Consider these two functions:
F(x) = 2cos(πx)
G(x) = 1/2cos(2x)
What are the amplitudes and periods of the two functions?
Answers
Answer:
\(\mathrm{pK}_{\mathrm{a}}+\mathrm{pK}_{\mathrm{b}}=\mathrm{pK}_{\mathrm{w}}\) for \(\mathrm{HCl}\) \& \(\mathrm{ClOH}\)
Answer:
f(x): Amplitude = 2, Period = 2
g(x): Amplitude = ¹/₂, Period = π
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftFunction f(x)
\(f(x)=2 \cos (\pi x)\)
Comparing this with the standard form of a cosine function:
Amplitude = 2\(\sf Period = \dfrac{2 \pi}{\pi}=2\)Function g(x)
\(g(x)=\dfrac{1}{2} \cos (2x)\)
Comparing this with the standard form of a cosine function:
\(\sf Amplitude=\dfrac{1}{2}\)\(\sf Period = \dfrac{2 \pi}{2}=\pi\)Learn more about the cosine graph here:
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Related Questions
what is 88,000 divided by 100
Answers
Answer:
880
Step-by-step explanation:
I hope this answer helps!
the sonar system that detect a sunken ship 1500 m ahead with an angle of elevation of 90° to the highest part of the sunken ship. How many meter is Mr. submarine rise to pass over the sunken ship?
Answers
The value of tangent (90°) is 1, so the rise in distance for the submarine to pass over the sunken ship is 1500 m.
What is value?Value is the worth of something as measured by its usefulness, importance, or desirability. It is something that is sought after and appreciated by individuals and society. Value is subjective and can vary among people and cultures, but can be broadly defined as the quality of something that makes it worth having or doing.
To calculate the distance the submarine must rise to pass over the sunken ship, we must use the tangent function. The tangent of an angle is equal to the opposite side (in this case, the rise in distance for the submarine) divided by the adjacent side (in this case, the 1500 m distance to the sunken ship).
Therefore, the formula to calculate the rise in distance for the submarine is:
Tangent (90°) = Rise / 1500 m
Solving for the rise, we get:
Rise = 1500 m x Tangent (90°)
Using a calculator, the value of tangent (90°) is 1, so the rise in distance for the submarine to pass over the sunken ship is 1500 m.
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Because the tangent (90°) value is 1, the distance travelled by the submarine to cross over the sunken ship is increased by 1500 m.
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle that can be used to illustrate various trigonometric functions. Standard angles in geometry include 0°, 30°, 45°, 60°, and 90°. The trigonometric functions are real functions that link the angle of a right-angled triangle to side length ratios. The sine, cosine, and tangent angles are the main classification of trigonometric functions. The primary functions can be used to determine the three functions cotangent, secant, and cosecant.
According to the question draw the graph we should solve the length of BC
tan A = BC/AC
tan90° = BC/1500
BC = 1500 tan90°
= 516.5 (m)
The value of BC is 516.5 m
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The third term and the sixth term of A geomatric sequence are 2 and 16 respectively. Find the first term and the common ratio
Answers
The first term of the geometric sequence is 1/2 and the common ratio is 2.
What is the geometric sequence?
A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:
a, ar, ar², ar³, ar⁴, ...
where 'a' is the first term, 'r' is the common ratio, and the subscripts represent the position of the term in the sequence.
Let's denote the first term of the geometric sequence by "a" and the common ratio by "r".
We know that the third term of the sequence is 2, which means that:
a * r² = 2 (1)
We also know that the sixth term of the sequence is 16, which means that:
a * r⁵ = 16 (2)
Now we can solve for "a" and "r" by dividing equation (2) by equation (1):
(a * r⁵)/(a * r²) = 16/2
Simplifying, we get:
r³ = 8
Taking the cube root of both sides, we get:
r = 2
Now we can use equation (1) to solve for "a":
a * 2² = 2
Simplifying, we get:
4a = 2
a = 1/2
Therefore, the first term of the geometric sequence is 1/2 and the common ratio is 2.
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Look at the screenshot
Answers
Answer:
37.5 is the answer to the problem
The first two steps in the derivation of the quadratic formula by completing the square are shown below. Which answer choice shows the correct next step?
Answers
Answer:
c on edge
Step-by-step explanation:
trust me bro
Write an expression for double the quantity x
Answers
Answer:
2x
Step-by-step explanation:
The expression for " double the quantity x " is 2x.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
We have to double the quantity x.
Here double means two times of the quantity.
As, we have the quantity x.
Then, two times of the quantity is 2(x) = 2x
Hence, the expression for " double the quantity x " is 2x.
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f(x) is a function.
true or false?
30 points!!!
Answers
False:
A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type. It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.
Answer:
False
Step-by-step explanation:
One input can't have multiple outputs but one output can have multiple inputs
Draw a line tangent to the circle at the point (0, 4). Write an equation for this tangent line. Explain your work.PLEASE HELP
Answers
Answer:
y = 1/4x + 4
Step-by-step explanation:
Find the volume. Help please it’s due tomorrow
Answers
Answer:
2cm
Step-by-step explanation:
vbjufdxcvhjjkknvxzdhjkbcxdf
Divide Using Synthetic Division
Answers
The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
What is polynomial?A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.
The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.
To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:
Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:
-3 | 1 8 9 -18 0
Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.
-3 | 1 8 9 -18 0
-3
Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.
-3 | 1 8 9 -18 0
-3
-3
Step 4: Add the result to the 8, and place the new result in the next row.
-3 | 1 8 9 -18 0
-3
-3
5
Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.
-3 | 1 8 9 -18 0
-3
-3
5
-15
-15
18
Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0
Carlos is a software salesman. Let y represent his total pay (in dollars). Let x represent the number of copies of History is Fun he sells. Suppose that x and y are related by the equation 2500+110x=y. Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Carlos's total pay for each copy of History is Fun he sells?
What is Carlos's total pay if he doesn't sell any copies of History is Fun?
Answers
The total pay change for each issue of Math is Fun sold by Carlos is $110. If he doesn't sell copies of Math is Fun, Carlos's gross wages are $2500 for him.
Given that:
x represents the number of copies of Math is Fun he sells. Suppose that x and y are related by the equation 2500 + 110x = y.
Equation: The equation is the values of two expressions that are equal.
Here,
For equation,
y = 2500 + 110x
The change in Carlos's total pay for each copy of Math is Fun he sells,
Differentiate the equation,
dy/dx = 110
The total pay for each copy of Math is Fun he sells is $110.
Carlos's total pay if he doesn't sell any copies of Math is Fun,
x = 0
y = 2500
Carlos's total pay if he doesn't sell any copies of Math is Fun is $2500.
Thus, the change in Carlos's total pay for each copy of Math is Fun he sells is $110. Carlos's total pay if he doesn't sell any copies of Math is Fun is $2500.
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The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 84 square inches. Solve for the dimensions (length and width) of the poster.
Answers
Step-by-step explanation:
w = width
2w + 2 = Length
Area = W x L = 84 = w (2w+2)
84 = 2w^2 + 2w
0 = 2w^2 + 2w - 84 Use Quadratic Formula
a = 2 b=2 c = -84
to find
W = 6 then L = 14 inches
i really need help, can someone please help me with this math question
Answers
The functions for this problem are defined as follows:
(t + s)(x) = x³ + 5x².(ts)(x) = \(5x^5\)(t - s)(-2) = -28.How to obtain the functions?The functions for this problem are given as follows:
s(x) = 5x².t(x) = x³.The addition and subtraction functions for this problem are given as follows:
(t + s)(x) = x³ + 5x².(t - s)(x) = x³ - 5x².At x = -2, the numeric value of the subtraction function is given as follows:
(t - s)(-2) = -2³ - 5(-2)²
(t - s)(-2) = -28.
The product function for this problem is given as follows:
(ts)(x) = \(5x^5\)
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The temperature in Abu Dhabi is 28°C. The temperature in Moscow is 16°C colder. What is the temperature in Moscow
Plss help
Answers
Answer:
12 degrees celsius
Step-by-step explanation:
28 - 16=12
hope it helps
please help sneakynuggests
Answers
Answer:
You plug in the values of x's and then minus 1 and you get your y
= Answer:
Find the y-intercept of 2x - y = -16
Answers
Find the trigonometric functions for angle e and angle d
Answers
Answer:
∠E = tan
∠D = tan
Step-by-step explanation:
Common sense, only perpendicular and base is present.
Let f(x) = logx
What is the average rate of change of f(x) from 4 to 6?
Round to the nearest hundredth.
(a.) 0.09
(b.) 0.18
(c.) 0.20
(d.) 0.41
Answers
(a.) 0.09
equation:
f(x) = log(x)
rate of change:
\(\sf \rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}\)
\(\sf \rightarrow \sf \dfrac{log(4) -log(6)}{4-6}\)
\(\sf \rightarrow 0.088\)
\(\sf \rightarrow 0.09\)
Answer:
\(A.\: 0.09\)
Step-by-step explanation:
Rate of Change is: \(\frac{y{_1-y{_2} } }{x_2-x_1}\)
\(\frac{log(4)-log (6)}{4-6}\)
\(0.088\)
\(0.09\)
24 pieces of candy in 3 bags how much candy's per bag
Answers
OK WHAT IS THE FRACTION FORM OF THE RATIO 1:3
Answers
Answer:
Part A is 1/4
Part B is 3/4
Step-by-step explanation:
1(A):3(B)
brainliest?
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
How do I graph y−3=1/2(x+3) on this graph? :c
Answers
From point (0, 9/2) and (-9, 0) we get a straight line.
What is Straight line?A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.
Here, given equation:
(y − 3) = 1/2(x + 3)
at x = 0,
y - 3 = 1/2 (0 + 3)
y - 3 = 1/2 X 3
y = 3/2 + 3
y = 9/2
at y = 0,
0 - 3 = 1/2 (x + 3)
-3 = 1/2 (x + 3)
-6 = x + 3
x = -6 - 3
x = -9
Thus, from point (0, 9/2) and (-9, 0) we get a straight line.
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Which equation of a line is parallel to the graph of y = 3x -5 and passes through the point
(1,5)?
Answers
What is 43609 in expanded form
Answers
Answer:
That would be
40,000 + 3,000 + 600 + 9
Answer:
40,000+3,000+600+9
Step-by-step explanation:
40,000= 4 is in the ten thousands place
3,000= 3 is in the thousands place
600= 6 is in the hundreds place
9= is in the ones place
Hope that helps :)
The scale on a map states that 1 centimeters correspond to 40 kilometers on the map two cities are 1.3cm apart
Answers
Step-by-step explanation:
The scale may be 1 cm = 100 km. small-scale maps. One centimeter on a 1:1 000 000 scale map is equal to 1 000 000 centimeters (or 10 000 meters – 10 kilometers) on the ground; four centimeters on the map, therefore, represents 40 kilometers on the ground (10cm = 100km).
In a game, a player rolls two number cubes with sides numbered 1 through 6. All possible rolls are shown in the table. the outcome 1 comma 1 the outcome 1 comma 2 the outcome 1 comma 3 the outcome 1 comma 4 the outcome 1 comma 5 the outcome 1 comma 6 the outcome 2 comma 1 the outcome 2 comma 2 the outcome 2 comma 3 the outcome 2 comma 4 the outcome 2 comma 5 the outcome 2 comma 6 the outcome 3 comma 1 the outcome 3 comma 2 the outcome 3 comma 3 the outcome 3 comma 4 the outcome 3 comma 5 the outcome 3 comma 6 the outcome 4 comma 1 the outcome 4 comma 2 the outcome 4 comma 3 the outcome 4 comma 4 the outcome 4 comma 5 the outcome 4 comma 6 the outcome 5 comma 1 the outcome 5 comma 2 the outcome 5 comma 3 the outcome 5 comma 4 the outcome 5 comma 5 the outcome 5 comma 6 the outcome 6 comma 1 the outcome 6 comma 2 the outcome 6 comma 3 the outcome 6 comma 4 the outcome 6 comma 5 the outcome 6 comma 6 If the sum of the numbers is greater than 8, the player moves the number of spaces equal to the sum. Otherwise, the player does not move. Question What is the probability that a player will move on a turn?
Answers
The probability that the player will move on a turn is given as follows:
5/18.
How to obtain a probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes when two dice are rolled is given as follows:
6² = 36.
The outcomes in which the sum is greater than 8 are given as follows:
(3,6).(4,5).(4,6).(5,4).(5,5).(5,6).(6,3).(6,4).(6,5).(6,6).Meaning that the number of desired outcomes is of 10, hence the probability is of:
p = 10/36
p = 5/18.
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there are 30 cupcakes in a tin. 16 of the cupcakes are iced of which 3 contain walnuts. 5 cupcakes are neither iced nor contain walnuts. work out the probability that the cupcake picked at random contains walnuts
Answers
The probability that the cupcake picked at random contains walnuts is given as follows:
0.4 = 40%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:
30.
The number of cupcakes with walnuts is given as follows:
3 that are also iced.30 - (16 + 5) = 9 that are not iced.Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:
p = (3 + 9)/30
p = 12/30
p = 0.4.
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The diameter of a cylindrical water tank is 8ft, and its height is 6ft. What is the volume of the tank?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
If the diameter of a cylindrical water tank is 8ft, and its height is 6ft, the volume of the water tank is approximately 302 cubic feet.
To find the volume of the cylindrical water tank, we need to use the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Since we are given the diameter of the tank, which is 8ft, we can find the radius by dividing it by 2. Thus, the radius of the tank is 4ft. The height is given as 6ft.
Substituting these values into the formula, we get:
V = π(4ft)²(6ft)
V = π(16ft²)(6ft)
V = 96π ft³
Now we can approximate this volume by using the value of π as 3.14 and rounding the answer to the nearest whole number.
V ≈ 96(3.14) = 302.4
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can anyone explain to me what ratios and rates are with examples? I really need help i have a retake.
Answers
Answer:
Explanation on ratio and rates.
Step-by-step explanation:
So rates are when you compare two things. For example let's say there are 12 boys and 10 girls. The ratio would be 12:10 or 6:5. Rates is also comparing two things but in fraction format. For example if you drive 30 miles in 3 hours the rate would be 30/3. 10 miles per hour is a unit rate since it is 1 hour, 10/1. I hope this helps you, have a good day.
DQ2 Do all linear transformations have a matrix representation? If so, what theorem establishes this? If not, provide a counter-example
Answers
Not all linear transformations have a matrix representation. A counter-example is a linear transformation that changes the dimension of the vector space.
What is Linear transformation?
The function g(x) is a linear transformation if each term of each component of g(x) is a number times one of the variables.
For example, consider the linear transformation T: R^2 -> R^3 defined by:
T(x, y) = (x, y, 0)
This transformation maps each point in the xy-plane to a point in the x,y,z-space with z-coordinate 0. It is a linear transformation, since it preserves addition and scalar multiplication. However, it cannot be represented by a matrix, since it changes the dimension of the vector space.
The theorem that establishes the existence of a matrix representation for every linear transformation is known as the matrix representation theorem. It states that every linear transformation from a finite-dimensional vector space to another finite-dimensional vector space can be represented by a matrix with respect to suitable bases of the vector spaces. However, it does not apply to linear transformations that change the dimension of the vector space.
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