used an inequality with the symbol ≤ which means less than or equal to. It means that their sum could be less than or equal to 35. So, the equation is
x + y ≤ 35
Solving the equation,
5 + 2y + y ≤ 35
3y ≤ 35-5
3y ≤ 30
y ≤ 10
Thus, Andy's greatest age could be 10 years old.
Solve the equation for x and round your answer to the nearest hundreth. 5 = ln(x + 1)
Answers
e^5=e^(ln(x+1))
e^5=x+1
x=e^5-1
x≈147.41 (to nearest hundredth)
How long does it take to drive 25 miles at 60 mph?
Answers
60 mph = 1 mile per minute ( 60 minutes per hour)
so it would take 25 minutes to drive 25 miles
Answer:
25 min
Step-by-step explanation:
25/60=5/12=25 min
A man travels from town x to town y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he mage the round trip at an average of 55 mph. What is the distance from town x to town y
Answers
D/60 + D/50 = 2D/55 - 1/2
find common denominator ( 3300)
3300/60 = 55
3300/50 = 66
3300/55=60
so then you get 55D +66D= 60(2D)-1650
121D=120D-1650
D=1650 miles
check
1650/60 =27.5, 1650/50 = 33, 27.5 + 33 = 60.5 hours total
1650/55 = 30, 30 x 2 = 60
60.5-60 = 0.5 longer
so distance = 1650 miles
How do bearing in Gr11 trig work? I was doing this question and I can't seem to get the right answer: The observation deck on a tower is 166m above the tower, a tourist notices two boats on water from above.
- the bearing of boat A is 180, at an angle of depression of 40
- the bearing of boat B is 250, at an angle of depression of 34
Calculate the distance between the two boats.
Please help, thank you!
Answers
Boat A distance would be 166Tan(50)
Boat B distance would be 166Tan(56)
The angle between them would be 250-180 = 70 degrees
Then use the Law of Cosines to solve for the distance between them:
d^2 = A^2 + B^2 - 2AB(Cosine 70)