a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2).
b) The joint density function for X and Y is given by: f(x,y) = 1/2 for 0 < x < y < 2.
c) The marginal probability density for Y is given by: fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.
d) The conditional probability density of X, conditional on Y = y, is given by: fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2.
This only exists for 0 < y < 2.
a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2). This is because the lengths of the two pieces of the ruler must be non-negative and must add up to 2.
b) The joint density function for X and Y is given by:
f(x,y) = 1/2 for 0 < x < y < 2.
c) The marginal probability density for Y is given by:
fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.
d) The conditional probability density of X, conditional on Y = y, is given by:
fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2. This only exists for 0 < y < 2.
Note: The factor of 1/2 in the joint density function accounts for the uniform distribution of the two breaks on the ruler, while the factor of 2 in the conditional density function accounts for the change of variables from the joint density to the conditional density.
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Question in Screenshot
The functions for this problem are given as follows:
a) (f + g)(x) = x² - 16x + 43.
b) (f - g)(x) = x² - 8x + 29.
c) (fg)(x) = -4x³ + 71x² - 284x + 301.
d) (f/g)(x) = (x - 6)²/(7 - 4x), x different of 7/4.
How to obtain the functions?The functions in this problem are defined as follows:
f(x) = (x - 6)² = x² - 12x + 36.g(x) = 7 - 4x.Then the addition function, combining the like terms, is given as follows:
(f + g)(x) = x² - 12x + 36 + 7 - 4x = x² - 16x + 43.
The subtraction function, combining the like terms, is given as follows:
(f - g)(x) = x² - 12x + 36 - (7 - 4x) = x² - 12x + 36 - 7 + 4x = x² - 8x + 29.
The product is given as follows:
fg(x) = (x² - 16x + 43)(7 - 4x) = -4x³ + 71x² - 284x + 301.
(multiplying all the terms applying the associative property and then combining the like terms).
The quotient is given as follows:
(f/g)(x) = f(x)/g(x) = (x - 6)²/(7 - 4x), x different of 7/4.
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when 2610 11.7 0.22 are added, the answer to the correct number of decimal places is . group of answer choices 2621.9 2600 2620 2621.92 2621
Answer: 2621.92
Step-by-step explanation:
The addition of the numbers 2610 and 11.7 and 0.22 is 2621.92.
Hence the correct option is given by (D).
Addition is a mathematical operation to sum up between two or more than two mathematical quantities or numbers specially.
Here given the numbers are 2610 and 11.7 and 0.22.
So the addition of the numbers 11.7 and 0.22 is given by,
= 11.7 + 0.22
= 11.92
So the sum of 2610, 11.7 and 0.22 is given by,
= 2610 + 11.7 + 0.22
= 2610 + 11.92
= 2621.92
Hence the correct option is given by (D).
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data from what length of time are represented on a climograph? view available hint(s)for part b data from what length of time are represented on a climograph? 30 years 300 years it varies from one climograph to another; there is no standard length of time. 30 days 30 months submit
Option b is the correct answer. It varies from one climograph to another; there is no standard length of time.
A climograph is a graphical representation of climate data that shows the average temperature and precipitation patterns over a certain period of time. The length of time represented on a climograph can vary and there is no set standard. It could be a few months, a year, several years, or even decades. It depends on the specific data and purpose of the climograph. Some climographs may show data from the last 30 years, while others might show data from the last 300 years. The important thing to remember is that the length of time represented on a climograph will vary and there is no set rule for how long it should be.
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The complete question is:
data from what length of time are represented on a climograph? view available hint(s)for part b data from what length of time are represented on a climograph?
a. 30 years 300 years
b. it varies from one climograph to another
c. there is no standard length of time.
d. 30 days 30 months submit
Select the correct answer from each drop-down menu. The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units. The general form of the equation of a circle that has the same radius as the above circle is .
The equation of this circle in standard form is (x + 21)² + (y + 19)² = 849.
The center of the circle is at the point (-21, -19), and its radius is √849 units.
The general form of the equation of a circle that has the same radius as the above circle is x² + y² - 50x - 30y + 1 = 0.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.In order to transform the general form of the equation of a circle to a standard form, you can either make use of completing the square method or convert the equation x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h² + k² - r²) = 0.
By using the following expression x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0, we would determine the center (h, k) and radius of this circle as follows;
-2h = 42
h = 42/2
h = -21
-2k = 38
k = 38
k = -19
For the radius (r), we have:
-47 = h² + k² - r²
-47 = (-21)² + (-19)² - r²
r² = 849
Radius, r = √849
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Write \frac{\sqrt[4]{v^{9}}}{\sqrt[3]{v^{4}}}
3
v
4
4
v
9
as a single radical using the smallest possible root.
Answer:
[tex]\mbox {\large \boxed{\sqrt[12]{v^{11} }}}\\[/tex]
Step-by-step explanation:
[tex]\textrm{We are asked to simplify\:$\dfrac{\sqrt[4]{v^9}}{\sqrt[3]{v^4}}$}[/tex]
Using the fact that [tex]\sqrt[n]{x} = n^{{1/n}}[/tex]
[tex]\mbox{\large {\sqrt[4]{v^9}} =\left(v^9)^{1/4} = v^{9/4}}\\\\[/tex]
[tex]\mbox{\large {\sqrt[3]{v^4}}} = (v^4)^{1/3} = v^{4/3}}[/tex]
[tex]\mbox{\large $\dfrac{\sqrt[4]{v^9}}{\sqrt[3]{v^4}}$}[/tex] [tex]= \mbox{\large \dfrac{v^{9/4}}{v^{4/3}}}[/tex]
Using the fact that [tex]\dfrac{x^a}{x^b} = x^{a-b}[/tex]
[tex]\mbox{\large \dfrac{v^{9/4}}{v^{4/3}} = v^{9/4 - 4/3}}[/tex]
[tex]\dfrac{9}{4} - \dfrac{4}{3} = \dfrac{9 \cdot 3 - 4 \cdot 4}{12} = \dfrac{27-16}{12} = \dfrac{11}{12}[/tex]
[tex]\mbox{\large \dfrac{v^{9/4}}{v^{4/3}} = v^{9/4 - 4/3}= v^{11/12} } = \sqrt[12]{v^{11} }}[/tex]
Answer
[tex]\mbox {\large \boxed{\sqrt[12]{v^{11} }}}\\[/tex]
Please help me, it would be helpfull
Answer:
A:[tex]y = 4x + 3[/tex]
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write a multiplication equation that represents this model
The multiplication equation represented by the diagram is:
3*2 = 6
Which is the multiplication represented by the model?On the model we can see a diagram, in that diagram there are:
2 red rectangles.
3 purple rectangles
6 blue rectangles.
We can assume that we are taking the product between the red ones and the purple ones, then we can write:
3*2 = 6
That is a true equation, so that is the multiplication equation represented by the model.
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Solve for the 2 problems below, show your work and submit the answers.
In the isosceles triangle, the value of x for the first figure is 15
for the second figure,
x = 5the missing angle is 110How to find the value of xThe value of x is solved using the knowledge of isosceles triangle
An isosceles triangle has the base angles equal hence
2x - 5 = 35
2x = 35 - 5
2x = 30
x = 15
Second figure
7x = 35
x = 5
let the angle at the peak be p
35 + 35 + p = 180 (sum of angles in a triangle)
70 + p = 180
p = 180 - 70
p = 110
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based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). which of the following statements is true?
90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch. Hence, the correct statement is option (d).
A confidence interval is a range of values that are expected to contain the true population parameter with a certain degree of confidence, usually expressed as a percentage. Here, a 90% confidence interval means that if we were to repeatedly take random samples of 50 students and compute a 90% confidence interval for each sample, we would expect that 90% of these intervals would contain the true mean amount of money that all students spend on lunch at this high school.
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The complete question is -
Based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). Which of the following statements is true?
(a) 90% of the time, the mean amount of money that all students spend on lunch at this high school will be between $3.45 and $4.15.
(b) 90% of all students spend between $3.45 and $4.15 on lunch at this high school.
(c) 90% of all random samples of 50 students obtained at this high school would result in a sample mean amount of money students spend on lunch between $3.45 and $4.15.
(d) 90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.
ank the following functions in increasing order of (asymptotic) magnitude dragged and dropped options will be automatically saved. for keyboard navigation...show more press space or enter to grab [math] log {3} n [/math] press space or enter to grab [math] n log (3 n) [/math] press space or enter to grab [math] 3 n [/math] press space or enter to grab [math] n^{3} [/math] press space or enter to grab [math] (3!)^{3} [/math] press space or enter to grab [math] 3^{n} [/math]
The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n.
The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n. This means that the function with the smallest asymptotic magnitude is (3!)3, while the function with the largest asymptotic magnitude is 3n.
To confirm this, let's calculate the growth rate of each function. The growth rate of (3!)3 is 3!3 ≈ 216, which is less than the growth rate of 3n (3n) = 3n, which is greater than the growth rate of n log(3n) (n log3n) = n log3n, which is greater than the growth rate of n3 (n3) = n3, which is greater than the growth rate of 3n (3n) = 3n, which is greater than the growth rate of 3n (3n) = 3n.
Therefore, we can conclude that the order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n.
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Answer:The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n
Step-by-step explanation:
let j, s, and k denote the propositions that jasmine, samir, and kanti attend, respectively. express the given conditions using logical connectives.
Jasmine (j) and Samir (s) will attend the event, while Kanti (k) will not. This can be expressed using the logical connective (∧) and its negation (¬).
j ∧ s ∧ ¬k
j - Jasmine attends
s - Samir attends
¬k - Kanti does not attend
∧ - Logical And operator
j ∧ s ∧ ¬k -
Jasmine (j) and Samir (s) will attend the event, while Kanti (k) will not. This can be expressed using the logical connective (∧) and its negation (¬). The resulting statement is j ∧ s ∧ ¬k. This statement means that Jasmine and Samir will attend the event, but Kanti will not. This statement can be read as "Jasmine and Samir attend and Kanti does not attend".The resulting statement is j ∧ s ∧ ¬k. This statement means that Jasmine and Samir will attend the event, but Kanti will not. This statement can be read as "Jasmine and Samir attend and Kanti does not attend".
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s) determine which of the following subsets of p2 are subspaces of p2. you should use the subspace test from the lectures to show that a given subset is a subspace, or, if it is not a subspace, exhibit one of the axioms of a vector space that fails to be satisfi
To determine which of the following subsets of P2 are subspaces of P2, you should use the subspace test from the lectures.
For each subset, you need to check if it is closed under vector addition, closed under scalar multiplication, and contains the zero vector. If the subset satisfies all three conditions, then it is a subspace.
For example, the subset S = {2x2+3x+1, x2+3x+2} is a subspace of P2 because it is closed under vector addition (2x2+3x+1 + x2+3x+2 = 3x2+6x+3) and closed under scalar multiplication (2*(2x2+3x+1) = 4x2+6x+2).
Additionally, it contains the zero vector (0x2+0x+0). Therefore, it is a subspace of P2.
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8) Mrs. Smith drove 20 miles at a speed of 55 mph. She then drove 40 miles at a spe)ed of 60 mph. How
far did Mrs. Smith drive?
The total distance travelled by Mrs. Smith was 60 miles
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Speed is the ratio of the total distance travelled to total time taken. It is given by:
Speed = distance / time
Mrs. Smith drove 20 miles at a speed of 55 mph. She then drove 40 miles at a speed of 60 mph. Hence:
Total distance = 20 miles + 40 miles = 60 miles
The total distance travelled was 60 miles
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[tex]}\frac{4}{x-2} =14[/tex]
Try This question out and I’ll give you brainliest
The horizontal distance rounded to the nearest hundredth will ve 139.5 feet. Then the correct option is A.
What are the roots of the equation?Let the equation be ax² + bx + c = 0. Then the roots of the equation will be given as,
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
Paulo hit a baseball. The path of the ball was h = - 0.01d² + 1.37d + 3.5.
Then the horizontal distance is given as,
h = 0
- 0.01d² + 1.37d + 3.5 = 0
0.01d² - 1.37d - 3.5 = 0
Solve the equation by formula, then we have
d = [-(-1.37) ± √{(-1.37)² - 4 × 0.01 × (-3.5)}] / (2 × 0.01)
d = (1.37 ± 1.42) / 0.02
For the plus sign, then we have
d = 2.79 / 0.02
d = 139.5 feet
The horizontal distance rounded to the nearest hundredth will ve 139.5 feet. Then the correct option is A.
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Graph the function.
f(x)=√x+4
State four points on the graph of the function: the leftmost point and three additional points.
Answer: The function f(x) = √x + 4 describes a radical function that maps a real number x to its square root, shifted to the right by 4 units. The graph of this function is an upward-opening parabola that intersects the x-axis at x = -4.
Here are four points on the graph of the function:
The leftmost point: (0, 4)
An additional point to the right of the leftmost point: (1, 4.5)
Another additional point: (2, 5)
The third additional point: (9, 5.5)
Note: The values of x used in these examples are arbitrary and can be any real numbers. These points are only intended to give you an idea of what the graph of the function might look like
Step-by-step explanation:
7. Higher Order Thinking A bagel is cut
into same-size pieces. Some
friends share the bagel.
Each friend gets one piece.
How many friends share
the bagel?
friends
The number of friends sharing the bagel will be n.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A bagel is cut into same-size pieces. Some friends share the bagel. Each friend gets one piece.
Let the same size pieces of the bagel be 1/n. Then the number of friends who share the bagel is given as,
⇒ 1 / (1/n)
⇒ 1 x n / 1
⇒ n
The number of friends sharing the bagel will be n.
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Change this radical to an algebraic expression with fractional exponents.
The required algebraic form of the given radical form ∛a is [tex]a^{1/3}[/tex].
What is an algebraic expression?The algebraic expression consists of constant and variable. eg x, y, z, etc.
Here,
Given expression,
= ∛a
since we know that, [tex]a^{1/n} = \sqrt[n]{a}[/tex]
So ∛a = [tex]a^{1/3}[/tex].
Thus, the required algebraic form of the given radical form ∛a is [tex]a^{1/3}[/tex].
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An artist invests in a mutual fund account paying 5% and $5000 more than four times as much in a mutual fund account paying 4%. Her total annual interest income from the investments is $1145. How much does she invest at each rate?
The artist invests $4500 in the 5% account and $23000 in the 4% account.
Let's call the amount invested in the 5% account x. Then, the amount invested in the 4% account is 4x + 5000.
The total annual interest income from the investments is 1145, so we can write an equation:
0.05x + 0.04(4x + 5000) = 1145
Expanding the second term:
0.05x + 0.04(4x) + 0.04(5000) = 1145
0.05x + 0.16x + 200 = 1145
0.21x + 200 = 1145
0.21x = 945
x = 4500
So the artist invests $4500 in the 5% account and $18000 + 5000 = $23000 in the 4% account.
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Suppose X,Y and Z are three different random variables. Let X obey a Bernoulli Distribution. The probability distribution function is. c is a constant here.
Let Y obey the Standard Normal (Gaussian) Distribution, which can be written as Y N(0,1). X and Y are independent. Meanwhile, let Z = XY.
Calculate the covariance of Y and Z (Cov(Y, Z)) and determine whether values of c would affect the correlation.
The value of c does not affect the covariance of Y and Z.
How did we arrive at this assertion?The covariance of Y and Z can be calculated as Cov(Y, Z) = E[YZ] - E[Y]E[Z]. Since X is Bernoulli with parameter p and E[X] = p, we have E[Z] = pE[Y]. Hence,
Cov(Y, Z) = E[YZ] - E[Y]E[Z]
= E[YXY] - pE[Y]^2
= pE[Y^2 X] - pE[Y]^2
= p(E[Y^2]E[X] + Var[Y]p) - pE[Y]^2
= p(1 * p + 1 * p^2) - p^2
= p - p^2
It can be seen that the value of c does not affect the covariance of Y and Z.
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Simplify: (4w³ - 4) + (2w³ + 6w + 9)
Bring the like terms together by rearranging the question4w³+2w³+6w+9-4Answer 6w³+6w+5
fill in the blank. a simple linear regression equation relates r and w as follows: the explanatory variable is___, and the dependent variable is___. the slope parameter is___, and the intercept parameter is___. when w is zero, r equals___. for each one unit increase in w, the change in r is___units.
w, r, the coefficient of w, the constant term in the equation, the intercept parameter, equal to the slope parameter in units are ans of fill in the blank respectively.
A simple linear regression equation is used to model the relationship between two variables, where one variable is the independent or explanatory variable and the other is the dependent or response variable. The equation has the form:
y = β0 + β1x,
where y is the dependent variable, x is the explanatory variable, β0 is the intercept parameter, and β1 is the slope parameter. The intercept parameter represents the value of y when x is zero, and the slope parameter represents the change in y for each one-unit change in x. In this problem, the explanatory variable is w, and the dependent variable is r. The slope and intercept parameters need to be estimated from the data to obtain the regression equation. The equation can be used to make predictions about the response variable given a certain value of the explanatory variable.
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A water park keeps track of the number of times each visitor goes down water slides during their visit . The data shows the number of times 12 visitors went down a water slide.
4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11, 1
Create a histogram of this data.
To create a histogram, hover over each age range on the x-axis. Then click and drag up to plot the data.
Histogram of given data is attached below.
What is histogram?A histogram is a graphical representation of data points organized into user-specified ranges.
Given,
Data shows the number of times, 12 visitors went down a water slide.
4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11, 1
Histogram can be drawn as below,
Hence, following is the histogram of given data.
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What is the product of 2.8\times 10^32.8×10
3
and 9.7 \times 10^39.7×10
3
expressed in scientific notation?
The product of two numbers 2.8 × 10³ and 9.7 × 10³ can be represented in scientific notation as, 2.716 x 10⁷
What is the scientific notation of a number?The standard form for a number is a method by which we write number in a format like b×10ˣ. The value of b should be in between 0 to 10.
Given that,
The numbers,
2.8 × 10³
And 9.7 × 10³
the product in scientific notation = ?
the product in scientific notation = 2.8 × 10³ x 9.7 × 10³
It is known that,
if same numbers are in multiplication form,
their powers can be added
the product in scientific notation = 27.16 x 10³⁺³
= 27.16 x 10⁶
It can be further written as,
multiplied and divide by 10
the product in scientific notation = 27.16 x 10⁶x10/10
= 2.716 x 10⁷
Hence, the product is 2.716 x 10⁷
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Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible
quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest
he earns during t = 0 to t = 1. Find the exact value of R.
Let X be the amount Mr Saver invests at t = 0.
The interest he earns during t = 0 to t = 1 can be expressed as:
Interest = X * R * (1/4)
The interest he earns during t = 0.5 to t = 1.5 can be expressed as:
Interest = X * R * (3/4)
Since the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1, we can set up the following equation:
X * R * (3/4) = 1.0816 * (X * R * (1/4))
Solving for R, we get:
R = 4.3264 Therefore, the exact value of R
You have a 10% sugar salutation and a 30% sugar salutation and you need a 25% sugar salutation how many cups of each salution do you need to get 8 cup of 25% sugar salution let x represent numbernof cups of 10% and y represent numberbof cups 30% sugar salution what eqution represent the total valume
2 cups of 10% sugar solution and 6 cups of 30% sugar solution.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements
Let,
x = number of cups of the 10% solution
y = number of cups of the 30% solution
As this is the whole amount we need, the two mixtures sum up to 8 cups. Consequently, the first equation is just x + y = 8
Solve for y to get y = 8-x. We'll use this equation later.
The second equation is a bit more tricky.
0.10x = amount of pure sugar from just the 10% batch
0.30y = amount of pure sugar from just the 30% batch
0.10x+0.30y = total amount of pure sugar from both batches
25% of 8 = 0.25×8 = 2 = total amount of pure sugar required
0.10x+0.30y = 2 is the second equation
Apply substitution to solve for x and y
0.10x+0.30y = 2 ..... start with the second equation
0.10x+0.30(8-x) = 2 ....... plugin y = 8 - x
0.10x + 2.4 - 0.30x = 2 ..... distribute
- 0.20x + 2.4 = 2 - 0.20x = 2-2.4 ....... subtract 2.4 from both sides
-0.20x = - 0.4
x = -0.4/(-0.20)
x = 2
Now that we know the value of x, we can find y.
y = 8 - x
y = 8 - 2 ... plug in x = 2
y = 6
So we need 2 cups of the 10% solution and 6 cups of the 30% solution.
As a check,
x + y = 2 + 6 = 8 works out
0.10x + 0.30y = 0.102 + 0.306 = 0.2 + 1.8 = 2 works out as well
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Jim has gotten scores of 78 and 73 on his first two tests. What score must he get on his third test to
keep an average of 94 or greater? Write your answer as an interval.
The range of score Jim must get to have an average score of 94 or more is x≥ 131
What is inequality?inequality, In mathematics is a statement of an order relationship with greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Average is the sum of items divided by the number of items.
Represent the theirs score by x
(78+73+x)/3 ≥ 94
151+x ≥ 94×3
151 + x ≥ 282
x ≥ 282-151
x≥ 131
therefore for Jim to get an average greater than 94, his third score must be greater than 131
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first, use trigonometric identities to write 8cos4(4x) as an expresion involving only sines and cosines to the first power.
8cos(4x) can be written as an expression involving only sines and cosines to the first power as 8 - 16sin^2(2x)
The expression 8cos(4x) can be written in terms of sines and cosines to the first power using the double angle identity:
cos(2θ) = 1 - 2sin^2(θ)
First, we can rewrite 4x as 2(2x), and then apply the double angle identity:
cos(4x) = cos(2(2x)) = 1 - 2sin^2(2x)
Next, we can use the identity:
cos(θ) = cos(-θ)
to rewrite cos(2x) as cos(-2x):
cos(4x) = 1 - 2sin^2(2x) = 1 - 2sin^2(-2x)
Finally, we can multiply both sides by 8:
8cos(4x) = 8(1 - 2sin^2(-2x)) = 8 - 16sin^2(-2x)
And since sin(-θ) = -sin(θ), we can write this as:
8cos(4x) = 8 - 16sin^2(2x)
So, 8cos(4x) can be written as an expression involving only sines and cosines to the first power as:
8 - 16sin^2(2x)
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Graph the points A (1, 6) and B (9, 6). Find the
midpoint of AB. Find the distance of AB
Answer:
Step-by-step explanation:
Midpoint= x1-2/y1-y2
8/0
Midpoint = 0,0
_ / 6 < 9/6 what is the missing number?
The complete expression is 8/6 < 9/6
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
_ / 6 < 9/6
Express properly
So, we have the following representation
_ / 6 < 9/6
Represent the blank with x
x / 6 < 9/6
Multiply both sides of the expression by 6
So, we have the following representation
x < 9
This means that x is any value less than 9
An instance is 8
Hence, the solution to the expression is 8/6 < 9/6
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