Answers
[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\[/tex]
[tex]\bf \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]
now, with that template above in mind, let's see.
reflected over the x-axis, that means A is negative.
vertically shrunk by 0.25 or 1/4, that means A is negative 4, or -4.
shifted to the left, that means C/B is positive
shifted by 65°, that means, we could use the default B = 1, and C = 65°, that way we end with C/B = 65/1 or just +65
and shifted downwards by 1 unit, that means D = -1.
[tex]\bf f(x)=-4sin(1x+65^o)-1\implies f(x)=-4sin(x+65^o)-1[/tex]
and looks more or less like the picture below.
Related Questions
Explain why the functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.
Answers
Please see attached document for the graphs:
The functions with the given graphs can't be solutions of
the differential equation dy dt = et(y − 1)2.
(a) won’t work, since it has negative slope on portions of its solutions. The
slope, e t (y − 1)2 , is a nonnegative function.
(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.
Functions with given graphs cannot be solutions to the differential equation dy / dt = e^t(y-1)^2 because their graphs don't satisfy the conditions imposed by the equation, such as non-oscillatory behavior and non-linear variation with time.
Explanation:The question pertains to why certain functions represented by their graphs cannot be solutions to the differential equation dy / dt = et(y-1)2. The explanation lies in the structure of the given differential equation and the properties of function graphs.
Equation dy / dt = et(y-1)2 is a non-linear first order differential equation. To be a solution to this equation, a function's graph must satisfy certain conditions imposed by the equation. However, if certain function graphs represent an undefined curve or if their graphs demonstrate oscillatory behavior, they do not satisfy these criteria.
For instance, the differential equation demands non-oscillatory behavior as seen in the general solution provided in the reference: Yn(x) = Ce-Bx +De+Bx. This form describes a gradual attenuation of y(x), i.e., it does not oscillate. Similarly, if a graph represents a function that varies non-linearly with time (like In[A] vs. Time), it does not represent a solution to the differential equation as well.
Thus, the inability of certain function graphs to satisfy the conditions required by the given differential equation is the reason they cannot be its solutions.
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Today only, a table is being sold for $333 . This is 74% of its regular price. What was the price yesterday?
Answers
Among 170 households surveyed, 44 have a video camera, 40 have a snapshot camera, 51 have binoculars, 9 have a video camera and a snapshot camera, 8 have a snapshot camera and binoculars, and 5 have all three products. what is the probability that a household will have a snapshot camera or binoculars? express the answer as a fraction.
Answers
Process average or mean: is computed by dividing the total of the measurements made on the process by the number of measurements used to compute the total approximates the center of the distribution of measurements made on the process a measure of
Answers
Which lines are Parallel? Justify your answer
Answers
Answer:
Lines e and f are parallel since their alternate exterior angles 75 ad 75 are congruent.
Step-by-step explanation:
Parallel lines mean that angle relationships exits where specific angles are congruent to each other. 75 and 75 are in the position of alternate exterior angles for lines e and f. Since they are congruent, these lines must be parallel. However, a and b have same side exterior angles which must add to 180. 75 + 115 does not equal 180. It equals 190. Therefore a and b cannot be parallel.
Answer:
E and F on edgenuidy
Step-by-step explanation:
did it rn
A baseball manager has 12 players of the same ability how many nine player starting lineup starting create
Answers
Given: F(x) = 3x 2 + 1, G(x) = 2x - 3, H(x) = x
Answers
I think it's 2(x+3).
Answer: 2(x+3)
paralyzed;live
In 1996, funding for a program increased by 0.62 billion dollars from the funding in 1995. In 1997, the funding increased 0.29 billion dollars over the funding in 1996. For those three years, the funding was 11.25 billion dollars. How much was funded in each of these three years?
Answers
1996 = x + 0.62
1997 = x + 0.62 + 0.29
x + x + 0.62 + x + 0.62 + 0.29 = 11.25
3x + 1.53 = 11.25
3x = 11.25 - 1.53
3x = 9.72
x = 9.72 / 3
x = 3.24 <== 1995 = 3.24 million
1996 = 3.24 + 0.62 = 3.86 million <==
1997 = 3.24 + 0.62 + 0.29 = 4.15 million <==
A 250 ml glass of orange juice contains 22 grams of sugar. how much sugar is in a two-liter (2,000 ml) bottle of orange juice?
Answers
cross multiply
(250)(x) = (2000)(22)
250x = 44,000
x = 44,000/250
x = 176 grams of sugar <==
Orange juice contains some amount of sugar in it. There is 176 g of sugar present in a 2000 ml bottle of orange juice.
Given:
A 250 ml glass of orange juice contains 22 grams of sugar.
It is required to calculate the amount of sugar present in the 2000 ml bottle of juice.
Now, the amount of sugar present in 1 ml of juice will be,
[tex]\dfrac{22}{250}=\dfrac{11}{125}\rm \; g[/tex]
So, the amount of sugar in 2000 ml of juice will be,
[tex]\dfrac{11}{125}\times 2000=11\times 16\\=176\rm \; g[/tex]
Therefore, there is 176 g of sugar present in a 2000 ml bottle of orange juice.
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It takes 23 minutes for 6 people to paint 6 walls. How many minutes does it take 9 people to paint 7 walls?
Answers
Once you have this rate you can find how many minutes it takes to do any number of walls with any number of people.
Lets call this unit rate 'r'. Number of people = n, Number of walls = w.
By multiplying the unit rate by 'n', you get the speed n people can paint a wall. Example, if it takes 4 min to paint 1 wall the unit rate = 1/4. The speed for 8 people is 8*(1/4) = 2 walls per minute. Time = 1/rate. So 2 walls per minute = 1/2 min per wall. Now multiply time by w. If there are 10 walls, (1/2)*10 = 5 , It takes 8 people 5 min to paint 10 walls.
The general formula is:
[tex]t = \frac{w}{n*r} \\ \\ r = \frac{w}{n*t}[/tex]
Now apply to given problem:
Time = 23 min, n = 6, w = 6
Solve for unit rate 'r'
[tex]r = \frac{6}{6*23} = \frac{1}{23} [/tex]
Find time, given
n = 9, w = 7
[tex]t = \frac{7}{9*(1/23)} = \frac{7*23}{9} = 17.89[/tex]
Answer:
it takes 17.89 min or 17 min 53 sec
Which of the following points lies on the line y = x + 1?
A. (2,3)
B. (2,-3)
C. (-2,3)
D. (-2,-3)
Answers
2 + 1 = 3
3 = 3
how do I solve 12-3(x-5)=21
Answers
Distribute
12-3x+15=21
Combine like terms
27-3x=21
Subtract 27 from both sides
-3x= -6
Divide both sides by -3
x=2
Final answer: x=2
A pool can be filled by one pipe in 4 hours and by a second pipe in 12 hours. How long will it take using both pipes to fill the pool?
Answers
t=3 hour
The individual pipes can fill the pool in 4 hours and 12 hours respectively then using both pipes together, it will take 3 hours to fill the pool.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Give that,
One pipe can fill the pool in 4 hours.
Another pipe can fill the pool in 12 hours.
The first pipe fills the pool in 4 hours,
So its rate is 1/4 of the pool per hour.
Similarly,
The second pipe fills the pool in 12 hours,
So its rate is 1/12 of the pool per hour.
To find the combined rate, when both pipes are used together,
Add their individual rates:
(1/4 + 1/12) = 3/12 + 1/12 of the pool per hour.
(1/4 + 1/12) = 1/3 of the pool per hour.
Now, to find the time it takes to fill the pool using both pipes,
Take the reciprocal of the combined rate,
1 / (1/3) = 3 hours.
Hence,
Using both pipes together, it will take 3 hours to fill the pool.
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boiling point of water is 212 Fahrenheit Paul wants to boil water to make pasta right now he only has ice which is at a temperature of -4 degrees how many degrees must Paul change the temperature of the water for it to become boiling water
Answers
Paul must increase the temperature by 216 degrees Fahrenheit to boil his ice and be able to cook his pasta.
Explanation:Paul needs to raise the temperature of the ice he has from -4 degrees Fahrenheit to the boiling point of water, which is 212 degrees Fahrenheit. To determine how many degrees Paul needs to change the temperature, we subtract the current temperature of the ice from the desired temperature to boil water. Here is the step-by-step calculation: Subtract -4 from 212. The result is that Paul needs to increase the temperature by 216 degrees Fahrenheit for the ice to reach the boiling point and cook his pasta.
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Three tables are placed side by side. One table is 2 feet 9 inches wide, another is 4
feet 8 inches wide, and the third is 6 feet 11 inches wide. How wide are they combined?
Write your answer in feet and inches. Use a number less than 12 for inches
Answers
Final answer:
The combined width of the three tables is 14 feet 4 inches, calculated by first converting each table's width to inches, adding them together, and then converting the total back to feet and inches.
Explanation:
To find the combined width of the three tables placed side by side, you need to add the widths together. First, convert all measurements to inches, add them, and then convert back to feet and inches.
Table 1: 2 feet 9 inches = (2 × 12) + 9 = 24 + 9 = 33 inches
Table 2: 4 feet 8 inches = (4 × 12) + 8 = 48 + 8 = 56 inches
Table 3: 6 feet 11 inches = (6 × 12) + 11 = 72 + 11 = 83 inches
Now, add the inches: 33 + 56 + 83 = 172 inches.
To convert 172 inches back to feet and inches, divide by 12 (since there are 12 inches in a foot): 172 ÷ 12 = 14 feet 4 inches (since 172 divided by 12 is 14 with a remainder of 4).
Therefore, the combined width of the tables is 14 feet 4 inches.
Susan invests
3
times as much money at
11
%
as she does at
7%
. If her total interest after
1
year is
$2000
, how much does she have invested at each rate?
Answers
now, she invested at 11% three times as much, so 3*a or "3a"
how much is 7% of a? well, (7/100)*a or 0.07a
how much is 11% of 3a? well (11/100)* 3a or 0.11(3a)
now, we know her total yield in interest is 2000 bucks, so whatever 0.07a is and 0.11(3a) are, they add up to 2000
0.07a + 0.11(3a) = 2000
solve for "a".
How many integers between 100 and 300 inclusive,are divisible by 10?
Answers
10≤n≤30
So the number of multiples of 10 from 100 to 300 inclusive is:
(30-10+1)=21
The final answer is 21.
Evaluate the expression 3c – d for the given variable. d = -c + 7
Answers
3c-(-c+7)
3c+c-7
4c-7
Final answer: 4c-7
In 2006,111.7 million household owned at least
Answers
In 2006, 112.8 million households owned at least one TV set. About 5.8 million households owned 3 or more TV sets in 2006. What percentage of those owning atleast one TV set was this? Round to the nearest integer
5.8 / 112.8 = 0.051418 which is 5.1418 percent, rounds down to 5%.
Use the percent of change to find the new amount 120 pounds decreased by 30%
Answers
In 2008, there were 6.7 × 109 people living on earth. What is that number in standard notation?
A.) 6,700,000
B.)6,700,000,000
C.)67,000,000
D.)67,000,000,000
Answers
Answer:
B) 6,700,000,000 people.
Step-by-step explanation:
We have been given that in 2008, there were [tex]6.7\times 10^9[/tex] people living on earth. We are asked to convert our given population in standard notation.
While changing scientific notation to standard notation we just move the decimal as many times as the exponent indicates. We can see that our exponent is 9, so we will move the decimal to 9 places right.
[tex]6.7\times 10^9=6.7\times 1000000000[/tex]
[tex]6.7\times 10^9=6700000000[/tex]
Therefore, there were 6,700,000,000 people living on earth and option B is the correct choice.
Answer:
B.)6,700,000,000
Step-by-step explanation:
SO when you have to transform from the scientific notation into standar notation, you just have to move the decimal point to the right the number of positions that the scientific notation has as the exponent, in this case it is 9, so you move one position the decimal point to the right to make the number 67, and then add 8 zero´s to the right:
6,700,000,000
As you can see you moved the decimal point 9 positions to the right.
So that´s how you can convert scientific notation to standard notation.
what are characteristics of complex numbers
Answers
You put $100 in an account. The account earns $2 simple interest in 6 months. What is the annual interest rate?
Answers
A square has an area that is less than 100m^2. What is a reasonable range for the graph of the squares side
Answers
A = s^2, where s is the side length of the square
So, when the area does not exceed 100 m^2, then the upper limit is 100. Thus, the maximum side should be
100 > s^2
s < 10 m
The range is the coverage of the dependent variable. With that being said, the range is therefore from 0 to 100 square meters. Negative values are impossible so the lower limit is 0.
Simplify 2 square root of 10 times 3 square root of 12
answers
A.6squar rootof120
B.12squar rootof60
C.12squar rootof30
D.5squar rootof120
Answers
The simplified form of the expression [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] is [tex]6\sqrt{120}[/tex] which corresponds to answer choice A.
Given: [tex]2\sqrt{10} \times 3\sqrt{12}[/tex]
To find: simplify
We can break down the expression [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] and multiply the roots and whole numbers as follows:
[tex]\text{product is} = 2\sqrt{10} \times 3\sqrt{12} \\\text{product is} = 2 \times 3 \times \sqrt{10} \times \sqrt{12}\\\text{product is} = 6 \times \sqrt{120}\\\text{product is} = 6\sqrt{120}[/tex]
The simplified form of the given expression is 6√120, which corresponds to answer choice A.
Can the remainder in a division problem ever equal the divisor? Why or why not
Answers
8/4=1 r 4
answer should be 2
Write 800 as a product of its prime factors
Answers
2*400
2*2*200
2*2*2*100
2*2*2*2*50
2*2*2*2*2*25
2*2*2*2*2*5*5
Final answer: 800=2^5 * 5^2
2. Wandabaked168cookies,packagedtheminboxesof12,andsoldeachboxfor $1.20. How many boxes of 12 can be packaged if there are 168 cookies? What was the total amount of money that Wanda made for all of the boxes sold?
Answers
------------------------------------------------------
This question is solved using proportions.
In each box, there are 12 cookies.She baked 168 cookies.Thus, to find the number of boxes, we use a rule of three.
1 box - 12 cookies.
x boxes - 168 cookies.
Applying cross multiplication:
[tex]12x = 168[/tex]
[tex]x = \frac{168}{12}[/tex]
[tex]x = 14[/tex]
Thus, 14 boxes can be packaged.
------------------------------------------------------
Now, we find the amount of money she made.
She sold 14 boxes.Each box for $1.20.Thus:
[tex]T = 14 \times 1.2 = 16.8[/tex]
She made $16.8.
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If the unit selling price is $2.50 and the unit cost is $1.00, what action is need to maintain the gross margin percentage when unit cost increases $0.25
Answers
If the cost increases to $1.25 then the selling price needs to increase to $1.25 x 2.5 = $3.13
the equation of a curve is xy=12 and the equation of a line l is 2x+y=k where k is a constant .In the case where k=11 find the coordinates of the points of intersection of l and the curve.
Answers
solve one for either x or y, and plug it into the other one to get coord. I'll solve for x.
I first solve the problem on the left for y, and plug it into the second one, giving me only one variable to solve for. solving left for y is y=12/x
Plug new y value into second equation and solve for x.
2x +12/x=11
mult both sides by x to clear denominator. You get...
2x^2-11x+12=0
now factor and get (2x-3)(x-4)
Make them both equal to zero and solve for x.
You get x=3/2 and x=4
Plug these into your original xy=12 equation to get the corresponding y coordinate for that specific x value. You get
(3/2, 8) and (4,3). Your lines intersect twice, at these two points.
The coordinates of the points of intersections of [tex]l[/tex] and the curve are [tex](x_{1}, y_{1}) = (4,3)[/tex] and [tex](x_{2}, y_{2}) = (1.5, 8)[/tex].
According to the statement, we get the following nonlinear system of equations:
[tex]x\cdot y = 12[/tex] (1)
[tex]2\cdot x + y = 11[/tex] (2)
Now we proceed to solve for each variable by algebraic means. By (1):
[tex]y = \frac{12}{x}[/tex]
Then we apply the formula in (2):
[tex]2\cdot x + \frac{12}{x} = 11[/tex]
[tex]2\cdot x^{2}+12 = 11\cdot x[/tex]
[tex]2\cdot x^{2}-11\cdot x +12 = 0[/tex]
Roots are found by the quadratic formula and (1):
[tex]x_{1} = 4[/tex], [tex]y_{1} = 3[/tex]
[tex]x_{2} = 1.5[/tex], [tex]y_{2} = 8[/tex]
The coordinates of the points of intersections of [tex]l[/tex] and the curve are [tex](x_{1}, y_{1}) = (4,3)[/tex] and [tex](x_{2}, y_{2}) = (1.5, 8)[/tex].
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