When is it better to use the sine function and when is it better to use the cosine function when modeling sinusoids behavior
Answers
A sine function is as shown below
A cosine function is as shown below
The combination of both sine and cosine function is as shown below
It can be observed from the above combination that:
Cosine is better when the maximum is on the y- axis and sine is better if the midline is at the center.
Related Questions
if a cone and cylinder share the same radius and height what would be the volume of a cylinder if the volume of the cone is 30 cm
Answers
if a cone and cylinder share the same radius and height what would be the volume of a cylinder if the volume of the cone is 30 cm
step 1
Volume of the cone is equal to
[tex]\begin{gathered} V=\frac{1}{3}\cdot B\cdot h \\ 30=\frac{1}{3}\cdot B\cdot h \\ 90=B\cdot h \end{gathered}[/tex]where
B is the area of the base and h is the height of cone
step 2
the volume of cylinder is equal to
[tex]V=B\cdot h[/tex]Evaluate the expression when b=48 and c=7.b+2c3Simplify your answer as much as possible.
Answers
You have the following expression:
b + 2c³
where b = 48 and c = 7. By replacing these values into the previous expression you obtain:
b + 2c³ = 48 + 2(7)³ = 48 + 2(343) = 48 + 686 = 734
Hence, the result is 734
1.Jackson is building a bookshelf and has a piece ofwood that is foot long. He needs to cut piecesthat are 16 foot long. How many pieces canJackson cut?A. 23 pieces of woodB. 10 pieces of woodC. 7 pieces of woodD. 19 pieces of woodShow all of your
Answers
SOLUTION
Step 1 :
In this question, we are told that Jackson is building a bookshelf and has a piece that is
[tex]\frac{5}{8}\text{ foot long.}[/tex]He needs to cut pieces that are
[tex]\frac{1}{16\text{ }}\text{ foot long.}[/tex]Step 2 :
We are asked to find the number of pieces that Jackson can cut.
Solving this, we have the following:
[tex]\begin{gathered} \frac{5}{8\text{ }}\text{ } \\ \text{divided by } \\ \frac{1}{16} \end{gathered}[/tex][tex]\frac{5}{\text{ 8}}\text{ x }\frac{16}{1}\text{ = }\frac{80}{8}\text{ = 10 pieces of wood --- OPTION B}[/tex]CONCLUSION :
The final answer is 10 pieces of wood ---- OPTION B .
match the equation on the left with the correct solution on the right -5x² = -500 ?(x+2)² = 169 ?x²-49=0 ?x² =25 ?x = -5'5x= -10,10x = -15,11x = -7,7
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the first equation is,
[tex]\begin{gathered} -5x^2=-500^{} \\ 5x^2=500 \\ x^2=\frac{500}{5} \end{gathered}[/tex]solve further,
[tex]\begin{gathered} x^2=\frac{500}{5} \\ x^2=100 \\ x=\sqrt[]{100}=\pm10 \\ x=10,-10 \end{gathered}[/tex]the second equation is
[tex]\begin{gathered} (x+2)^2=169 \\ x+2=\sqrt[]{169} \\ x+2=\pm13 \\ x=13-2,\text{ -13-2} \\ x=11,-15 \end{gathered}[/tex]the equation third is.
[tex]\begin{gathered} x^2-49=0 \\ x^2=49 \\ x=\sqrt[]{49} \\ x=\pm7 \\ x=7,-7 \end{gathered}[/tex]the fourth equation is,
[tex]\begin{gathered} x^2=25 \\ x^2=\sqrt[]{25} \\ x=\pm5 \\ x=5,-5 \end{gathered}[/tex]Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, hasno solution, or has an infinite number of solutions. If the system has one solution, find the solution.- 2x + y = 7- 2x + y = -6
Answers
Answer:
Explanations:
Given the system of equations:
- 2x + y = 7 .................................... 1
- 2x + y = -6 .................................. 2
Subtract both equations from each other to have;
-2x-(-2x) + (y-y) = 7 - (-6)
0x = 7 + 6
0x = 13
Divide both sides by 0
0x/0 = 13/0
x = 13/0
x = ∞
This shows that the system of equations has no solution
The half life of silicon -32 is 710 years. If 30 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)
Answers
The half-life exponential decay equation is
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\lambda} \\ \text{where} \\ \lambda=\frac{t}{t_{\frac{1}{2}}} \end{gathered}[/tex]N_0 is the initial quantity of the substance, t_1/2 is the half-life and t is the time.
In our case,
[tex]\begin{gathered} \lambda=\frac{300}{710}=\frac{30}{71} \\ N_0=30 \end{gathered}[/tex]Therefore,
[tex]N(300)=\frac{30}{2^{\frac{30}{71}}}=22.3833\ldots\approx22.383_{}[/tex]The answer is 22.383 grams.
How do I get the answer to this? (+7) - (+12)=
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The given equation is +7 - (+12)
Now when two opposite signs are multiplied the answer is always negative.
Then,
- x + = -
Hence,
+7 - (+12) = +7 - 12 = -5
Sot he answer is -5.
8(x + 5) - 4(x + 4)Simplify please help ASAP.
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To simplify this expression, we can following the next steps:
First, apply the distributive property:
[tex]8x\text{ + 40 - 4x -16}[/tex]Then, sum similar terms:
[tex]8x-4x\text{ + 40 - 16 = 4x + }24[/tex]Therefore, the simplified expression is
[tex]4x+\text{ 24}[/tex]We can even write the previous expression as
[tex]4(x\text{ + 6)}[/tex]Since 4 is a common factor in the expression.
Write the equation of the vertical line, through the point (2,−5).
Answers
Answer:
Explanation:
Given:
Point (2,-5)
To find the equation of the vertical line, we use:
x = a
where:
a= the value that x takes
Based on the given point (2,-5), the x value is 2. So,
x=a
x=2
Therefore, the equation of the vertical line is:
x=2
Rodrigo puts $200.00 into an account to use for school expenses. The account earns 9%interest, compounded annually. How much will be in the account after 4 years?Round to nearest cent
Answers
Given:
Rodrigo puts $200.00 into an account to use for school expenses.
So, P = 200
The account earns 9% interest
so, r = 9% = 0.09
compounded annually ⇒ n = 1
We will find the balance after 4 years ⇒ t = 4
We will use the following formula:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Substitute with the given data:
[tex]A=200\cdot(1+\frac{0.09}{1})^{1\cdot4}=200\cdot1.09^4=282.3163[/tex]Rounding to the nearest cent
so, the answer will be the balance after 4 years = $282.32
A wildlife sanctuary has two elephants. One has a weight of 11,028 pounds and the other has a weight of 5.2 tons. A platform can hold 22,000 pounds. Can the platform hold both elephants? Explain your reasoning. (1 ton = 2,000 pounds)
Answers
Step 1:
Write the weight of both elephant
11028 pounds and 5.2 tons
Total weight of the platform = 22000 pounds
Step 2:
Convert tons to pounds
1 ton = 2000 pounds
5.2 tons = 5.2 x 2000 = 10400 pounds
Step 3:
Add the total weight of both elephants
= 11028 + 10400
= 21428 pounds
Step 4:
Final answer
The platform can hold both elephants because the weight of the platform is 572 pounds heavier than the combined weight of the two elephants.
Solve for s.1/2s=7/2s=1/7s=2/7s=3s=7
Answers
Solving a linear equation
Then
1/2s = 7/2
(1/2)s = 7/2
Its important to use correctly parenthesis
In 1/2s, s is dividing
In (1/2)s , s is multiplying
Then
1/2s = 7/2
1/(7/2) = 2s
2/7 = 2 s
1/7 = s
And , using parenthesis if
(1/2)s = 7/2
s = (7/2)/(1/2) = 7
Which is a graph of with any vertical or horizontal asymptotes indicated by dashed lines?
Answers
Given the function
[tex]f(x)=\frac{6x-3}{x-1}[/tex]The graph of the given function is
Let E be the event where the sum of two rolled dice is even. List the outcomes in Ec (complement of E)
Answers
We have an event E that represent the outcomes where the sum of the two rolled dice is even.
This includes all the combinations when both dices are even or both dices are odd.
We have to list the outcomes for Ec, the complement of E. This event Ec will represent all the outcomes where the sum of the two dices is odd.
All outcomes where one dice is even and the other is odd are part of Ec.
Then, we can list them as:
(1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4), (3,6)
(4,1), (4,3), (4,5)
(5,2), (5,4), (5,6)
(6,1), (6,3), (6,5)
This represents half of the sample space. The other half corresponds to outcomes that are part of event E.
Answer: all the outcomes that correspond to Ec are (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3) and (6,5).
Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor. IN NI -------4-2 LE M 122 HE Figure LMNO is VI congruent to Figure EFGH because rigid motions | be used to map Figure LMNO onto Figure ERGH. can Figure LMNO is dilations can similar to Figure EFGH because rigid motions and/or be used to map Figure LMNO onto Figure EFGH. The scale factor from Figure LMNO to Figure EFGH is 1
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Given: the figures LMNO and EFGH
WE will find the length of each side of the figure LMNO
AS shown:
[tex]\begin{gathered} LM=3 \\ MN=\sqrt[]{2^2+4^2}=\sqrt[]{20}=2\sqrt[]{5} \\ NO=\sqrt[]{6^2+2^2}=\sqrt[]{40}=2\sqrt[]{10} \\ OL=\sqrt[]{1^2+2^2}=\sqrt[]{5} \end{gathered}[/tex]Now, we will find the length of each side of the figure EFGH:
[tex]\begin{gathered} FG=4 \\ GH=\sqrt[]{3^2+3^2}=\sqrt[]{18}=3\sqrt[]{2} \\ HE=\sqrt[]{1^2+3^2}=\sqrt[]{10} \\ EF=\sqrt[]{2^2+4^2}=\sqrt[]{20}=2\sqrt[]{5} \end{gathered}[/tex]By comparing the lengths of the corresponding sides
The figures are not congruent and not similar
So, the answer will be neither congruent nor similar
Last week you worked 32 hours, and earned $304. What is your hourly pay rate? per hour Give your answer in dollars and cents (like 5.50)
Answers
32 hours worked corresponds to $304 earned. To find how much you earned after 1 hour, we can use the next proportion:
[tex]\frac{32\text{ hours}}{1\text{ hour}}=\frac{304\text{ \$}}{x\text{ \$}}[/tex]Solving for x:
[tex]\begin{gathered} 32\cdot x=1\cdot304 \\ x=\frac{304}{32} \\ x=9.5 \end{gathered}[/tex]Your hourly pay rate is $9.50
I remind you that the answer will be always available in your profile
per hour
May I please get help with a and b? I have tried many times but still could not get the correct answerAnswering A.
Answers
We can look at each triangle separately.
For ΔABC, we have two internal angles:
[tex]\begin{gathered} m\angle A=40\degree \\ m\angle B=70\degree \end{gathered}[/tex]The sum of the internal angles of any triangle is equal to 180°, so:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 40\degree+70\degree+m\angle C=180\degree \\ 110\degree+m\angle C=180\degree \\ m\angle C=180\degree-110\degree \\ m\angle C=70\degree \end{gathered}[/tex]So, the measure of m∠C is 70°.
For ΔDEF, we have the same two internal angles:
[tex]\begin{gathered} m\angle D=40\degree \\ m\angle E=70\degree \end{gathered}[/tex]So, we can use the same formula of the sum of the internal angles:
[tex]\begin{gathered} m\angle D+m\angle E+m\angle F=180\degree \\ 40\degree+70\degree+m\angle F=180\degree \\ 110\degree+m\angle F=180\degree \\ m\angle F=180\degree-110\degree \\ m\angle F=70\degree \end{gathered}[/tex]So, the measure of m∠F is 70°.
16. A hamster drinks cup of water each day. If Melissa pours 6 cups of water into the hamster's drink cylinder, how many days will the water last?
Answers
According to the information, the drink cylinder will last 6 days.
Because
1 cup --------------------- 1 day
6 cups -------------------- x
x = (6 x 1) / 1
x = 6/1
x = 6 days
5. Melvin Cooper rents a condominium for $1,045 a month. Hepays a $140 monthly fee for all maintenance work. His annualexpenses are: insurance, $292; lost interest, $45; and utility bills$3,240. What is his average monthly expense?
Answers
To determine the monthly expense, we will add each amount but we have to determine the monthly amount out of the annual expenses.
To determine the monthly amount of the annual expenses, we divide the sum of the annual expenses by 12:
[tex]\frac{292+45+3240}{12}\approx298.01\text{ dollars.}[/tex]Finally, we add all the monthly expenses:
[tex]298.01+1045+140=1483.01\text{ dollars.}[/tex]Answer: [tex]1,483.01\text{ dollars.}[/tex]Which phrase best describes the relationship between age and height at Liam’s school?
Answers
A Correlation coefficient is used to measure how strong a relationship is between two variables. There are several types of the correlation coefficient, but the most popular is Pearson’s. Pearson’s correlation (also called Pearson’s R) is a correlation coefficient commonly used in linear regression.
R can take a value between -1 and 1, if R is;
1, we say that there is a perfect positive correlation.
-1, we say that there is a perfect negative correlation.
0.5 and upward but not 1, we say there is a strong positive correlation
-0.5 and downward but not -1, we say there is a strong negative correlation
between 0 to 0.5, we say there is a weak positive correlation
between 0 to -0.5, we say there is a weak positive correlation
The question says r = 0.25, hence Age and Height share a weak positive relationship
Exercises 12.3 Complete the following: 1. Complete the squares for each quadratic, list the center and radius, then graph each labeling its translated center: ra) x² + 2x + y² - 4y=4 (b) x² + y2 - 4x = 0) (c) 2x2 + 2y2 + 3x - 5y = 2 (d) x² + y²– 2x-3y=8 (e) x2 + y2 + 3x = 4 - (1) 4x² + Any? - 16x + 2Any = -2 (g) x2 + y2 + 4x = 0 (h) x2 + y2 – 7y = 0 (i) x2 + y2 + 2mx - 2ny = 0 (j) x2 + y2 - 2ax + 2by =
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1) Let's complete the square, and label the Center, and the radius
x² + 2x + y² - 4y=4 Dividing the coefficients of x and y by 2
x² +2x +1 +y²-4y+4=4+5 Adding on both sides the new addends
(x+1)²+(y-2)²=9
Looking at the Diagram what is the correct theorem,ASA Or AAS
Answers
In the given image, you have the following:
- side OP (first triangle) is congruent to side QR
- angle N is congruent to angle S
- angle O is congruent to angle Q
if angles N and S, and O and Q are equal, it is necessary that angles P and R are equal. Do to all interioir angles are equal, it is necessary that all sides of both trangles have the same length (beacuse one of such sides is equal to one side of the other triangle.)
Hence, you can conclude that both triangles are congruent:
ΔOPN ≅ ΔQRS
moreover, the specific theorem to express the congruent of both triangles is:
AAS
The sum of the interior angles of an n-gon is 3420°. How many sides does the n-gon have?
Answers
In order to solve we remember that the sum of internal angles of a polygon is given by:
[tex]\text{anlge}=(n-2)\cdot180[/tex]Where "n" is the number of sides.
So, we solve now:
[tex]3420=(n-2)\cdot180\Rightarrow n-2=19[/tex][tex]\Rightarrow n=21[/tex]So, the polygon has 21 sides.
I need geometry help.
Answers
Question:
Solution:
A translation is called a rigid transformation or isometry because the image is the same size and shape as the pre-image. In this translation that maps ΔABC to ΔA'B'C', the distances from the pre-image points to the image points are equal, and the segments representing these distances are parallel.
Then we can conclude that the correct answers are:
The last two options.
The polynomial function f(x) is graphed below. Fill in the formbelow regarding the features of this graph.
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Note: The question does not include the form mentioned. However, I will go ahead to highlight the general features of the polynomial function f(x) shown:
From the plotted grapph of the polynomial function f(x) shown, there are a lot of features that can be deduced:
1) As x tends to -ve infinity (i.e. x → -∞), f(x) tends +ve infinity (i.e. f(x) → ∞)
2) As x tends to +ve infinity (i.e. x → ∞), f(x) tends to +ve infinity (i.e. f(x) → ∞)
3) f(x) has a minimum at x tends to 0 (i.e. x → 0)
4) The polynomial function f(x) has 4 zeros. (That is the point where f(x) = 0). It is also the point where the graph crosses the x axis
A ball is dropped from a height of 10 feet and returns to a height that is one-half of the height from which it fell the Ball continues to bounce half the height of the previous bounce each time. How far how far will the ball have traveled when it hits the ground for the fourth time? It might be helpful to sketch the part of ball.
Answers
To solve this problem we can write a general equatio so:
[tex]y=10(1-0.5)^x[/tex]whre y is the high and x are the number of bounces so for 4 will be:
[tex]\begin{gathered} y=10(0.5)^4 \\ y=0.62ft \end{gathered}[/tex]When adding subtracting dividing multiplying parentheses and exponents, what operation would we do first?
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According to the accronym P.E.M.D.A
When k³-17k+32 is divided by k+5,find the quotient and match the letters to the terms to fill the blank? Can you show me how to set it up and the answer please
Answers
Given the equation k³-17k+32
it will be divided by k + 5
So,
k^2 - 4k
--------------------------------------------------------
k + 4 ll k³ - 17k + 32
ll k³ + 4 k^2
-----------------------------------------------
-4 k^2 - 17 k + 32
-4 k^2 - 16 k
------------------------------------------------
- k + 32
I’m having trouble with this problem please help?The second part of the question is at the beginning of the Answer Tab.
Answers
To answer this question, we have the following points for the line:
(2018, $3200) and (2020, $2000).
Since we want to find the relationship between the number of years after 2018, x, and the value of the computer, y, we need to have the year 2018 as the starting year, and we can replace it with 0. The rest of the years will be the number of years after 2018. For example, the year 2020 will be 2 years after 2018. The year 2022 will be 4 years after 2018 and so on.
Therefore, we have to find the equation of the line for the following points:
• (0, $3200), (2, $2000)
Then to find the equation line, we have to apply the two-point form of the line equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)_{}[/tex]If we label each point first, we have:
[tex]\begin{gathered} x_1=0,y_1=3200 \\ x_2=2,y_2=2000 \end{gathered}[/tex]Now, we can substitute these values into the two-point form of the line equation:
[tex]\begin{gathered} y-3200=\frac{2000-3200}{2-0}(x-0) \\ y-3200=\frac{-1200}{2}x \\ y-3200=-600x \\ y-3200+3200=-600x+3200 \\ y=-600x+3200 \\ f(x)=y=-600x+3200 \end{gathered}[/tex]Therefore, the relationship between years after 2018 (x) and the value of the computer (y) is as follows:
[tex]y=-600x+3200[/tex]Estimating the value of the computer in the year 2022We can see that the year 2022 is four (4) years after the year 2018:
[tex]2022-2018=4[/tex]Therefore, we can estimate the value of the computer in the year 2022 substituting x = 4 into the linear function:
[tex]\begin{gathered} y=-600(4)+3200 \\ y=-2400+3200 \\ y=800 \end{gathered}[/tex]Hence, the value of the computer, following this linear model is in the year 2022 of $800.
Estimating the value of the computer in the year 2024
We need to find the number of years in 2024 after 2018:
[tex]2024-2018=6[/tex]Now, we have to substitute this value into the linear equation as follows:
[tex]\begin{gathered} y=-600x+3200 \\ y=-600(6)+3200 \\ y=-3600+3200 \\ y=-400 \end{gathered}[/tex]We have that the value of the computer is -$400.
In this case, it does not have any sense to calculate this value. The item, in this case, is "creating" losses to the company (we can see it is a negative value), and we can sell the item before its value is zero. In a few words, it does not have any sense to calculate or estimate the value of the computer in 2024 because the item has become totally depreciated before that year.
Find the inverse of the following function:(x) = 5x + 4Answer 5 Points-'(x) =
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Hello there. To solve this question, we'll have to remember some properties about inverse functions.
First, an inverse function is the same as reflecting the function on the function f(x) = x, that is called the identity for inverse functions.
First, graphing the function:
[tex]f(x)=5x^3+4[/tex]We have
In order to reflect this function, we have to change x by y and solve for y i this case.
Think of this as changing coordinates for which [x y]^T goes to [y x]^T and we want to find the image of this function in this new coordinates.
Changing the variables, we get
[tex]x=5y^3+4[/tex]Subtract 4 on both sides of the equation
[tex]x-4=5y^3[/tex]Divide both sides of the equation by a factor of 5
[tex]y^3=\dfrac{x-4}{5}[/tex]Take the cuberoot on both sides of the equation
[tex]y=\sqrt[3]{\dfrac{x-4}{5}}[/tex]This is the inverse of this function, that we write as
[tex]f^{-1}(x)=\sqrt[3]{\dfrac{x-4}{5}}[/tex]And its graph is as follows (complementing the first image):