Which of the following could be the equation of the function below? On a coordinate plane, a curve crosses the y-axis at y = 2. It has a maximum at 5 and a minimum at negative 1. It goes through one cycle at pi. y = negative 3 sine (2 (x + pi)) + 2 y = negative 3 sine (x + pi) + 2 y = 3 sine (4 (x minus pi)) + 4 y = 3 sine (2 (x + pi)) + 2
Answers
Answer:
b
Step-by-step explanation:
We want to find a sine function such that:
it has a y-intercept equal to 2.it has a maximum of at 5, and a minimum at -1.it goes through one cycle at pi.The given options are:
y = -3*sin(2*(x + pi)) + 2 y = -3*sin(x + pi) + 2 y = 3*sin(4*(x - pi)) + 4 y = 3*sin(2*(x + pi)) + 2Notice that the first information that we have, implies that y must be equal to 2 when x = 0.
Knowing that we can discard the third option which has a y-intercept of 4.
Now the second. Remember that for a general function:
y = A*sin(k*x) + M
Where A is the amplitude and M is the midline, the maximum and minimum are given by:
A + M
-A + M
In all the remaining options we have:
A = ± 3
M = 2
We can see that with these we get the maximum and minimum of 5 and -1.
Finally, we know that it goes through one cycle at pi.
This means that if f(x) is the function, then:
f(x) = f(x + pi)
Also remember that for a general sine function, we have:
sin(x) = sin(x + 2*pi)
Ok, now let's analyze the options (only the sine part)
1) sin(2*(x + pi)) = sin( 2*x + 2*pi) = sin(2*x)
if we evaluate this in x + pi, we will get:
sin(2*( x + pi + pi)) = sin(2*(x + 2*pi)) = sin( 2*x + 4*pi) = sin(2*x)
So yes, option 1 is a correct option (you also can see that option 4 has the exact same sine part, so that option is also correct.)
2) for the second option the sine part is:
sin(x + pi)
if we evaluate this in x + pi we get:
sin(x + pi + pi) = sin(x + 2*pi) = sin(x)
and we have:
sin(x +pi) ≠ sin(x)
Then this function does not go through one cycle at pi.
We can conclude that the two options that meet all the conditions are the first one and fourth one:
1) y = -3*sin(2*(x + pi)) + 2
4) y = 3*sin(2*(x + pi)) + 2
We can't say which one is correct if we do not look at the graph.
If the function starts increasing, then (2) is the correct one, if the graph starts decreasing, then (1) is the correct one.
Below, you can see a graph of both functions:
The green one is y = 3*sin(2*(x + pi)) + 2, the blue one is y = -3*sin(2*(x + pi)) + 2
If you want to learn more, you can read:
https://brainly.com/question/14068845
Related Questions
Solve the system of equations.
- 4x + 1ly = 15
x = 2y
Answers
x=2y
-4(2y)+11y=15
-8y+11y=15
-3y=15
-3y/-3=15/-3
Y=-5
X=2y
X=2(-5)
X=-10
What is the volume of the right cone below?
Answers
Answer:
The answer is A.
Step-by-step explanation:
You have to use the formula of volume of cone,
[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
Given that the diameter of cone is 10 units so the radius is 5. Then substitute the followung values into the formula :
Let r = 5 units,
Let h = 45 units,
[tex]v = \frac{1}{3} \times \pi \times {5}^{2} \times 45[/tex]
[tex]v = \frac{1}{3} \times \pi \times 1125[/tex]
[tex]v = 375\pi \: \: {units}^{3} [/tex]
Answer:
[tex]375\pi \: \: units ^{3} [/tex]
Answer A is correct.Step-by-step explanation:
[tex]v = \pi {r}^{2} \frac{h}{3} \\ =\pi \times 5 \times 5 \times \frac{45}{3} \\ = \pi \times 25 \times 15 \\ = 375\pi \: \: units ^{3} [/tex]
What is the slope of the line that passes through the points (3, 4) and (0,–2)?
Write your answer in simplest form.
Answers
Answer:
Slope = 1/2
Whole equation: y = 1/2x - 2
Step-by-step explanation:
Equation: y = mx + b
(3 , 4) and (0 , -2)
[tex]\frac{0 - 3}{-2 - 4} = \frac{-3}{-6} = \frac{1}{2}[/tex]
y = 1/2x + b
---------------------------------------------------------------------------------------------
-2 = 1/2(0) + b
-2 = b
Find the domain and range
Answers
Answer:
Domain: x = all reals
Range: y is less than or equal to -4
14 adults and 20 children attended a piano recital. If two people are selected to receive door prizes at the recital, what is the probability that both will be children? Write your answer as a fraction and a decimal rounded to the nearest hundredth.
Answers
Answer: 0.34
Step-by-step explanation:
From the question, 14 adults and 20 children attended a piano recital. This means that there are 14 + 20 = 34 people who attended the paint recital.
If two people are selected to receive door prizes at the recital, the probability of selecting the first child will be 20/34 while the second child will be 19/33. To get the probability of both being children, we have to multiply the fractions
= 20/34 × 19/33
= 380/1122
= 0.34
Evaluate.
4+ (3+5)*3 =
Answers
Answer: 28
Step-by-step explanation: Follwing PEMDAS, add the 3 and 5 in the parentheses first. You get 8, then multiply by 3, which gives you 24. Add 4 to 24 and it will give you 28.
Answer:
If i'm not mistaken, using PEMDAS which is parenheses, exponents, multiplication, division, adding and subtracting, the answer will be 28.
Step-by-step explanation:
3+5=8
8 * 3= 24
24 + 4= 28
I NEED HELP QUICKKKKKKKKK PLZ
-1/2(-3y+10)
Answers
Answer:
I think its 1.5y-5
Step-by-step explanation:
-1/2×3y=1.5y
-1/2×3=-5
Order the following numbers from least to greatest.
Put the lowest number on the left.
24. 72. 48. -24.
Answers
Answer:
-24, 24,48,72
Step-by-step explanation:
Simplify the expression
Answers
Look at the attached picture
Hope it will help you....
Good luck on your assignment
Answer:
for number one the it is c
Step-by-step explanation:
(6-3)^2
3^2=9
because 3 times 3 equal to 9
it just like saying what is the answer when you multiply the number by its self
Please help me as soon as possible!
Answers
......
What is the volume of a rectangular prism that measures 45units long, 25 units wide, and 35 units high?
Answers
Answer:
39375
Step-by-step explanation:
All you have to do is just multiply the length x width x height.
Answer:
Find a rectangular prism in your house exactly the same as this one,them you'll know the answer
A letter L with a height of 9 inches is drawn on the actual flag. What should be the height and inches of a letter L in the scale drawing? Explain plzzz....
Answers
Answer:
0.5 inch on the drawing
Step-by-step explanation:
The following information is missing:
The scale factor of the drawing to the actual flag is represented by the ratio 1:18.
This scale factor means that 1 inch on the drawing are equivalent to 18 inches o n the actual flag. We want to know the height on the drawing, given that a height of 9 inches is drawn on the actual flag. The following proportion must be satisfied:
1 inch on the drawing / x inch on the drawing = 18 inches o n the actual flag / 9 inches o n the actual flag
x = 9/18 = 0.5 inch on the drawing
If x+y = b and −x+3y=a, then what is y?
Answers
37.5(3.8-x)+90x=300 please help me
Answers
Answer:
I’m just copying his answer which is 3
Step-by-step explanation:
at least I tried
Answer: 3
Step-by-step explanation:
37.5 (3.8-x) + 90x = 300
First, you have to simplify, by using the Distributive Property.
142.5 - 37.5x + 90x = 300
Now, add the like terms
142.5+ 52.5x = 300
Now, isolate the variable, meaning the variable has to be on one side on its own. You would have to subtract 142.5 and move it to the other side
52.5x = 300 - 142.5
52.5x = 157.5
Then, you divide!
[tex]\frac{52.5x}{52.5x}[/tex] = [tex]\frac{157.5}{52.5x}[/tex]
= 3
In the expression 16x + 2x – 5y + 17, which terms are “like terms”?
Also i didn't mean to say exam on last question, turns out it was a quiz, my bad it just has alot of questions over 4, it has 6.
Answers
Answer:
16x and 2x have like terms
6% of x = 1.2; what is x
Answers
Answer:
x =20
Step-by-step explanation:
6% of x = 1.2
Change percent to decimal form
.06x = 1.2
Divide each side by .06
.06x / .06 = 1.2/.06
x =20
Pls someone I need help
Answers
Answer:
B. Dan walked uphill, then downhill.
Step-by-step explanation:
The place that the slope went up is based on the distance from the starting point, so the distance is up then down. I hope this helped and please mark me as brainliest!
4
A ramp made of solid concrete for wheelchairs is to be made to the dimensions shown below. How many
cubic meters of concrete will be needed to make the ramp?
2m
0.6m
20m
Answers
Answer:???
Step-by-step explanation:
help pls!!!!!!!!!!!!
Answers
Answer:
w=9z
Step-by-step explanation:
For each z value, w is 9 times that. For instance, 18 is 9 times 2, and 45 is 9 times 5. Therefore, the equation that would describe this is w=9z. Hope this helps!
Answer:
z = (1/9) w or w = 9z
Step-by-step explanation:
w = 18 , z = 2
if relationship is proportional than z = k (constant) *w
2 = k * 18 divide each side by 18
k = 2/18 = 1/9
The frequency table represents the results of a survey comparing the average age of household members to the way that they watch non-network television. A 4-column table with 3 rows titled Television Viewing Method. The first column has no label with entries internet, cable, total. The second column is labeled average household age under 40 with entries 54, 81, 135. the third column is labeled average household age 40 or older with entries 23, 92, 115. the fourth column is labeled total with entries 77, 173, 250. Madigan converts the frequency table to a conditional relative frequency table by row. Television Viewing Method A 4-column table with 3 rows titled Television Viewing Method. The first column has no label with entries internet, cable, total. The second column is labeled average household age under 40 with entries W, Y, 0.54. The third column is labeled average household age 40 or older with entries X, Z, 0.46. The fourth column is labeled total with entries 1.0, 1.0, 1.0. Which value should she use for X? Round to the nearest hundredth. 0.09 0.20 0.25 0.30
Answers
Answer:
For X they would have to divide the number from the first given chart for average household of the people that are ages 40 or under, which is 23, by the total internet, which is now 77.
Therefore, X = 23/77 = 0.2987, which would round to 0.30
Mark as brainliest please, I need a few more :)
Answer:
.30
Step-by-step explanation:
< 40 > 40 total
internet 54 23 77
cable 81 92 173
total 135 115 250
< 40 > 40 total
internet w x 1
cable y z 1
total .54 .46 1
x is 23 /77 =.29870
how many faces does this pyramid have?
ASAP WILL MARK BRAINLIEST!!!
Answers
Answer:
I believe it is 5
Step-by-step explanation:
by counting all sides
Answer:
5
Step-by-step explanation:
hi annalise!
Hello, I need help to figure out the arc measure of AH and GC. Could someone please give me the answer as well as the work ?
Thank you in advance!
Answers
Answer:
AH=AB and GC=CB
Step-by-step explanation:
Asphere and a cylinder have the same radius and height. The volume of the cylinder is 64 m3.
hl
.
Answers
Answer:
r=21.3 h=32
Step-by-step explanation:
If a cube has a volume of 27mm3,
what is the length of one side?
Answers
Answer:
Step-by-step explanation:
Answer:
9mm
Step-by-step explanation:
since volume is l x w x h, you have to divide 27 by 3. you can do this because it is a cube
Factor out the Greatest Common Monomial Factor 8a + 86
Answers
Answer:
-1.12044185014
Step-by-step explanation:
i think this is the answer. i looked it up.
Answer:
2(4a + 43)
Step-by-step explanation:
8a + 86
2(4a + 43)
-1 3/7 • (-3 2/5)
Find the product simplify if possible
Answers
Answer:
6 4/5
Step-by-step explanation:
-1 3/7 • (-3 2/5)
Let's turn them both into fractions with no whole numbers to make this easier:
-10/7 • -17/5
Now we can multiply straight across much easier!
170/35 (the negatives canceled each other out)
34/5 (simplified)
6 4/5 (answer)
Hope this helps! Please mark Brainliest :)
Find the 43rd term of each sequence.
1. 21,12,9,3,...
Answers
Answer:
-231
Step-by-step explanation:
21, 12, 9, 3,...
Below is image
Answer:
-357
Step-by-step explanation:
a + (n-1)d
21+(42)(-9)
21-378
HELP PLEASEEEE FAST
128
164
140
Answers
Answer: 140 m3
Step-by-step explanation:
Multiply the area of the trapezoid face by the length .
Since the area is 20, you multiply it by 7 to get 140
Answer:
140 m^3
Step-by-step explanation:
This is a prism with a trapezoid base.
The volume if a prism is
V = (area of base) * height
The base is the trapezoid in the front face. The height is the distance between bases which is 7 m.
area of trapezoid = (b1 + b2)h/2
In the area of the trapezoid, h is the height of the trapezoid which is the distance between parallel bases. It is 4 m in this case.
V = (area of base) * (height of trapezoid)
V = (8 m + 2 m)(4 m)/2 * 7 m
V = 20 m^2 * 7 m^2
V = 140 m^3
Please, someone, help me quickly!!
Answers
Answer:
(B)
Step-by-step explanation:
The value of 9 is more than the value than 4.
Therefore,
9 > 4.
4 is not greater than 9, and nine is not less than four.
Brainilest Appreciated!
The volume of the cylinder below is 108π cm^3.
Select the correct radius.
a.) 3 cm
b.) 6 cm
c.) 12 cm
d.) 36 cm
Answers
Answer:
i think it is d or c idk
Step-by-step explanation
108 divided by 3 is 36 idk if you have to divide by 2 but i think its d
