The graph of y=cosx (dashed line) has been transformed to give graph G
The equation of graph g has the form of y = a+cos(x+b)
Find the values of a and b
Answers
The values of a and b in the equation y = a + cos(x + b) are a = -1 and b = -pi/2.
To find the value of a, we need to find the vertical shift or displacement of graph G from the graph of y=cosx. From the graph, we can see that graph G has a minimum value of -2. To get this minimum value, we need to subtract 2 from the amplitude of the cosine function, which is 1. So a = -2+1 = -1.
To find the value of b, we need to find the horizontal shift or phase shift of graph G from the graph of y=cosx. From the graph, we can see that graph G is shifted π/2 units to the right. We know that the graph of y=cos(x+b) is shifted b units to the left if b is positive. Therefore, to get a phase shift of π/2 units to the right, we need to substitute -π/2 for b. So b = -π/2.
Hence, the equation of graph G is y = -1+cos(x-π/2).
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Related Questions
If the number of bacteria in a colony doubles every 33 hours and there is currently apopulation of 50,000 bacteria, what will the population be 66 hours from now?
Answers
Answer:
200,000
Step-by-step explanation:
Population now: 50,000
Population in 33 hours: 100,000
Population in 66 hours: 200,000
Answer: 200,000
A baby weighs 100 ounces. Find the baby's weight in pounds and ounces.
Answers
Work Shown:
1 pound = 16 ounces
100/16 = 6.25
100 ounces = 6.25 pounds
100 ounces = 6 pounds + 0.25 pounds
-------
1 pound = 16 ounces
0.25*1 pound = 0.25*16 ounces
0.25 pounds = 4 ounces
------
100 ounces = 6 pounds + 0.25 pounds
100 ounces = 6 pounds + 4 ounces
100 ounces = 6 pounds, 4 ounces
PLEASE HELP!!!!!
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2?
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18
Answers
The equation of a line that passes through the point (4, 3) and has a slope of 1 / 2 is y = 1 / 2 x + 1.
How to find the equation of a line?The equation of a line that passes through a point can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (4, 3) and the slope is 1 / 2.
Hence, let's find the y-intercept using (4, 3)
y = 1 / 2 x + b
3 = 1 / 2 (4) + b
3 = 2 + b
b = 3 - 2
b = 1
Therefore, the equation of the line is y = 1 / 2 x + 1.
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Please Help! I'll mark first to answer brainliest!!!!!
Answers
Answer:
wooooow i wish i remembered how to do that sry
Step-by-step explanation:
1.A 15-passenger van is rented for a family
vacation. The van rental is $60.00 per day, plus a
$145.00 insurance fee. How many days can the
van be rented if they want to spend no more than
$625.00 on the van rental? Write and solve an
inequality.
2. Marco is limited to 7 hours of screen time
each week. He decides to watch a movie that is 1
hour and 20 minutes on Sunday. If he divides the
remainder of the time equally amongst the other
six days, then how many minutes can he watch
each day? Write and solve an inequality.
I need the inequality and solution please
Answers
Answer:
they can rent it for 9 days
Let triangle ABC have side lengths AB=13, AC=14, and BC=15. There are two circles located inside angle BAC which are tangent to rays AB, AC, and segment BC. Compute the distance between the centers of these two circles.
Answers
The distance between the centers of the two circles located inside angle BAC is equal to the length of the angle bisector of angle BAC.
In triangle ABC, let D be the point where the incircle of triangle ABC is tangent to side BC.
Since the two circles in question are tangent to rays AB and AC, as well as segment BC, they are both internally tangent to angle BAC.
∴The centers of these circles lie on the angle bisector of angle BAC.
By the Incenter-Excenter Lemma, the distance between the centers of the two circles is equal to the length of the angle bisector of angle BAC. To find this length, apply the Angle Bisector Theorem.
The length of the angle bisector is given by:
AD = \(\frac{(BC X AB)}{(AB + AC)}\)
Substituting the given values,
AD = \(\frac{(15 X 13)}{(13 + 14)}\) = \(\frac{195}{27}\)
Hence, the distance between the centers of the two circles is \(\frac{195}{27}\) units.
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The set b = (1 + t2,t + t21 + 2t + t2) is a basic for p2. Find the coordinate vector of p(t)=1 + 4t + 7t2 relative to B.
Answers
The coordinate vector of p(t) = 1 + 4t + 7t² relative to B is (2, 6, -1).
What is the coordinate vector?
A coordinate vector is a numerical representation of a vector that explains the vector in terms of a specific ordered basis. A simple example would be a position in a 3-dimensional Cartesian coordinate system with the basis being the system's axes.
Here, we have
Given: The set b = (1 + t², t + t², 1 + 2t + t²) is a basic for P₂.
Now, let coordinate vector of P(t) = 1 + 4t + 7t² relative to B is (C₁, C₂, C₃).
Then,
1 + 4t + 7t² = C₁(1 + t²) + C₂(t + t²) + C₃(1 + 2t + t²)
(C₁+C₃) + ( C₂+2C₃)t + (C₁+C₂ +C₃)t² = 1 + 4t + 7t²
C₁+C₃ = 1
C₂+2C₃ = 4
C₁+C₂ +C₃ = 7
Now, to find C₁, C₂, C₃ we solve the system.
The augmented matrix of the given system is:
= \(\left[\begin{array}{ccc}1&0&1|1\\0&1&2|4\\1&1&1|7\end{array}\right]\)
Now, we apply row reduction and we get
R₃ = R₃ - R₁
= \(\left[\begin{array}{ccc}1&0&1|1\\0&1&2|4\\0&1&0|6\end{array}\right]\)
R ⇔ R
= \(\left[\begin{array}{ccc}1&0&1|1\\0&1&0|6\\0&1&2|4\end{array}\right]\)
R₃ = R₃ - R₁
= \(\left[\begin{array}{ccc}1&0&1|1\\0&1&0|6\\0&0&2|-2\end{array}\right]\)
R₃ = 1/2R₃
= \(\left[\begin{array}{ccc}1&0&1|1\\0&1&0|6\\0&0&1|-1\end{array}\right]\)
R₁ = R₁ - R₃
= \(\left[\begin{array}{ccc}1&0&0|2\\0&1&0|6\\0&0&1|-1\end{array}\right]\)
C₁ = 2, C₂ = 6, C₃ = -1
Hence, the coordinate vector of p(t) = 1 + 4t + 7t² relative to B is (2, 6, -1).
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For number 8 find the variable using the properties of a parallelogram
Answers
Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.
QuadrilateralsThere are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.
the opposite sides are equal and parallelthe opposite angles and the diagonals are equal.the adjacent angles are supplementary.The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:
6x+12x=180
18x=180
x=10°
Therefore, 6x= 6*10=60° and 12x=12*10=120°.
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Please! I don't understand this question! Help!
Zachary purchased a computer for $ on a payment plan. months after he purchased the computer, his balance was $. months after he purchased the computer, his balance was $. What is an equation that models the balance y after x months?
Answers
I need help with this questions
1) If R is the midpoint of QS,find QS
2) If B is the midpoint of AC ,and AC =8x-20, find BC
Answers
BC=5x-19
I think so...
Two kids at a summer camp, Antonio and Kenneth, are competing in a potato sack race. Antonio is younger, so he is given a head start of 14 meters. When the race starts, Antonio hops at a rate of 1 meter per second, and Kenneth hops 3 meters per second. Eventually, Kenneth will overtake Antonio. How long will that take? How far will Kenneth have to hop?
Answers
Answer: 21m
Step-by-step explanation:
Kenneth will have to hop 21 meters.
The time required for the overtake and the distance hopped by Kenneth are given as 7 seconds and 21 m respectively.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
Suppose the time taken for the overtake be x.
Now, as per the question the distance travelled by both during x second is given as,
Distance travelled by Antonio = 14 + 1 × x = 14 + x.
And, distance travelled by Kenneth = 3x.
At the time of overtake the distances travelled by them is equal.
Thus, the following equation can be made for this case as,
3x = 14 + x
⇒ 3x - x = 14
⇒ 2x = 14
⇒ x = 7
The distance travelled by Kenneth is 3 × 7 = 21 m.
Hence, the time for overtake and the distance travelled by Kenneth are given as 7 seconds and 21 m respectively.
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What is the reflection image of P(0, 0) after two reflections, first across x = −3 and then across y = 4?
Answers
Answer:
(-6, 8)
Draw the point, draw the lines of reflection, reflect, find coordinates.
a mass weighing 48 lb stretches a spring 6.0 in. the mass is also attached to a damper with coefficient γ. determine the value of γ for which the system is critically damped. assume that g=32 ft/s2.
Answers
the system to be critically damped, the value of the damping coefficient γ should be approximately 17.35 lb⋅s/ft.
For a critically damped system, the damping coefficient γ is equal to the square root of 4 times the mass (m) multiplied by the spring constant (k). Mathematically, it can be expressed as:
γ = 2 × √(m × k)
First, we need to convert the mass from pounds to slugs, since the unit of mass in the equation is slugs. Since 1 slug = 32.2 lb⋅s^2/ft, the mass in slugs can be calculated as:
m = 48 lb / (32.2 lb⋅s^2/ft) ≈ 1.49 slugs
Next, we calculate the spring constant (k). The force exerted by the spring (F) is equal to the product of the spring constant and the displacement (x). In this case, the displacement is 6.0 in = 0.5 ft, and the force is the weight of the mass, which is 48 lb. Therefore, we have:
F = k × x
48 lb = k × 0.5 ft
k = 48 lb / 0.5 ft = 96 lb/ft
Now, we can calculate the damping coefficient γ:
γ = 2 × √(m × k) = 2 × √(1.49 slugs × 96 lb/ft) ≈ 17.35 lb⋅s/ft
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\sqrt[3]{1728} please help me with this
Answers
Simplifying the above expression: 26 × 33
Simplifying further: 123
Therefore, the cube root of 1728 by prime factorization is (2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3)1/3 = 12
Solve for x : 4/5 x − 2 = 7
Answers
Answer: x = 45/4
Step-by-step explanation:
Answer:
11 1/4 simplified form
45/4 exact form
11.25 decimal form
4 yz and 2y^2
Find the gcf of each group of monomials
Answers
Answer:
2y
Step-by-step explanation:
To find the GCF ( Greatest Common factor), for an algebraic expression like the one given, all you have to do if look over the expression and circle all the terms they both share, in this case, both 4yz and 2y^2 had 2y in them, except in different forms.
If you find it difficult to recognize the similarities, divide the expressions as much as you can.
Hope this helps
I just need some help with the math for this 3-part problem.
Data for this question. A 180-cm3 soil sample was collected three days after a drenching rain when
the soil was assumed to be at field capacity (Not Saturated!). The wet weight of the sample was 274.1 g
and after drying overnight in an oven the sample weighed 214.7 g.
1. What was the gravimetric moisture content of this soil at field capacity?
1a. What is the dry bulk density of this sample?
1b. What is the porosity of this sample as a percent of the total volume?
Answers
1) The gravimetric moisture content of the soil at field capacity is approx 27.62%.
2) The dry bulk density of the sample is approximately 1.193 g/cm^3.
3) The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.
1) The gravimetric moisture content of the soil at field capacity can be calculated using the following formula:
Gravimetric Moisture Content = ((Wet Weight - Dry Weight) / Dry Weight) * 100
Given:
Wet Weight = 274.1 g
Dry Weight = 214.7 g
Using the formula, we can substitute the values:
Gravimetric Moisture Content = ((274.1 - 214.7) / 214.7) * 100
Gravimetric Moisture Content = (59.4 / 214.7) * 100
Gravimetric Moisture Content ≈ 27.62%
The gravimetric moisture content of the soil at field capacity is approximately 27.62%.
The gravimetric moisture content represents the amount of water present in a given mass of soil. By subtracting the dry weight of the soil from the wet weight and dividing by the dry weight, we can determine the proportion of water in the sample. Multiplying by 100 gives the moisture content as a percentage.
1a. The dry bulk density of the sample can be calculated using the following formula:
Dry Bulk Density = Dry Weight / Sample Volume
Given:
Dry Weight = 214.7 g
Sample Volume = 180 cm^3
Substituting the values into the formula:
Dry Bulk Density = 214.7 g / 180 cm^3
Dry Bulk Density ≈ 1.193 g/cm^3
The dry bulk density of the sample is approximately 1.193 g/cm^3.
Dry bulk density refers to the mass of dry soil per unit volume. To calculate it, we divide the dry weight of the soil by the sample volume.
1b. The porosity of the sample can be calculated using the following formula:
Porosity = (1 - (Dry Bulk Density / Particle Density)) * 100
The particle density for soil is usually around 2.65 g/cm^3.
Given:
Dry Bulk Density = 1.193 g/cm^3
Particle Density = 2.65 g/cm^3
Substituting the values into the formula:
Porosity = (1 - (1.193 / 2.65)) * 100
Porosity ≈ 54.96%
The porosity of the sample, as a percentage of the total volume, is approximately 54.96%.
Porosity represents the void space within a soil sample. It is calculated by subtracting the ratio of the dry bulk density to the particle density from 1 and multiplying by 100 to get the percentage. In this case, the particle density of 2.65 g/cm^3 is a typical value for soil.
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-1/10 dived by 1/8. please answer in fraction form
Answers
Answer:
-4/5
Step-by-step explanation:
I calculated it and the answer came directly
Answer:
\( -\dfrac{4}{5} \)
Step-by-step explanation:
\( -\dfrac{1}{10} \div \dfrac{1}{8} = \)
\( = -\dfrac{1}{10} \times \dfrac{8}{1} \)
\( = -\dfrac{1 \times 8}{10 \times 1} \)
\( = -\dfrac{8}{10} \)
\( = -\dfrac{4}{5} \)
A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games.
A) Design a simulation for this event,
B) what counts as a successful outcome?
C) Estimate the probability using your simulation.
Can anyone help me? I’m kind of confused on this problem
Answers
Answer:
C. Estimate the probability using your simulation.
Step-by-step explanation:
Consider the modified Harrod-Domar Growth model: c(g+δ)=(s
π
−s
W
)(
Y
π
)+s
W
As a planner, you're targeting a 4\% growth rate. If depreciation (delta) =0.03, capitaloutput ratio (c)=3,pi/Y=0.5, and savings out of capital income, s(pi)=25%. At what rate should the wage earners and rural households save? (Note: Write in \%, no decimal)
Answers
The rate at which the wage earners and rural households should save is 21%.
Given that:
Depreciation (δ) = 0.03
Capital output ratio (c) = 3
Profit share of income (π/Y) = 0.5
Savings out of capital income (sπ) = 25% = 0.25
We know that the modified Harrod-Domar growth model is given as:
c(g+δ) = (sπ - sW)(Yπ) + sW
We can rearrange the above equation to find the value of savings out of wage income as follows:
sW = c(g+δ - sπ(Yπ))/ (sπ - π/Y)
Plugging in the given values:
sW = 3(0.04 + 0.03 - 0.25(0.5))/ (0.25 - 0.5)
On solving the above equation, we get:
sW = 0.21 or 21%
Hence, the rate at which the wage earners and rural households should save is 21%. Therefore, the required answer is 21%.
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Find the whole if the part is 69 and the percent is 12.
Answers
Answer:
575
Step-by-step explanation:
if 69 = 12% then find what is 1%
69 / 12 = 5.75 = 1%
To get 100% :
5.75 x 100
:. 575 is the whole number
The whole of the given parameters part and percentage is gotten as; 575
How to solve fractions?We are given;
Part = 69
Percentage = 12%
Let the whole be x. Thus;
69/x * 100 = 12
This can be simplified by using multiplication property of equality to get;
x = 6900/12
x = 575
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gabe goes to the mall. if k is the number of items he bought, the expression 17.55k+27 gives the amount he spent in dollars at one store. then he spent 24 dollars at another store. find the expression which represents the amount gabe spent at the mall. then estimate how much gabe spent if he bought 4 items.
Answers
Answer:
68.55
Step-by-step explanation:
T/F when sampling with replacement, the standard error depends on the sample size, but not on the size of the population.
Answers
True, the standard error depends on the sample size, but not on the size of the population.
What is the standard error?
A statistic's standard error is the standard deviation of its sample distribution or an approximation of that standard deviation. The standard error of the mean is used when the statistic is the sample mean.
We know that ;
Standard error = σ/√n
The given statement is true.
The standard error is the standard deviation of a sample population.
Hence, the standard error depends on the sample size, but not on the size of the population.
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is 8.33865… rational
Answers
Answer:
no, 8.33865... is not rational
Step-by-step explanation:
it's an irrational number
6 divided by 3/4 ..............................................
Answers
Answer:
8
Step-by-step explanation:
6/1÷3/4
6/1×4/3
24/3
8
HELP giving brainless and 100 points!!
Answers
Answer:
b
Step-by-step explanation:
3 1/2 x 3 x 1/2= 5.25 or 5 and 1/4
Answer:
B
Step-by-step explanation:
Little tip, if you don't know a question or aren't sure, pick options b or c, they are statistically the most used options.
please help me with math
Answers
The area of triangle BMN is 124.7 square centimeter.
What are similar triangles?Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.
Analysis:
AB = AC = BC = 50cm
AH = AC/2 = 50/2 = 25cm
From Δ ABH, using Pythagoras theorem to find BH.
\((BH)^{2}\) = \((AB)^{2}\) - \((AH)^{2}\)
\((BH)^{2}\) = \(50^{2}\) - \(25^{2}\)
\((BH)^{2}\) = 2500 - 625
\((BH)^{2}\) = 1875
BH = \(\sqrt{1875}\) = 43.3cm
ΔBMN and BHC are similar,
so, BM/BH = MN/HC
BM/43.3 = 12/25
25BM = 12 X 43.3
BM = 519.6/25 = 20.78cm
Area of ΔBMN
= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter
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we find t=2.73 with 5 degrees of freedom. what is the appropriate p-value.
Answers
The appropriate p-value for a t-value of 2.73 with 5 degrees of freedom is approximately 0.05. This indicates that there is a 5% chance of observing a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true.
In statistics, the p-value measures the strength of evidence against the null hypothesis. The null hypothesis states that there is no significant difference or effect in the population being studied. The p-value is calculated by determining the probability of obtaining a test statistic (in this case, the t-value) as extreme as or more extreme than the observed value, assuming the null hypothesis is true.
To determine the appropriate p-value for a t-value, we typically consult a t-distribution table or use statistical software. In this case, with 5 degrees of freedom and a t-value of 2.73, we look up the critical value or use software to find the corresponding p-value. The p-value associated with a t-value of 2.73 and 5 degrees of freedom is approximately 0.05.
The p-value of 0.05 indicates that there is a 5% chance of obtaining a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true. Generally, a p-value of 0.05 or lower is considered statistically significant, implying that the observed result is unlikely to have occurred by chance alone. If the p-value is below a predetermined significance level (often denoted as α, commonly set at 0.05), we reject the null hypothesis in favor of an alternative hypothesis. If the p-value is above the significance level, we fail to reject the null hypothesis.
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For what amount of exit proceeds would these two structures yield the same amount of carried interest?
.20 (Z-250) = .30 (Z-200)
Solve for Z.
Answers
Answer:
Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"
Find two integers whose sum is 4 and product is -45
Answers
Answer:
9 and -5
Step-by-step explanation: