Solve the following for the equation:•Symmetric with respect to ___So the function is even or odd?•X and y intercepts•Period beginning and ending0 ≤ ( __ ) ≤ 2π•10 points on the graph.(2 periods)•Label graph with x and y values.
Answers
We have the function:
\(y=-\frac{5}{2}+\cos \lbrack3(x-\frac{\pi}{6})\rbrack\)a) We have to find if this function has any symmetry.
As this function can be considered a linear transformation of the cosine function and the argument is also a linear transformation of x, this function may have the same symmetries of the cosine function.
The cosine function is an odd function, as it is symmetric around the origin. It satisfy the following expression:
\(\begin{gathered} f(x)=-f(-x) \\ \cos (x)=-\cos (-x) \end{gathered}\)But in this case, as y is translated 5/2 units down, so this condition does not apply anymore.
Then, this function is neither even nor odd.
It is periodic around y = -5/2 but it is not symmetric.
b) It has nox-intercepts, as the maximum value of the function is -3/2.
The y-intercept happens when x = 0 and can be calculated as:
\(\begin{gathered} y=-\frac{5}{2}+\cos (3(0-\frac{\pi}{6}) \\ y=-\frac{5}{2}+\cos (-\frac{\pi}{2}) \\ y=-\frac{5}{2}+0 \\ y=-\frac{5}{2} \end{gathered}\)c) To calculate the period, we take into account that the period of a periodic function is the difference of the values of x that have the same y-value and derivative.
In this case, we can compare the value for this points:
\(\begin{gathered} \cos (0)=\cos (2\pi) \\ x_1\Rightarrow3(x_1-\frac{\pi}{6})=0\Rightarrow x_1=\frac{\pi}{6} \\ x_2\Rightarrow3(x_2-\frac{\pi}{6})=2\pi \\ x_2-\frac{\pi}{6}=\frac{2}{3}\pi \\ x_2=(\frac{2}{3}+\frac{1}{6})\pi \\ x_2=\frac{5\pi}{6} \end{gathered}\)Then, the function will have completed a cycle between x = π/6 and x = 5π/6.
The period will be the difference between those two values:
\(T=x_2-x_1=\frac{5\pi}{6}-\frac{\pi}{6}=\frac{4\pi}{6}=\frac{2\pi}{3}\)NOTE: we could have estimated the period from the argument of the cosine. We have a frequency of 3 multiplying the variable (-π/6 is the phase), so we can divide the cycle 2π by 3 and get 2π/3 as period.
The period is 2π/3.
d) We can use the extreme values of the cosine function and relate them to x and y.
We can complete the table:
Then, graping the points we can sketch the function as:
To graph the function, we can divide the x values in intervals of π/6.
We start with x = 0, for which y = -5/2.
Then we increase x by π/6 and y will increase to -3/2, its maximum value.
Then, we increase x by π/6 again (to π/3) and y will decrease to the mean value of -5/2.
If we increase x by π/6 again (to 3π/6 = π/2), y will decrease to its minimum value of -7/2.
Finally, if we increase x by π/6 (to 4π/6 = 2π/3), y will increase to the mean value of -5/2 and we have now completed a cycle.
We can increase x by π/6 and this cycle will be repeated.
NOTE: from the graph we can see that the function can be considered symmetric around the point (0,-5/2).
Answer:
The function is symmetric around the point (0,-5/2).
The function is neither even nor odd.
There are no x-intercepts and the y-intercept is at y = -5/2.
The period is T = 2π/3.
Related Questions
whats 2+2 UnU thats a hard one ToT
Answers
Answer:
4
MARK ME BRAINLIEST CUZ IM DA SMARTEST :))
the answer to that is 4
18-3(4.5-5) ÷ 10-2(3·2-16) =
Answers
Answer: 38.15
Step-by-step explanation:
18 - 3 x (-0.5) / 10 - 2 (6-16)
18 + 0.15 - 2 x (-10)
18 + 0.15 + 20
= 38.15
Please break down how to do these pls
Answers
The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.
Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\) 2. 2\(x^{0}\)\(y^{-2}\)
Expression for x =2 and y=5
-4x-2 + 3y0
= -4(2)-2 + 3(5)0
= 16+3
=19
Now
2x0y-2
= 2(2)0x(5)-2
= 2 x (1/25)
= 2 x 0.04
= 0.08
Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
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Find the range of the data
27,13,35,19,71,12,66,47,39
Answers
Answer:
The range is 59
Which equation is NOT a linear function?
y = 17
y=-4x – 12
y = x2-2
y = 5x
I ready
Answers
Answer:
y=x^2-2
Step-by-step explanation:
this equation is not a linear function because the equation is that of a quadratic function
suppose there are 3 identical red balls and 3 identi al blue balls. three balls are drawn one at a time, randomly, without replacementA.How many distinc sequence of balls could appear?B.Calculate the probability of seeing the sequence i.BBii. RRRC.Repeat (a) and (b) suppsing instead that jar has 3 identical red balls and 10 edintical blue balls, notice that the change from 3 to 10 blue balls dosen’t affect (a) but affect (b)
Answers
The change from 3 to 10 blue balls affects the probability of seeing the sequence BB and RRR, but does not affect the number of possible distinct sequences.
A. There are 6 possible distinct sequences of balls that could appear when 3 balls are drawn at random without replacement. The 6 possible sequences are: RRR, RRB, RBR, BRR, RBB, and BBB.
B. The probability of seeing the sequence i. BB ii. RRR is:
P(BB and RRR) = P(BB) x P(RRR)
= (3/6) x (3/5) = 1/10
C. When the jar contains 3 identical red balls and 10 identical blue balls, the number of possible distinct sequences is still 6. The probability of seeing the sequence i. BB ii. RRR is now:
P(BB and RRR) = P(BB) x P(RRR)
= (10/13) x (3/12) = 5/39
The change from 3 to 10 blue balls affects the probability of seeing the sequence BB and RRR, but does not affect the number of possible distinct sequences.
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9. The height of a triangle is 3 inches less than twice the length of its base. If the total area
of the triangle is 7 square inches, then find the lengths of the base and height.
Answers
Check the picture below.
\(\textit{area of a triangle}\\ A = \cfrac{1}{2}bh~~ \begin{cases} A = area\\ b = base\\ h = height\\[-0.5em] \hrulefill\\ A = 7\\ h = 2b - 3 \end{cases}\implies 7 = \cfrac{1}{2}b(2b-3)\implies 7=\cfrac{b(2b-3)}{2} \\\\\\ 14 = b(2b-3)\implies 14 = 2b^2-3b\implies 0 = 2b^2-3b-14\)
\(0 = (b+2)(2b-7)\implies\blacktriangleright b= \begin{cases} -2\\ \frac{7}{2}~~\textit{\large \checkmark} \end{cases}\blacktriangleleft \\\\\\ \stackrel{\textit{we know that}}{h = 2b - 3}\implies h = 2\left( \frac{7}{2} \right)-3\implies h = 7 - 3\implies \blacktriangleright h = 4 \blacktriangleleft\)
On a given day, a particular raccoon will eat the trash from one of three different houses. If he eats from the trash of a particular house, he has a 50% chance to eat from the same house the next day, and a 25% chance each to eat from one of the other two houses. What is the stochastic matrix for this scenario
Answers
Answer:
Step-by-step explanation:
On a given day , a particular raccoon will eat the trash from one of three different houses.
Let assume \(Y_n\) be a random variable that illustrating the house raccoon will eat on an unknown given nth day.
If he eats from the trash of a particular house, he has a 50% chance to eat from the same house the next day, and a 25% chance each to eat from one of the other two houses.
There are three states given in the above statement.
So, we can have state 1, state 2 and state 3
Assuming that:
state 1 = house 1
state 2 = house 2
state 3 = house 2
If he eats from the trash of a particular house,
For state 1 : he has a 50% chance to eat from the same house the next day
i.e state 1 = 0.50
and a 25% chance each to eat from one of the other two houses.
For state 2 and state 3: = 0.25
i.e state 2 = 0.25
state 3 = 0.25
NOW:
\(\mathtt{P[Y_{n+1 }= 0 \ | \ Y_n = 0] = 0.5}\)
\(\mathtt{P[Y_{n+1 }= 1 \ | \ Y_n = 0] = 0.25}\)
\(\mathtt{P[Y_{n+2}= 2 \ | \ Y_n = 0] = 0.25}\)
\(\mathtt{P[Y_{n+1 }= 0 \ | \ Y_n = 1] = 0.25}\)
\(\mathtt{P[Y_{n+1 }= 1 \ | \ Y_n = 1] = 0.5}\)
\(\mathtt{P[Y_{n+1 }= 2 \ | \ Y_n = 1] = 0.25}\)
\(\mathtt{P[Y_{n+1 }= 0 \ | \ Y_n = 2] = 0.25}\)
\(\mathtt{P[Y_{n+1 }= 1 \ | \ Y_n = 2] = 0.25}\)
\(\mathtt{P[Y_{n+1 }= 2 \ | \ Y_n = 2] = 0.5}\)
The stochastic matrix for this scenario can be computed as:
0 1 2
\(P = \left\begin{array}{c}0\\1\\2\end{array}\right \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\)
\(\mathbf{ P =\left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right] }\)
In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
Answers
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
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On a map. 1 inch equals 19.4 miles. If two cities are 3.5 inches apart on the map, how far are they actually apart?
Answers
Answer:
67.9 miles
Step-by-step explanation:
Since 1 inch equals 19.4 miles, multiply the number of inches by 19.4
3.5 × 19.4 = 67.9
The two cities are 67.9 miles apart.
Find the 59th term of the arithmetic sequence 26, 17, 8,.
Answers
From the present question. we can find the following relation, where n stands for the position:
\(A_n=35-9n\)The 59th term is given by:
\(\begin{gathered} A_{59}=35-9\times59=35-531 \\ A_{59}=-496 \end{gathered}\)The 59th term is -496PLEASE HELP ASAP
solve -1/6[3-15(1/3)2]
![PLEASE HELP ASAP solve -1/6[3-15(1/3)2]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/C0Nx4ldjSdyeTD1pu34mYu8d7IAOliwi.png)
Answers
Answer:
C) -2/9
Step-by-step explanation:
\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)
Answer:
Hence, Option (C) - 2/9 is the Answer:
Step-by-step explanation:
-1/6 [3 -15(1/3)^2]
-1/6(3 -15)(1/9))
-1/6(3 - 5/3)
-1/6 (4/3)
Hence, Option (C) - 2/9 is the Answer:
I hope it helps!
HELP PLS ASAPPP!!!
algebra problem; solving linear inequalities !!! :)
Answers
Answer: x = -3/2
Step-by-step explanation:
A number increased by 35
Answers
Answer:
x+35
Step-by-step explanation:
Find a positive and a negative coterminal angle for each given angle.
Answers
A positive and a negative co - terminal angle for each given angle is 1) -π/2 and -9π / 2 and 2) 7π / 2 and -π / 2 .
Given :
a positive and a negative co - terminal angle for each given angle
1 )
= -5π / 2
To find positive and negative co - terminal angle we need to add and subtract by 2π .
= -5π / 2 + 2π
= -5π + 4π / 2
= -π/2
= -5π / 2 - 2π
= -5π - 2 * 2π / 2
= -5π - 4π / 2
= -9π / 2
or =
2 )
= 3π / 2
= 3π / 2 + 2π
= 3π + 2 * 2π / 2
= 3π + 4π / 2
= 7π / 2
= 3π / 2 - 2π
= 3π - 4π / 2
= -π / 2
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Tell whether the angles are adjacent or vertical. Then find the value of x. (4x-25)
Answers
Answer:
i dont see the angles but heres how to solve for X
Step-by-step explanation:
y=2 x − 12 has how many real roots?
Answers
Answer: One root
Reason:
The term "root" refers to the x intercept.
We plug in y = 0 and solve for x to get the x intercept
y = 2x-12
0 = 2x-12
2x = 12
x = 12/2
x = 6
The root is 6.
The single x intercept is located at (6,0).
it takes carina on average 20 minutes to assemble product x . how many of products x can carina be expected to assemble in 3 hours and 40 minutes if she takes a 20 minute work break during her assembly time
Answers
Carina can assemble 10 products within the give time
please helpppppp
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Greg bought a regular-sized box of his favorite cereal. A regular-sized box contains 12 servings.
Part A: If Greg eats 1 1/2 servings for breakfast every day, how many breakfasts can Greg eat from 1 box? Show all work.
Part B: The regular-sized box of cereal costs $4.29. How much does 1 breakfast from a regular-sized box of cereal cost Greg? Round to the nearest hundredth. Show all work.
Part C: If Greg purchased the family-sized box of cereal that contains 18 servings, how many more breakfasts could Greg eat from 1 box? Show all work.
Answers
a. Greg can eat 8 breakfasts from 1 box.
b. The cost of 1 breakfast from a regular-sized box is $34.32.
c. Greg will enjoy 4 breakfast more.
How to calculate the fraction?a. A regular-sized box contains 12 servings. If Greg eats 1 1/2 servings for breakfast every day, the number of breakfasts that Greg can eat from 1 box will be:
= 12 ÷ 1 1/2
= 12 ÷ 1.5
= 8
b. Since the regular-sized box of cereal costs $4.29. The cost of 1 breakfast from a regular-sized box of cereal cost Greg will be:
= 8 × $4.29
= $34.32
c. If Greg purchased the family-sized box of cereal that contains 18 servings, the number of breakfasts will be:
= 18 ÷ 1.5
= 12 breakfast
The difference will be:
= 12 - 8
= 4 breakfast more.
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Find the slope P=(-4,-1) Q=(-3,-3)
Answers
The slope of P=(-4,-1) Q=(-3,-3) is -2.
Given,
P=(-4,-1)
Q=(-3,-3)
The slope between two points P=(x₁, y₁)
Q=(x₂ ,y₂)
slope = (y₂-y₁)/(x₂-x₁)
So slope between P=(-4,-1) Q=(-3,-3) is
[(-3)-(-1) ]/ [(-3)-(-4)]
=-2/1
=-2
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
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Please guys help to solve this problem
Answers
9514 1404 393
Answer:
300
Step-by-step explanation:
Since nobody failed, the number who passed one or the other was 100%.
P(O + W) = P(O) +P(W) -P(O&W)
100% = 80% +70% -P(O&W)
P(O&W) = 50% = 150 students
If 150 students are 50% of the examinees, then 100% will be 300 students.
Answer:
\(300\)hope it helps
#CARRYONLEARNINGA survey of 100 high school students provided this frequency table on how students get to school. What is the probability that a randomly selected student is a junior who takes the bus?
Answers
The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.
The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.
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i dont under stand 0=
Answers
Answer:
b = 90°
Step-by-step explanation:
There are three angles indicated in this image: 244°, 23°, and m∠b and the sum of these three angles is equal to 360° because they make full angle.
So to find the measure of m∠b, we need to add all given angles:
244° + 23° + m∠b = 360°
Add like terms.267° + m∠b = 360°
Subtract 267° from both sides to isolate b.m∠b = 93°
20, 18, 21, 18, 22, 24, 18, 23, 23, 24 Explain the meeting of the interquartile range as it relates to the number of students in the kindergarten classes
Answers
The interquartile range of the data-set is of 5.5, which means that the middle 50% kindergarten classes has a number of students that differ by at most 5.5.
What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile(Q1) is the median of the first half of the data-set, and is also the 25th percentile.The third quartile(Q3) is the median of the second half of the data-set, and is also the 75th percentile.The interquartile range(IQR) represents the middle 50% of the distribution, and is given by Q3 - Q1.For this problem, the ordered data-set is given by:
18, 18, 18, 20, 21, 22, 23, 23, 24, 24.
There are 10 elements, hence:
The first half is 18, 18, 18, 20, which has median (18 + 18)/2, hence Q1 = 18.The second half is 23, 23, 24, 24, which has median (23 + 24)/2, hence Q3 = 23.5.Then the IQR is:
Q3 - Q1 = 23.5 - 18 = 5.5.
The IQR is of 5.5, which means that the middle 50% kindergarten classes has a number of students that differ by at most 5.5.
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Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
Answers
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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which expression represents the situation "add seven to the product of a number and ten?
A-10(z+7)
B-7+z+10
C-10z+7
D-7z+10z
Which one?
Answers
The situation "add seven to the product of a number and ten" can be represented by the expression 10z + 7, where z is the number. The expression 10z represents the product of a number and ten, and adding 7 to it gives the final result. Therefore, the correct answer is C-10z+7.
if a small cup is 10 oz and cost 2.69 what is the cost per ounces
Answers
Answer:
The cost per ounce of the small cup is $0.269
Step-by-step explanation:
To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.
Cost per ounce = Cost of the cup ÷ Number of ounces in the cup
Cost of the cup = $2.69
Number of ounces in the cup = 10 oz
So,
Cost per ounce = $2.69 ÷ 10 oz
Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)
Therefore, the cost per ounce of the small cup is $0.269.
You lease a car at $23,495 for 3 years at $429.95 a month with a $500 down payment. The interest is 30% of the payments and $4,643.46 in interest is paid over 3 years. What is the remaining balance when the lease ends? How did you arrive at $12,160.26?
Answers
Answer:
Step-by-step explanation:
total interest paid is given as $4,643.46.
total payments = $429.95 x 36 months = $15,478.20
total lease payments = total payments - total interest
total lease payments = $15,478.20 - $4,643.46 = $10,834.74
Remaining balance = Total cost of the lease - Total lease payments
$23,495 - $10,834.74 = $12,660.26
An arborist is preparing the fuel mix for her chainsaw before climbing a tree to remove a dead limb. The two-stroke chainsaw
requires a 5% mix of engine oil to gas-that is, the amount of oil should be 5% of the amount of gas. How much engine oil should
be added to a jerry can that contains 3.8 gallons of gas?
(Type a whole number or a decimal)
Answers
Answer:
To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:
0.05 x 3.8 = 0.19
So, 0.19 gallons of engine oil should be added to the jerry can.
Please help me
Find product
Answers
Answer:
s^2u^2−5stu+6t^2
Step-by-step explanation:
Answer:
6t^2-5tsu+s^2u^2
Step-by-step explanation: