Answer: There is no function below
Step-by-step explanation:
Step 1 upload picture below question
The following points are a minimum and a maximum of a sinusoid. Complete the following steps to
model the curve using the sine function.
(4.5, 2), (1.5, 22)
a) What is the vertical shift, k, of this curve?
b) What is the amplitude, a, of this curve?
c) What is period and frequency factor, b, of this curve?
d) Write an equation using the sine function that models this curve.
Answer: K= 12
A=10
P= 6
B=pi/3
Equation: y=10sin(pi/3(x))+12
Step-by-step explanation: You can find k by finding the midline, or adding the minimum and maximum y values together and then dividing by 2.
You find a by using the midline value (12) and subtracting it from the maximum y value to get the amplitude.
To find the period, find the difference between the min and max x values, which is 3, then double it to get the full period.
To find the b value, plug it into the 2pi/b=p equation, using the period value you found before you should get pi/3.
When assembling the equation use this format: y=asin[b(x-h)]+k.
You can also graph it with a graphing calculator to check to be sure the max and min points line up.
A sine function is represented as: [tex]\mathbf{y = A\sin(Bx) + k}[/tex]
The vertical shift is 12The amplitude is 10The period is 6, and the frequency factor is [tex]\mathbf{\frac{\pi}{3}}[/tex].The sine function is [tex]\mathbf{y = 10\sin(\frac{\pi}{3}x) + 12}[/tex]The given parameters are:
[tex]\mathbf{(x_1,y_1) = (4.5,2)}[/tex]
[tex]\mathbf{(x_2,y_2) = (1.5,22)}[/tex]
(a) The vertical shift (k)
The vertical shift is calculated using:
[tex]\mathbf{k = \frac{y_1 + y_2}{2}}[/tex]
So, we have:
[tex]\mathbf{k = \frac{2 + 22}{2}}[/tex]
[tex]\mathbf{k = \frac{24}{2}}[/tex]
[tex]\mathbf{k = 12}[/tex]
(b) The amplitude (A)
The amplitude is calculated using:
[tex]\mathbf{A = \frac{y_2 - y_1}{2}}[/tex]
So, we have:
[tex]\mathbf{A = \frac{22 - 2}{2}}[/tex]
[tex]\mathbf{A = \frac{20}{2}}[/tex]
[tex]\mathbf{A = 10}[/tex]
(c) The period (p) and the frequency factor (b)
The period is calculated using:
[tex]\mathbf{p = x_1 + x_2}[/tex]
So, we have:
[tex]\mathbf{p = 4.5 + 1.5}[/tex]
[tex]\mathbf{p = 6}[/tex]
The frequency factor (b) is calculated using:
[tex]\mathbf{b = \frac{2\pi}{p}}[/tex]
So, we have:
[tex]\mathbf{b = \frac{2\pi}{6}}[/tex]
[tex]\mathbf{b = \frac{\pi}{3}}[/tex]
(d) The equation of the sine function
A sine function is represented as:
[tex]\mathbf{y = A\sin(Bx) + k}[/tex]
So, we have:
[tex]\mathbf{y = 10\sin(\frac{\pi}{3}x) + 12}[/tex]
Read more about sine functions at:
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-2x - 3(6x - 11) = -7
Answer:
x=40/21
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−3x−3(6x−11)=−7
−3x+(−3)(6x)+(−3)(−11)=−7(Distribute)
−3x+−18x+33=−7
(−3x+−18x)+(33)=−7(Combine Like Terms)
−21x+33=−7
−21x+33=−7
Step 2: Subtract 33 from both sides.
−21x+33−33=−7−33
−21x=−40
Step 3: Divide both sides by -21.
−21x
−21
=
−40
−21
Simplify the expression in part D to find the temperature of the water after Raul added the ice cubes. Show your work
70 + (-30)+2+(-9)+0.3+(-0.1)=[70+(-30)]+[2(-9)]+[0.3+(-0.1)]
Answer:
33.2°F
Step-by-step explanation:
[70 + (-30)] + [2 +(-9)] + [0.3 + (-0.1)]
=
40 + (-7) + 0.2
=
33 + 0.2
=
33.2°F
The temperature of the water dropped to 33.2°F after Raul added the ice cubes.
Hoped this helped!<3
Answer:
[70 + (-30)] + [2 +(-9)] + [0.3 + (-0.1)]
=
40 + (-7) + 0.2
=
33 + 0.2
=
33.2°F
The temperature of the water dropped to 33.2°F after Raul added the ice cubes.
Step-by-step explanation:
-10b + 5 = 7b + 5 what is b
Answer:
0?
Step-by-step explanation:
Original Equation:
-10b + 5 = 7b + 5
Add 10b to both sides
5 = 17b + 5
Subtract 5 from both sides.
0 = 17b
Divide both sides by 17
b = 0
Hope I helped :)
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Which algebraic equation represents the following scenario?
Ms. Cosby had 6 students in her room, and then an addition one-fifth of the 7th grade students. There here 25 students in her room in total.
A.
6.2x = 25
B.
6 + 0.2x = 25
C.
6 + 1.5x = 25
D.
(6 + x)0.2 =25
Answer:
C.
Step-by-step explanation:
please solve this question!!
Answer: see proof below
Step-by-step explanation:
Use the following Half-Angle Identities:
sin² A = (1 - cos 2A)/2
cos² A = (1 + cos 2A)/2
Proof LHS → RHS:
LHS: sin⁴ A
Expand: sin² A · sin² A
[tex]\text{Half-Angle:}\qquad \qquad \bigg(\dfrac{1-\cos (2A)}{2}\bigg)\bigg(\dfrac{1-\cos (2A)}{2}\bigg)[/tex]
[tex]\text{Distribute:}\qquad \qquad \dfrac{1-2\cos (2A)+\cos^2 (2A)}{4}[/tex]
[tex]\text{Half-Angle:}\qquad \qquad \dfrac{1-2\cos (2A)+\frac{1+\cos (2\cdot 2A)}{2}}{4}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{\frac{2}{2}[1-2\cos (2A)]+\frac{1+\cos (4A)}{2}}{4}[/tex]
[tex]=\dfrac{2-4\cos (2A) + 1 + \cos (4A)}{8}[/tex]
[tex]=\dfrac{1}{8}\bigg(3-4\cos (2A)+\cos (4A)\bigg)[/tex]
LHS = RHS [tex]\checkmark[/tex]
Let's start from LHS...
LHS = sin^4A = sin^2A * sin^2A
We can apply a few formulas here;
cos 2A = 1 - 2sin^2A
sin^2A = (1 - cos2A) / 2
cos2A = 2cos^2A - 1
cos^2A = (1 + cos2A) / 2
According to the second formula, sin^2A * sin^2A = (1 - cos2A) / 2 * (1 - cos2A) / 2.
(1 - cos2A) / 2 * (1 - cos2A) / 2 = 1/4(1 - cos2A)^2
We can simplify "(1 - cos2A)^2." Remember that (a - b)^2 = a^2 - 2ab + b^2. Similarly (1 - cos2A)^2 = (1 - 2cos 2A + cos^2 2A);
1/4(1 - cos2A)^2 = 1/4(1 - 2cos 2A + cos^2 2A)
According to the fourth formula, cos^2 2A = (1 + cos4A) / 2;
1/4(1 - 2cos 2A + cos^2 2A) = 1/4(1 - 2cos 2A + (1 + cos4A) / 2)
= (taking LCM) 1/4( (2 - 4cos 2A + 1 + cos4A)/2 )
= (simplified) 1/8(3 - 4cos 2A + cos 4A)
Kamal wrote the augmented matrix below to represent a system of equations
1 0 1-1
1 3 -1-9
3 2 0- 2
Which matrix results from the operation -3R2 R2?
Consider the operation is [tex]R_2\to -3R_2[/tex].
Given:
The augmented matrix below represents a system of equations.
[tex]\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right][/tex]
To find:
Matrix results from the operation [tex]R_2\to -3R_2[/tex].
Step-by-step explanation:
We have,
[tex]\left[\left.\begin{matrix}1&0&1\\1&3&-1\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-9\\-2\end{matrix}\right][/tex]
After applying [tex]R_2\to -3R_2[/tex], we get
[tex]\left[\left.\begin{matrix}1&0&1\\-3(1)&-3(3)&-3(-1)\\3&2&0\end{matrix}\right|\begin{matrix}-1\\-3(-9)\\-2\end{matrix}\right][/tex]
[tex]\left[\left.\begin{matrix}1&0&1\\-3&-9&3\\3&2&0\end{matrix}\right|\begin{matrix}-1\\27\\-2\end{matrix}\right][/tex]
Therefore, the correct option is A.
HELP ASAPPPPPPPPP ILL MARK BRAINLIEST
Answer:
the answer would be C
Step-by-step explanation:
the opposite of exponents is square root it
Please:) Ken bought some lolipops. He gave 1/2 of them to chin, 3 to Harris, and kept 6 for himself.how many lollipops did buy?
Answer:
18
Step-by-step explanation:
6+3=9
9*2=18
sorry if not right
A set of 4 consecutive even integers has a sum of 380. What is the least of the 4 integers ?
Answer:
92
Step-by-step explanation:
If the 4 consecutive even integers have a sum of 380, then the average value is 380/4.
380/4 = 95
There must be 2 integers less than 95 and 2 grater than 95.
The 4 integers are: 92, 94, 96, 98
Sum: 92 + 94 + 96 + 98 = 380
Answer: 92
The 4 consecutive even integers are 92,94,96 and 98 whose sum is 380.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The 4 consecutive even integers has a sum of 380.
x+2+x+4+x+6+x+8=380
Add the like terms
4x+20=380
Subtract 20 on both sides
4x=380-20
4x=360
Divide both sides by 4
x=90
So the four consecutive integers are
x+2=90+2=92
x+4=90+4=94
x+6=90+6=96
x+8=90+8=98
Hence, the 4 consecutive even integers are 92,94,96 and 98 whose sum is 380.
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Slope of 4 and a y-intercept of (0, 6)
Convert 11/3 to a mixed number
Answer:
3 2/3
Step-by-step explanation:
divide the 3 by 11 and your product is the whole number, with the remainder being the numerator.
11 / 3 = 9.2
9/3=3
3 2/3
SCIENCE NOT MATHEMATICS SORRY!!
Sucrose is an organic compound made by plants for quick energy. Sucrose is classified as a(n)
Domain
Kingdom
Phylum
Class
Order
Family
Genus
Species
Please help, thank you :) .
Unfortunately sucrose isn't classified as any of the above because it is not alive. Sucrose can however be classified as a disaccharide because it contains two monosaccharides (glucose and fructose). If you want to be more broad you can classify it as a carbohydrate.
is -4 < -5 1/2 a true statement?
Answer:
It is not true
Step-by-step explanation:
-4 is closer to 0 than -5 1/2
The closer the negative number to 0 the bigger it is
I need help asap, does anyone know what X is?
if f(x) = 1/2x + 5, what is f(8)
Answer:
9
Step-by-step explanation:
f(8)= 1/2(8) + 5
f(x)= 4 +5
f(x)= 9
LINE 1: (-9, 3), (-5, 7) LINE 2: (-11, 6), (-7, 2)
Parallel, perpendicular or neither ?
Answer:
neither
Step-by-step explanation:
they dont intersect with each other
What is the time that is 11 hours and 55 minutes before the time shown?
Answer:
11:30 AM
Step-by-step explanation:
Evaluate the expression below using the properties of operations. Show your steps.−36 ÷ 14 ⋅ (−18) ⋅ (−3) ÷ 6
Answer:
(-162)/7 or -23 1/7 as mixed fraction
Step-by-step explanation:
Simplify the following:
(-36)/14 (-18) (-3)/6
Hint: | Express (-36)/14 (-18) (-3)/6 as a single fraction.
(-36)/14 (-18) (-3)/6 = (-36 (-18) (-3))/(14×6):
(-36 (-18) (-3))/(14×6)
Hint: | In (-36 (-18) (-3))/(14×6), divide -18 in the numerator by 6 in the denominator.
(-18)/6 = (6 (-3))/6 = -3:
(-36-3 (-3))/14
Hint: | In (-36 (-3) (-3))/14, the numbers -36 in the numerator and 14 in the denominator have gcd greater than one.
The gcd of -36 and 14 is 2, so (-36 (-3) (-3))/14 = ((2 (-18)) (-3) (-3))/(2×7) = 2/2×(-18 (-3) (-3))/7 = (-18 (-3) (-3))/7:
(-18 (-3) (-3))/7
Hint: | Multiply -18 and -3 together.
-18 (-3) = 54:
(54 (-3))/7
Hint: | Multiply 54 and -3 together.
54 (-3) = -162:
Answer: (-162)/7
i need some help please
Answer:
X=2
Step-by-step explanation:
Make an equation: the scales are equal, so
x + x + 3 = 7
2x + 3 = 7
2x = 4
x = 2
91% of what is 108?
it's telling me I need to write more here to get an answer, but I don't have anything else to write, I literally just need the answer.
match each pair with their relationship Angles 1 and 3 Angles 4 and 8 Angles 4 and 6 Angles 3 and 5 Angles 7 and 8 Angles 1 and 7
ANSWER:
8,7
5,6
4,3
1,2
This is a angle of pair
Which are alternate exterior angles? HELPPP PLZZZ!
Answer:
b. angles 1 and 8
Step-by-step explanation:
alternate exterior angles theorm
Lorea is designing the top of a quilt which measures 2,160 square inches. Triangles will cover 432 square inches of the quilt, and squares will cover 180 square inches. The rest of the quilt will be parallelograms with a base of 2 inches and a height of 1.5 inches. How many parallelograms should she cut to complete the quilt?
516
528
617
720
Answer: Its 516. Hope this helps!
Step-by-step explanation:
Answer:
516
Step-by-step explanation:
What is the slope of the line represented by the equation y=-1/2x+1/4 ?
Answer:
-1/2
Step-by-step explanation:
The slope is always the value with the x.
Answer:
Slope = - 1/2x
Step-by-step explanation:
Express the function graphed on the axes below as a piecewise function.
Answer:
y = 2/3x +6 for x< -3
y = 2/3x +1 for x> 3
Step-by-step explanation:
The graph is a line for x < -3
( - 6,2) and ( -3,4)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 4-2)/(-3 - -6) = 2/ ( -3+6) = 2/3
The slope is 2/3
Using point slope form
y-y1 = m(x-x1) and the point ( -6,2)
y -2 = 2/3(x - -6)
y -2 = 2/3(x +6)
y-2 = 2/3 x +4
y = 2/3x +6 x< -3
The graph is a line for x > 3
(3,3) and ( 6,5)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 5-3)/(6-3) = 2/ (3) = 2/3
The slope is 2/3
Using point slope form
y-y1 = m(x-x1) and the point (6,5)
y -5 = 2/3(x - 6)
y-5 = 2/3 x -4
y = 2/3x +1 x> 3
which value of n will make the rational number -17 over n an integer
Is it A.18 B.102 C.170 or D. None of them
An integer is a whole number.
-17/n
Replace n with the choices:
-17/18 = -0.9444
-17/102 = -0.1666
-17/170 = -0.1
None of those are a whole number so the answer would be d. None of them.
If she has enough or not
Answer:
enough is the correct worf
Error Analysis: George was trying to rearrange the formula below to slope-intercept form, y = mx + b. by
solving for y. Identify her mistake and correct the error.
y + 20 = 2(x +20)
y + 20 = -x +20
PLEASE HELP!
Answer:
George's mistake would be:
Instead of 2x + 40, she has made - x + 20.
Step-by-step explanation:
Slope - Intercept Form = y = mx + b
y + 20 = 2(x +20)
y + 20 = 2x + 40
- 20 - 20
----------------------
y = 2x + 20
(Should have been the answer)
BUT,
George's Solving:
y + 20 = 2(x + 20)
y + 20 = -x + 20
George's Mistake would be her miscalculation during her 2nd step. Where instead of distributing 2 to (x + 20), she has changed it to -x + 20, when in reality, it should have been 2x + 40.
could someone help me out with this problem I've been trying to figure it out for the past five minutes
Answer:
A. c. F.
Step-by-step explanation: