17. Identify the amplitude, period, and vertical shift for the
function shown. Then write an equation that represents the curve.
m
A=
B=
P=
C=
f(x)=
Answers
Answer:
[tex]f(x)=2cos(x+\frac{\pi}{2})+3[/tex]
Step-by-step explanation:
Because the function is symmetric about the y-axis, using the cosine function is most appropriate.
Refer to the equation for a cosine function:
[tex]f(x)=acos(bx+c)+d[/tex]
Amplitude: [tex]|a|[/tex]
Period: [tex]\frac{2\pi}{|b|}[/tex]
Phase shift: [tex]-\frac{c}{b}[/tex]
Midline: [tex]y=d[/tex]
The amplitude would be the average of the maximum and minimum y-values of the function, which would be [tex]|a|=|\frac{5-1}{2}| =|\frac{4}{2}| =|2|=2[/tex].
The value of [tex]b[/tex] in [tex]\frac{2\pi}{|b|}[/tex] represents the length of the period, so since the length of the period is [tex]2\pi[/tex], this means that [tex]b=\frac{2\pi}{|2\pi|} =1[/tex].
The phase shift, [tex]-\frac{c}{b}[/tex], describes the horizontal shift of a function. Because the phase shift is [tex]-\frac{\pi}{2}[/tex], then we can set up the equation [tex]-\frac{\pi}{2}=-\frac{c}{1}[/tex] where we determine [tex]c=\frac{\pi}{2}[/tex].
The midline (or vertical shift), [tex]d[/tex], is the horizontal line that passes through between the maximum and minimum points, which the function oscillates. In this case, the midline would be located at the line [tex]y=3[/tex], therefore, [tex]d=3[/tex].
Putting all our information together, your final equation is:
[tex]f(x)=2cos(x+\frac{\pi}{2})+3[/tex]
Related Questions
can someone say what 45-49 is with regrouping? thanks!
Answers
Answer:
it's -4 i don't know what you mean by regrouping, sorry
Step-by-step explanation:
Answer:
45-49
=-4 ans!
this is the answer
Construct and interpret a 95% confidence interval to estimate the proportion of the earth that is water. Show all work. Make sure to check your conditions and state your conclusion.
1.) Randomly selected
2.) Less than 10% of population
3.) 50 (0.68)
50 (0.32)
Answers
the answer would be 2
I need help on this question it’s due tomorrow.
Answers
The transformation in the graph is 1 units vertically downwards.
The correct option is A: The graph of g(x) is the graph of f(x) shifted down 1 unit.
What is transformation on the graphs?Let the function f(x) and g(x) are two real functions.
And g (x) = f (x) + k, where k is real numbers.
Function can be sketched by shifting f (x), k units vertically.
The direction of shift can be found by the value of k:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
Given:
The function f(x) = eˣ,
and the function g(x):
g(x) = f(x)-1= eˣ-1.
The graph of both the functions are given in the attached images.
For the base function f (x) and a constant k, the function given by
The transformations in the graph is defined by:
g (x) = f (x) + k, where k is real numbers.
Function can be sketched by shifting f (x), k units vertically.
The value of k determines the direction of the shift. Specifically,
if k > 0, the base graph shifts k units upward, and
if k < 0, the base graph shifts k units downward.
Here, k = -1
And the graph of g(x) is the graph of f(x) is shifted down 1 unit.
Therefore, the f(x) is shifted to 1 unit downward.
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Solve 8 = 2x +4.(1 point)
01) x = -4
O2) x = -1
3) x = 0
4) x = 7
Answers
Answer:
x=2, should be the correct answer but that isnt a choice
Step-by-step explanation:
8=2x+4
4=2x
2=x
x=2
An online health and medicine company claims that about 50% of Internet users would go to an online sight first for
information regarding health and medicine. A random sample of 1318 Internet users was asked where they will go for
information the next time they need information about health or medicine; 606 said that they would use the Internet. Test
the claim that less than 50% of Internet users get their health questions answered online.
Answers
Answer:
The claim that less than 50% of internet users get their health questions answered online is correct, given that according to the survey, 45.98% of people do.
Step-by-step explanation:
Since an online health and medicine company claims that about 50% of Internet users would go to an online sight first for information regarding health and medicine, and a random sample of 1318 Internet users was asked where they will go for information the next time they need information about health or medicine; 606 said that they would use the Internet, to test the claim that less than 50% of Internet users get their health questions answered online, the following calculation must be performed:
1318 = 100
606 = X
606 x 100/1318 = X
60600/1318 = X
45.978 = X
Therefore, the claim that less than 50% of internet users get their health questions answered online is correct, given that according to the survey, 45.98% of people do.
The amount of gas that a helicopter uses is directly proportional to the number of hours
spent flying. The helicopter flies for 2 hours and uses 24 gallons of fuel
. Find the number of
gallons of fuel that the helicopter uses to fly for 5 hours,
Answers
Answer:
60 gallons
Step-by-step explanation:
We can create a ratio for this. If we consider 2 as the 1 in the ratio, we have a ratio of 1 : 2.5. Therefore, we just need to multiply 24 by 2.5, which equals 60.
Help!! Factor the common factor out of each expression
Answers
Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).
What is the equation?A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.
Here,
the two numbers' primary factors are as follows:
-25[tex]b^{2}[/tex] + 15b
Common prime factors can be multiplied to determine the GCF:
=> -25[tex]b^{2}[/tex] = -(5)(5) * [tex]b^{2}[/tex]
=> 15b = (5)(3)b
The expression can be factored in the following fashion because the GCF is 5b:
=> -(5)(5) * [tex]b^{2}[/tex] + (5)(3)b
=> (5b)(-5b+3)
Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).
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There are 120 students and 10 teachers at a small private school. To keep the same
student to teacher ratio, how many teachers are needed for 240 students?
Answers
Answer:
20
Step-by-step explanation:
Which of the following sentences is true?
Answers
Answer:
option a is correct
Step-by-step explanation:
any square is also a rhombus
Which is better 4:3 odds or 3:4 odds? Why?
Answers
Answer:
no problem?
Step-by-step explanation:
anyone know this click to see links will be reported
Answers
7
15
-5
1
-4
Find the inverse of the function.
Y = x + 8
Answers
Answer:
Im almost certain its x-8=y
Step-by-step explanation:
Answer:
[tex]f - 1(x) = x + 8[/tex]
i hope it helps
A: Tomato - 20
B: Cucumber- 9
C: Peas - 27
D: Onion - 6
Answers
Answer:
A(tomatos)
Step-by-step explanation:
So to sovle these, we have to look at the percentage chart, and take the percentage of each thing.
tomato - 30%cucumber - 15%peas - 45%onion - 10%We know that divide these numbers by 100 gets us the amount we can multiply the total by, which gives us our answer.
So tomato is .3, cucumber is .15, peas are .45, and onion is .1.
Now, lets mutiply these nubmers by the 60 and see what we get:
.1*60
=
6
That seems correcdt for the onion
.45 * 60
=
27. That looks correct for peas.
.15 * 60
=
9 That looks correct for cucumber
.3*60
=
18. Thats not 20! So that must be the answer!
Hope this helps!
When x^2-2x + 14 is divided by x-1 the remainder is?
Is it 13?
Answers
Yes, 13 is the remainder.
See dat pic for full solution.
Raina has to give medicine to her cat every morning for the next days. How many weeks is this?
Answers
Answer:
(number of days)/7
Step-by-step explanation:
1 week = 7 days
Divide the number of days by 7 to find the number of weeks.
 please let me know question 10
Answers
I need help with this?
Answers
The first equation will be multiplied by 3 and that of the second by 4.
What is an elimination method?An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.
Given that are two equations to be solved by using elimination method,
-4x+4y = 32.....(i)
3x-y = 12......(ii)
To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4
-12x+12y = 96.....(iii)
12x-4y = 48....(iv)
Solving the equations, we get,
8y = 144
y = 18
Put y = 18 in eq (ii)
3x-18 = 12
3x = 30
x = 10
Hence, the first equation will be multiplied by 3 and that of the second by 4.
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4 x 3/6 = [] x1/6
What number makes the equation true?
Answers
∫
1
/
√
1
+
(
ln
x
)
2
d
x
Answers
The integral ∫1/√1 +(lnx) 2dx is -x+2xln(x)+c
What is Integration?An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data
The given integral is ∫1/√1 +(lnx) 2dx
= ∫1 +2(lnx)dx
Apply the sum rule
∫f(x)±g(x)=∫f(x)±∫g(x)
= ∫1dx +2∫(lnx)dx
=x+2(xln(x)-x)+c
=-x+2xln(x)+c
Hence, the integral ∫1/√1 +(lnx) 2dx is -x+2xln(x)+c
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what is the surface area of this rectangular pyramid
Answers
Answer:
Hello! answer: 75
Step-by-step explanation:
5 × 5 = 25 for a square
for a triangle 5 × 5 = 25 25 ÷ 2 = 12.5 12.5 × 4 = 50 25 + 50 = 75 therefore the total area is 75 HOPE THAT HELPS!
need some help please
Answers
Answer:
what help I will help yoy
please help !!!!!!!!
Answers
8.96848786347
i think this should be right i did it with my 5th grade math skills and dont wory i have an a+
write the equation for the hyperbola with foci (-12,6) , (6,6)and vertices (-10,6), (4,6)
Answers
The equation for hyperbola with given foci is [tex]\frac{(x+3)^{2}}{49}-\frac{(y-6)^{2}}{32}=1[/tex]
What is hyperbola?
In analytical geometry, a hyperbola is a conic section that results from the intersection of a plane with a double right circular cone at an angle that touches both of the cone's halves. The two distinct unbounded curves that result from the intersection of the plane and cone are known as hyperbolas.
The standard equation of a horizontal hyperbola with center (h,k) is
[tex]\frac{(x-h)^{2}}{a^{2} } -\frac{(y-k)^{2}}{b^{2} }=1[/tex]
The given hyperbola has vertices at (–10, 6) and (4, 6).
The length of its major axis is 2a= 4-(-10)
2a=14
a=7
The center is the midpoint of the vertices (–10, 6) and (4, 6).
The center is [tex](\frac{-10+4}{2} , \frac{6+6}{2} )= (-3,6)[/tex]
Now, we need to use the relation a^2+b^2=c^2 in order to find b^2.
The c-value is the distance from the center (-3,6) to one of the foci (6,6)
c= 6-(-3)=9
So, 7^2+b^2=9^2
b^2= 9^2-7^2
b^2= 81-49
b^2= 32
Hence, on substituting the obtained values in the standard equation of hyperbola, we get
[tex]\frac{(x-(-3))^{2} }{7^{2}}-\frac{(y-6)^{2} }{32} =1[/tex]
[tex]\frac{(x+3)^{2} }{49}-\frac{(y-6)^{2} }{32} =1[/tex]
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Consider the function f(x) = 2x and the function g(x).
g(t) = f(x + 4)
= 2( + 4)
How will the graph of g(x) differ from the graph of Ax)?
OA
The graph of g(x) is the graph of Ax) shifted 4 units to the left.
OB The graph of g(x) is the graph of f(x) shifted 4 units upward.
C. The graph of g(x) is the graph of f(x) shifted 4 units downward.
D. The graph of g(x) is the graph of Ax) shifted 4 units to the right..
Answers
Answer:
c
Step-by-step explanation:
c
Answer:
a
Step-by-step explanation:
PLS HURRY! THANK YOU
A. y=(x+5)^2-1125
B. y=(x-5)^2+1125
C. y=-5(x+5)^2-1125
D. y=-5(x-5)^2+1125
Answers
Answer:
C. y=-5(x+5)^2-1125 i don't know is this is right
Answer: It’s D, y = -5 (x - 5)^2 + 1125
Step-by-step explanation:
Linda bought a total of 12 lb of flounder and shrimp and paid $20 for the flounder and $20 for the shrimp. If the price per pound of the shrimp is twice that of the flounder, how many pounds of each did she buy?
Select one:
a.
8 lb shrimp and 4 lb flounder
b.
4 lb shrimp and 8 lb flounder
c.
6 lb shrimp and 6 lb flounder
d.
2 lb shrimp and 10 lb flounder
Answers
Answer:
B: 4 lb shrimp and 8 lb flounder
Step-by-step explanation:
if the price of shrimp is twice the price for flounder, you will have twice as much flounder as you have shrimp, so in terms the only answer that applies to this is B.
speed getsa u brainle
Answers
Answer:
ye?
Step-by-step explanation:
1. Indicate whether the following statements are True (T) or False (B).
(a) Unicellular organisms have one-celled body.(t/f)
(b)
Muscle cells are branched.(t/f)
(c) The basic living unit of an organism is an organ.
(T/F)
(d) Amoeba has irregular shape.(T/F)
Answers
Answer:
true,false,false,true
Step-by-step explanation:
Answer:
a) T
b) F
c) F
d)T
Step-by-step explanation:
HELP PLSS I'M LOST PLSSSSSSSSSSSSSSSSS
Answers
Answer:
First Row:
75/100
0.75
75%
Second Row:
10/100 (or 1/10)
0.10
10%
Step-by-step explanation:
Count the squares that are shaded in out of the 100.
Just divide the fraction together for the decimal.
Move the decimal two places to the right to get the percentage
Which rules define the function graphed below? Edge
Answers
Answer:
B
Step-by-step explanation:
In the first part for every x, y is the value of x plus 2, while in the second part for every x. y is 5