Construct sinusoidal functionsThe graph of a sinusoidal function intersects its midline at (0, -3) and then has a maximum point at (2, -1.5).Write the formula of the function, where x is entered in radians.
Answers
We have a sinusoidal function.
[tex]y=A\cdot\sin (b\cdot x+c)+d[/tex]Its midline is intersected at (0,-3) and has a maximum point at (2,-1.5).
As the midline intersects at y=-3, we know that function has an offset of 3 units down.
This offset is the value of the parameter d, so we have:
[tex]y=A\cdot\sin (b\cdot x+c)-3[/tex]The maximum value happens at point (2,-1.5). The maximum value happens when the pure sin function reaches the value 1, so we can write:
[tex]\begin{gathered} y_{\max }=A\cdot1-3=-1.5 \\ A-3=-1.5 \\ A=-1.5+3 \\ A=1.5 \end{gathered}[/tex]The amplitude is A=1.5, so we can write:
[tex]y=1.5\sin (b\cdot x+c)-3[/tex]We can find the values of the parameters b and c using the x-values of the the points (0,-3) and (2,-1.5):
[tex]\begin{gathered} (x,y)=(0,-3) \\ y(0)=1.5\sin (b\cdot0+c)-3=-3 \\ 1.5\cdot\sin (c)=-3+3 \\ 1.5\cdot\sin (c)=0 \\ \sin (c)=0 \\ c=0 \end{gathered}[/tex][tex]\begin{gathered} (x,y)=(2,-1.5) \\ y(2)=1.5\cdot\sin (b\cdot2)-3=-1.5 \\ 1.5\cdot\sin (2b)=-1.5+3 \\ 1.5\cdot\sin (2b)=1.5 \\ \sin (2b)=1 \\ 2b=\frac{\pi}{2} \\ b=\frac{\pi}{2}\cdot\frac{1}{2} \\ b=\frac{\pi}{4} \end{gathered}[/tex]The function becomes:
[tex]y(x)=1.5\sin (\frac{\pi}{4}x)-3[/tex]The graph of the function is:
Answer: y(x) = 1.5*sin(pi/4 * x)-3
Related Questions
Define the range for this graph.A x is all the real numbers.B x>0©y23Oy> 0
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The range of the graph can be determined as,
[tex]y\ge0[/tex]As the graph is above the x-axis.
Thus,option (D) is correct.
I could really use some help understanding in answering this I keep getting the answer wrong
Answers
The general formula to calculate the simple interest is given to be:
[tex]I=P\times R\times T[/tex]where:
[tex]\begin{gathered} I=\text{ Simple Interest} \\ P=\text{ Loan Amount} \\ R=\text{ Rate in decimals} \\ T=\text{ Number of time periods (yearly)} \end{gathered}[/tex]To adjust for daily time periods, we will divide the rate by 365. Therefore, we have the following parameters:
[tex]\begin{gathered} P=300 \\ R=\frac{4}{100\times365}=\frac{1}{9152} \\ T=60 \end{gathered}[/tex]Note: We are working with the assumption that the rate is annual, although not clearly stated.
Substituting these parameters into the formula, we have:
[tex]undefined[/tex]Please help, it’s the last question on my worksheet and I’ve done all the rest of problems. I’m stuck on this one.
Line up decimals.
0 0.217 + ? = 456.3
Answers
Answer:
456.083
Step-by-step explanation:
Use basic algebra to solve this problem:
0.217 + x = 456.3 (x just means an unknown value)
Subtract 0.217 from both sides. When you do this, it cancels out on the left side. REMEMBER: whatever you do to one side, you MUST do it to the other.
0.217 - 0.217 + x = 456.3 - 0.217
x = 456.083
0.217 + 456.083 = 456.3
Hope that helps
Step-by-step explanation:
you must do inverse operation like:
0 0.217+? = 456.3
=456.3-0.217
= 456.083
The answer you get is the answer to ?
you can check it, you just add the answer to the question mark
Which statement is true regarding the graphed functions?12Ly108642-6 -5 -4 -3 -2 -1224 5 6 x99-4-6---10-121Of(0) = g(0)Of(-2) = 9(-2)Of(0) = g(-2)
Answers
We get that f(0)=g(0)
This figure shows the nose cone of a rocket used for launching satellites. The nose cone houses the satellite until the satellite is placed in orbit. What is the volume of the nose cone?
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The rule of the volume of the cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex]r is the radius of the base
h is the height of the cone
From the picture, we can see
The diameter of the base is 6 feet and the height is 15 feet
Since the radius is half the diameter, then
[tex]\begin{gathered} r=\frac{1}{2}d \\ r=\frac{1}{2}(6) \\ r=3 \end{gathered}[/tex]Substitute r by 3 and h by 15 to find the volume
[tex]\begin{gathered} V=\frac{1}{3}(\pi)(3)^2(15) \\ V=45\pi\text{ f}eet^3 \end{gathered}[/tex]The volume of the cone is 45pi feet^3
The answer is A
A box has dimensions of 15 inches long, 2.1 feet wide, and 6 inches high. What is the volume of the box? The formula for the volume is V = l ⋅ w ⋅ h.
Answers
Answer: 189
Step-by-step explanation:
15 x 2.1 x 6
[tex]e^x^-^3=(1/e^6)^x^+^2[/tex] e^x-3=(1/e^6)^x+2
Answers
The value of x in the given equation is -9/7.
Here, we are given an equation as follows-
[tex]e^{x-3} =(1/e^{6} )^{x+2}[/tex]
The expression on the right hand side can further be simplified as follows-
[tex]e^{x-3} =(e^{-6} )^{x+2}[/tex]
[tex]e^{x-3} =(e )^{-6(x+2)}[/tex]
now since the bases on both sides are equal to e, we can simply equate the powers to form the following equation-
x - 3 = -6(x + 2)
Now, we solve the equation to find the value of x as follows-
x - 3 = -6x + -6*2
x - 3 = -6x -12
x + 6x = -12 + 3
7x = -9
x = -9/7
Thus, the value of x in the given equation comes out to be -9/7.
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A plane flying horizontally at an altitude of 1 mi and a speed of 590 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 mi away from the station. (Round your answer to the nearest whole number.)
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(Sin 11 pi/36)(cos pi/18) - (cos 11pi/36)(sin pi/18). I have to find the exact value
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From the trigonometric identity of the sum of angles
[tex]\sin (\alpha-\beta)=\sin \alpha\cos \beta-\cos \alpha\sin \beta[/tex]we ca note that
[tex]\begin{gathered} \alpha=\frac{11\pi}{36} \\ \beta=\frac{\pi}{18} \end{gathered}[/tex]Then, by substituting these values into the formula, we have
[tex]\sin (\frac{11\pi}{36}-\frac{\pi}{18})=\sin \frac{11\pi}{36}\cos \frac{\pi}{18}-\cos \frac{11\pi}{36}\sin \frac{\pi}{18}[/tex]which is the same given expression. Then, we have that
[tex]\sin (\frac{11\pi}{36}\frac{\pi}{18})=\sin (\frac{11\pi}{36}-\frac{2\pi}{36})=\sin (\frac{11\pi}{36}-\frac{2\pi}{36})=\sin \frac{9\pi}{36}=\sin \frac{\pi}{4}[/tex]Then, the answer is:
[tex]\sin \frac{\pi}{4}=\frac{\sqrt[]{2}}{2}[/tex]
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.)
midpoint (-3, 4) endpoint (6,1)
What is the other endpoint
Answers
Answer:
12.52×34y+61yyou answer it tho srry
In a video game, Clare scored 50% more points than Tyler. If c is the number of points that Clare scored and t is the number of points that Tyler scored, which equations are correct? Select all that apply.
Answers
Nieshea, this is the solution:
A. c=1.5t (This is correct)
B.c=t+0.5 (This is not correct)
C. c=t+0.5t (This is correct)
D. c=t+50 (This is not correct)
E.c=(1+0.5)t (This is correct)
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Company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 10.5 years and a standard deviation of 1.8 years.
Answers
The probability that a randomly selected DVD player will have a replacement time of less than 4.9 years is 31.11 % or 0.3111
As per the question statement, a company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 10.5 years and a standard deviation of 1.8 years and we are supposed to tell the probability that a randomly selected DVD player will have a replacement time of less than 4.9 years.
Let "z" be the probability
z = (X - μ) / σ, where X = data, μ = mean, σ = standard deviation
z = (10.5 - 4.9) / 1.8
z = 0.3111 or 31.11%
Hence, the probability that a randomly selected DVD player will have a replacement time of less than 4.9 years is 31.11 % or 0.3111
Probability: The chance of happening of any event is its probability.Mean: The average of any given set of data is called mean and is calculated by dividing the sum of all observations by the total number of observations.Standard deviation: A number calculated to depict the degree of variation across the board for a group.To learn more about probability, click on the link given below:
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A) Write an expression for the given number trickB) Simplify the expression you came up with.
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A) The expression for the given number trick = 8(x + 7)
B) 8x + 56
Explanation:
A) Pick a number:
Let the number = y
Add 7:
it becomes = y + 7
Multiply by 8:
it becomes = 8(x + 7)
The expression for the given number trick = 8(x + 7)
B) We sipmlify the expression by opening the bracket:
8(x + 7) = 8 × x + 8×7
= 8x + 56
Please help it’s due tonight I will give a brainlist
Answers
24.8 %
The percentage of profit / selling price markup = 24.8 % , by rounding to nearest tenth.
What is profit?If the selling price is higher than the cost price, the difference between the two is referred to as profit. If the selling price is less than the cost price, the difference is referred to as the loss.Given this,
The seller's cost price is 210 dollars.
The seller's selling price is 279.30$.
We know that ,
Profit = selling price - cost price.
so, Profit = 279.30$ - 210$
= 69.3$.
To find the profit,
Profit /Selling Price Markup = (Profit/Selling Price)*100 .
-=> (69.3 / 279.30) x 100 = 24.81%
This is rounded to 24.8 %. ( by converting to nearest tenth).
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twice the sum of a circles radius and a squares side length is no more than 100 feetI have to translate English into algebra I need help can you help me please
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A motorboat traveling 310 km in five hours going upstream and 736 km in eight hours going down stream what is the rate of the boat in Stillwater and what is the rate of the current
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Solution
For this case we can create the following notation
B= velocity of boat
S= velocity of stream
Relative to the bank, the speed upstream is B-S.
The speed downstream is B+S.
And we can create the following equations:
(B-S)*5= 310
(B+S)*8= 736
We can solve for B and S and we have:
5B -5S = 310
8B+ 8S= 736
B= (310+5S)/5= 62+ S
Replacing in the second equation we got:
8(62+S) + 8S= 736
496 + 8S + 8S = 736
16S= 240
S= 240/16= 15
B= 62+15= 77
Then the velocity of current is 15km/hr and for the boat 77km/hr
8x + 6 - 5x - 4Answer ?
Answers
You have the following algebraic expression:
8x + 6 - 5x - 4
In order to simplify the previous expression, you take into account that you only can add or subtract similar terms. Similar terms are those ones with the same variable and same exponent, and also independent numbers are similar.
Then, you have:
8x + 6 - 5x - 4
= 8x - 5x + 6 - 4
= 3x + 2
Hence, the simplified expression is 3x + 2
Answer:
3x + 2
Step-by-step explanation:
Which statement is true about the function f(x)=√=-x?
O The domain of the graph is all real numbers.
O The range of the graph is all real numbers.
O The domain of the graph is all real numbers less than or equal to 0.
O The range of the graph is all real numbers less than or equal to 0.
Answers
Answer:
jfi6+_4655vud
Step-by-step explanation:
hiTeugdLast year, Yoko had $10,000 to invest. She invested some of it into an account that paid 10% simple interest per year, and she invested the rest in an account that paid 6% simple interest per year. After one year she received a total of $640 in interest. How much did she invest in each account?
Answers
Final answer:
At 10% interest, $1 000 was invested.
At 6% interest, $9 000 was invested.
Let "x" be the amount invested at 10%. The annual interest for this investment would be $ 0.1x
Now, the investment at 6% is (10 000 - x), and it would have an annual interest of 0.06(10 000 - x)
We will use the following equation to solve for this
[tex]interest_1+interest_2=totalinterest[/tex]interest 1 = 0.1x
interest 2 = 0.06(10 000 - x)
total interest = 640
Substitute these values
[tex]interest_1+interest_2=totalinterest[/tex][tex]0.1x+0.06(10000-x)=640[/tex]Solve for x
[tex]0.1x+0.06(10000-x)=640[/tex][tex]0.1x-0.06x=640-\lbrack(0.06)(10000)\rbrack[/tex][tex]0.04x=640-600[/tex][tex]0.04x=40[/tex]Divide both sides by 0.04
[tex]\frac{0.04x}{0.04}=\frac{40}{0.04}[/tex][tex]x=1000[/tex]Since the investment at 6% is equal to 10000-x,
[tex]interest_2=10000-x[/tex][tex]=10000-1000[/tex][tex]=9000[/tex]Final answer:
At 10% interest, $1 000 was invested.
At 6% interest, $9 000 was invested.
To check,
[tex]0.1x+0.06(10000-x)=640[/tex][tex]0.1(1000)+0.06(10000-(1000))=640[/tex][tex]640=640[/tex]Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $55, plus $15 per hour. What is the slope of this situation? 10 15 55 70
Answers
The linear equation that represents this situation is given by
y=15x+55
therefore
The slope is 15
3(y + 1) + 2y = 5( y - 1 ) + 5
Answers
Answer:
There are no values for y that make this equation true.
Step-by-step explanation:
Distribute the 3 and 5 to their respective parenthesized quantities:
[tex]3y+3+2y=5y-5+5[/tex]
Simplify:
[tex]5y+3=5y[/tex]
Subtract 5y from both sides:
[tex]3=0[/tex]
Note that 3 cannot equal zero, therefore this equation has no values for y which make it true.
4. The total views of an online video are tripling every ten days. Initially there are 22 views of the video. If v
represents the number of views and d represents days then answer the following.
(a) Write a model for the number of views, v, as a
function of the number of days, d, since there
were 22 views.
(b) By what percent, to the nearest tenth, are the
views increasing per day? Show how you
arrived at your answer.
Answers
Part (a)
[tex]v=22(3)^{d/10}[/tex]
Part (b)
We can rewrite the function as [tex]v=22(3^d)(3^{1/10})[/tex]. Thus, the percentage is [tex]100(1-3^{1/10})=11.6\%[/tex]
A model for the number of views, v, as a function of the number of days, d, since there were 22 views is [tex]v = 22(3)^{d/10}[/tex] and the views increasing per day by 11.6%.
What is exponential growth?Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given that, The total views of an online video are tripling every ten days. Initially there are 22 views of the video, v represents the number of views and d represents days
a) Since the number of views are tripling every ten days, so, the function will be = [tex]v = 22(3)^{d/10}[/tex]
b) We have function [tex]v = 22(3)^{d/10}[/tex]
So, percentage = [tex]100(1-3^{1/10})[/tex] = 11.6%
Hence, A model for the number of views, v, as a function of the number of days, d, since there were 22 views is [tex]v = 22(3)^{d/10}[/tex] and the views increasing per day by 11.6%.
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I sent a pic to the app and it gave me an answer my class hasn't gone over and so I need someone to walk through the equation with me. The instructions say "solve the systems by elimination".
Answers
The linear system:
[tex]\begin{gathered} \frac{1}{4}x+4y=2+\frac{3}{4} \\ 3x+\frac{1}{2}y=9+\frac{1}{4} \end{gathered}[/tex]Let's follow the steps to solve this linear system.
1) Multiply one equation by a constant to set up the elimination of one of the variables.
You can multiply equation 2 by - 8:
[tex]undefined[/tex]22 53 29 35 26 44 24 31 63 6223 56 62 39 44 52 26 33 84 39The amounts (in dollars) spent by 20 families for dinner at a restaurant are given on thenightAnswer parts (a) and (b) below.(2) Fal in the correct frequencies in the frequency table bass on the dataInterval Frequency10-19.99 020-29.99 630-39.9940-49.9950-59.9960-69.99
Answers
To find the frequency of data that falls in the range 10-19.99, we need to count how many values are in that range. The same procedure is valid for the rest of the ranges. Then the table is:
Interval | Frequency
10-19.99 | 0
20-29.99 | 6
30-39.99 | 5
40-49.99 | 2
50-59.99 | 3
60-69.99 | 4
x−2y=2 Find the y-intercept
Answers
Answer:
-1 trust me please
Jason likes to play video games. His parents allow him to play for 20 minutes plus 10 min for each half hour he does chores or studies. He can never play for more than 90 min/day.
The function f(x) = 20 + 10x models the number of minutes per day Jason could play where x represents the number of half hour increments he has done chores or studied. What is the practical range of the function?
Answers
Answer:
f(7)=20+10x
Step-by-step explanation:
the greater roadrunner bird can run 14 miles per hour that's 7 times faster than an ostrich can walk how fast does an ostrich walk Solve using skip counting
Answers
Answer:
14•7=98
Step-by-step explanation:
think its help have a good day
David is planning to build a triangular garden with a border made out of wood. Two of the sides will be 16.4 feet in length. The other side will be 3.3 feet. He has a total of 37 feet. Does he have enough wood to make the border? Explain. The total length of the border is feet. This is (Type a whole number or a decimal.) the length of wood David has. He enough wood to make the border.
Answers
He had 37 feet of wood and he needs 36.1 feet of perimeter for triangular garden , as 37 > 36.2, he has enough wood to make the border.
What is perimeter?The entire distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's outline or boundary. Depending on the dimensions, the perimeter of various figures can be the same size.
Consider a triangle made of an L-length wire as an example. If all the sides are the same length, then the same wire can be used to create a square. Take a look at the illustration below, which shows the bounds of a rectangular park.
David is planning to build a triangular garden with a border made out of wood.
Two of the sides will be length = 16.4 feet
= 2 × 16.4
= 32.8 feet
The other side will be 3.3 feet
The perimeter of the triangular garden
= 32.8 + 3.3
= 36.1
Thus, He had 37 feet of wood and he needs 36.1 feet of wood, as 37 > 36.2, he has enough wood to make the border.
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#!). Two planes leave New York at 10am, One heading for Europe at 600mph and one heading in the opposite direction at 150mph. At what time will they be 900 miles apart? How far has each traveled?
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Speed = Distance / time
Distance = Speed x time
In t hours, first plane travels = 600 t miles
In t hours, the second plane travels =150 t miles
After t hours the distance between the two planes is:
(600t+150t)= 750t ( since both travel in opposite directions)
When the distance is 900 miles:
750t= 900
Solve for t:
t= 900/750
t= 1.2 hours
After 1.2 hours.
1.2 x 60 = 72 minutes = 60 +12 = 1 hour and 12 minutes
Since both leave at 10 pm:
10am + 1 hour and 12 minutes : 11:12 am
They will be 900 miles apart at 11:12 am
Each one traveled:
Plane 1:
Distance: Speed x time = 600 mph x 1.2 = 720 miles
Plane 2:
Distance = Speed x time = 150 mph x 1.2 = 180 miles
ALLEMAAL Refer to the figure to find the following measure. If _C= 25° and mÃE = 100°, then moB 12.5° 50° 75°
Answers
The measure of an exterior angle is equal to half the difference of the measure of intercepted arcs. For the given extrior angle:
[tex]m\angle C=\frac{1}{2}(\text{mAE}-mDB)[/tex]Use the equation above to solve mDB:
[tex]\begin{gathered} 25=\frac{1}{2}(100-mDB) \\ \\ (2)25=(100-mDB) \\ \\ 50=100-mDB \\ \\ 50-100=-mDB \\ \\ -50=-mDB \\ \\ -50(-1)=mDB \\ \\ \text{mDB}=50 \end{gathered}[/tex]Then, the measure of arc DB is 50°