I need help with this image attached

Answer:

The given relation is not a function if there exist multiple values of y for a single value of x.

We cannot determine whether the relation is a function or not by looking at the first three pairs.

For the fourth pair, we need to ensure that there is only one value of y for any given value of x. Therefore, x cannot be equal to 12, -11, or 33 because those values have already been assigned a specific y value. If x is equal to any of those values, it would create a situation where there are multiple y values for the same x value, violating the definition of a function.

Therefore, x cannot be equal to 12, -11, or 33.

Answer:

Your answers are:

A, B and C

Step-by-step explanation:

So 12 over 3 is equal to 4 which is a Whole number. meaning Not a fraction, an Integer is a whole number (not a fractional number) that can be positive, negative, or zero. Rational numbers would include this example as well

Hope this helped have a wonderful day/night/afternoon

Answer: because it has the same numbers

Step-by-step explanation:

To prove that the series ∑_(n=2)^(∞) (x ln x)^(n-1) is continuous on the interval (1, ∞), we need to show that the series converges for all x in (1, ∞), and the limit of the series as x approaches any value in (1, ∞) exists.

Let's analyze the convergence of the series. We have:

∑_(n=2)^(∞) (x ln x)^(n-1)

This is a geometric series with the common ratio r = x ln x. In order for the series to converge, the absolute value of the common ratio should be less than 1:

|r| = |x ln x| < 1

Now, let's consider the interval (1, ∞). For any x in this interval, we have:

1 < x

Taking the natural logarithm of both sides, we get:

ln 1 < ln x

0 < ln x

Multiplying by x, we have:

0 < x ln x

Therefore, for all x in (1, ∞), we have 0 < x ln x < 1, which implies that |x ln x| < 1. Hence, the common ratio of the series is less than 1, and the series ∑_(n=2)^(∞) (x ln x)^(n-1) converges for all x in (1, ∞).

Now, let's analyze the uniform convergence of the series on (1, ∞). For uniform convergence, we need to show that the series converges uniformly on the interval (1, ∞), meaning that the series converges to the same limit for all x in (1, ∞).

To determine if the series converges uniformly, we can use the Weierstrass M-test. We need to find a sequence of positive constants M_n such that |(x ln x)^(n-1)| ≤ M_n for all x in (1, ∞) and n ≥ 2, and the series ∑ M_n converges.

Consider the function f(x) = x ln x for x in (1, ∞). Taking the derivative, we have:

f'(x) = 1 + ln x

Since ln x is positive for x in (1, ∞), f'(x) is always positive. This implies that f(x) is an increasing function on (1, ∞).

Let's choose M_n = f(2)^(n-1), where f(2) = 2 ln 2. Now, for all x in (1, ∞) and n ≥ 2, we have:

|(x ln x)^(n-1)| = |f(x)^(n-1)| ≤ |f(2)^(n-1)| = M_n

The series ∑ M_n = ∑ (2 ln 2)^(n-1) is a geometric series with the common ratio r = 2 ln 2, which converges since |r| = |2 ln 2| < 1.

By the Weierstrass M-test, since |(x ln x)^(n-1)| ≤ M_n and ∑ M_n converges, the series ∑_(n=2)^(∞) (x ln x)^(n-1) converges uniformly on the interval (1, ∞).

To summarize:

The series ∑_(n=2)^(∞) (x ln x)^(n-1) is continuous on the interval (1, ∞) because it converges for all x in (1, ∞).

The series ∑_(n=2)^(∞) (x ln x)^(n-1) is uniformly convergent on the interval (1, ∞) because it converges uniformly, as shown by the Weierstrass M-test.

Therefore, the series ∑_(n=2)^(∞) (x ln x)^(n-1) is both continuous and uniformly convergent on the interval (1, ∞).

Learn more about convergent here:

brainly.com/question/31701016

#SPJ11

Answer:

∠a and ∠d; ∠b and ∠c

Step-by-step explanation:

The two triangles as similar triangles and the scale factor is 2 : 1

The sides measuring 6 and 3 are corresponding sides

The sides measeuring 8 and 4 are ocrreposnding sides

⇒ ∠a and ∠d are corresponding angles

The sides measuring 8 and 4 are corresponding sides

The sides measeuring 4 and 2 are ocrreposnding sides

⇒ ∠b  and ∠c are corresponding angles

The area under the curve f(x)=3/x from x=1 to x=9 is 3 ln 9 square units.

The definite integral is a mathematical tool used to evaluate the area under a curve. Definite integrals are used to calculate the area between two points on a graph, which is a measure of the total amount of change between the two points.

A definite integral has a lower limit (a) and an upper limit (b). The formula for the definite integral of a function f(x) over the interval [a, b] is given as:∫[a,b] f(x) dx= [F(b) - F(a)]

Where F(x) is the antiderivative of the function f(x).

We can use this formula to find the area under the curve of the given function f(x)=3/x between x=1 and x=9. ∫[1,9] 3/x dx = [3 ln|x|] [1,9] = 3 [ln|9| - ln|1|] = 3 ln|9|

The area under the curve between x=1 and x=9 is approximately 8.69 square units, and it is equal to 3 ln(9).

Hence, the area under the curve f(x)=3/x from x=1 to x=9 is 3 ln 9 square units.

Learn more about Definite integral from the given link!

https://brainly.com/question/27746495

#SPJ11

Answer:

D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)

Step-by-step explanation:

hope this helps

Answer:  D has the largest perimeter

Step-by-step explanation:

The top numbers of fractions describe the vertex and  the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.

A.

P = 2(11) + 2(3)

P = 22+6

P=28

B.

P = 2(4) + 2(9)

p = 8 +18

P = 26

C.

P = 2(5) + 2(9)

P = 10 +18

P = 28

D.

P =  2(8) + 2(7)

P = 16 +14

P = 30

Answer:

Calculus Applied Calculus In Exercises 1–18, calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement. [ HINT: See Example 1.] Interval: [ 0.1 , 0.2 ] t ( hours ) 0 1.0 0.2 D ( t ) ( miles ) 0 3 6

Step-by-step explanation:

Answer:

16ft

Step-by-step explanation:

use pythagreom thereom

12^2+b^2=20^2 solve

144+b^2=400

b^2= 256 square it

b= 16

Answer:

b=16

Step-by-step explanation:

The solution to the given system of equations is x = 3 and y = 1.

To solve the system of equations by elimination, we'll eliminate one variable by multiplying one or both of the equations by appropriate constants so that the coefficients of one variable will cancel each other out when we add or subtract the equations.

Let's solve the given system:

1. Multiply the first equation by 3 and the second equation by 2 to make the coefficients of 'x' equal:

Equation 1: 2x + 4y = 10

Equation 2: 3x + 5y = 14

Multiply Equation 1 by 3: 3(2x + 4y) = 3(10) becomes 6x + 12y = 30

Multiply Equation 2 by 2: 2(3x + 5y) = 2(14) becomes 6x + 10y = 28

2. Now, subtract the equation (6x + 10y = 28) from (6x + 12y = 30) to eliminate 'x':

(6x + 12y) - (6x + 10y) = 30 - 28

6x - 6x + 12y - 10y = 2

2y = 2

y = 1

3. Substitute the value of 'y' (which we found to be 1) back into either of the original equations. Let's use the first equation:

2x + 4y = 10

2x + 4(1) = 10

2x + 4 = 10

2x = 10 - 4

2x = 6

x = 6/2

x = 3

Therefore, the solution to the given system of equations is x = 3 and y =1.

Learn more about Variables here:

https://brainly.com/question/15078630

#SPJ11

The lateral surface area of the triangular prism shown below is C.170 cm².

The concept that will be used here is triangular prism breakdown and calculation.

We can break down the triangular prism  so as to make it simpler as :

We have (2 triangles) as well as ( 2 side rectangles) and (1 back rectangle)

We can calculate the area of triangle  as ( ¹/₂ * base * height)

= (¹/₂ * 5 * 4)

=10cm

We can calculate the area of rectangle as ( length * width)

=(10 * 5)

=50

Then the Area of trapezoid = 2(10) + 3(50)

=20 + 150

= 170 cm²

Therefore, option C is correct.

Learn more about triangular prism at:

https://brainly.com/question/30501511

#SPJ1

Answer: A

Step-by-step explanation:

The direction of the cross product is perpendicular to both of the vectors being multiplied. So, the answer to the question of what is the direction of the cross product could be any of the six options provided (x direction, -x direction, y direction, -y direction, z direction, -z direction), depending on the orientation of the vectors being multiplied.

The direction of the cross product is determined by the right-hand rule. When you have two vectors, A and B, the cross product (A x B) will be perpendicular to both A and B in a third direction. To find this direction, point your fingers in the direction of vector A, and then curl them towards vector B. Your thumb will point in the direction of the cross product. The options you provided (x, -x, y, -y, z, -z) depend on the specific vectors you are working with. In general, the cross product direction will be in the z direction or -z direction for vectors lying in the xy plane.

To learn more about cross product click here: brainly.com/question/29097076

#SPJ11

Answer:

Use Pythagorean theorem:

#7

#8

A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

B. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.

C.  The sampling distribution of p is approximately normal.

D. We find that the probability is 0.0912 or about 9.12%.

E. We get:z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29

a. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

b. The sample proportion, p, is a random variable because it varies from sample to sample. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.

c. The sampling distribution of p is approximately normal if the sample size is sufficiently large and if np ≥ 10 and n(1-p) ≥ 10, where n is the sample size and p is the population proportion. In this case, we have:

Sample size (n) = 100

Population proportion (p) = 0.82 Thus, np = 82 and n(1-p) = 18, both of which are greater than 10. Therefore, the sampling distribution of p is approximately normal.

d. To calculate the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.85, we need to find the z-score and then look up the corresponding probability from the standard normal distribution table. The formula for the z-score is:

z = (p - P) / sqrt[P(1-P)/n]

where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:

z = (0.85 - 0.82) / sqrt[0.82(1-0.82)/100] = 1.33

Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0912 or about 9.12%.

e. Yes, it would be unusual for a survey of 100 Americans to reveal that 75 or fewer are satisfied with the way things are going in their life. To check if it is unusual or not, we need to calculate the z-score and find its corresponding probability from the standard normal distribution table. The formula for the z-score is:

z = (p - P) / sqrt[P(1-P)/n]

where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:

z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29

Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0106 or about 1.06%. Since this probability is less than 5%, it would be considered unusual to observe 75 or fewer Americans being satisfied with the way things are going in their life.

Learn more about   distribution  from

https://brainly.com/question/23286309

#SPJ11

We are 80% confident that the true population mean falls within this interval based on the given sample data. To construct an 80% confidence interval for the population mean (μ), we can use the formula:  

Confidence Interval = x ± Z * (σ/√n) Where:
x is the sample mean (46.17)
Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28)
σ is the population standard deviation (6.5)
n is the sample size (92)

Substituting the given values into the formula, we get:
Confidence Interval = 46.17 ± 1.28 * (6.5/√92)
Calculating the expression inside the parentheses first:
6.5/√92 ≈ 0.679. Then, plugging it back into the formula:
Confidence Interval = 46.17 ± 1.28 * 0.679

Calculating the product of 1.28 and 0.679: 1.28 * 0.679 ≈ 0.868
Finally, the confidence interval is: Confidence Interval = 46.17 ± 0.868
Rounding to two decimal places: Confidence Interval ≈ (45.30, 47.04)

Therefore, the 80% confidence interval for the population mean (μ) is approximately (45.30, 47.04).  

Learn more about mean here: brainly.com/question/31101410

#SPJ11

all you have to do is substitute all the Xs to and get a final y output.

for example:

if we take the number x is -1 all you do is:

y=-4(-1)+2

y=4+2

y=6

Answer:

80 degrees

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360 degrees. Adding up the known measures gives you 95 + 123 + 62 = 280. Then you can subtract that from 360. 360 - 280 = 80. So x has to be 80 degrees.

Answer:

Hope this helps

Step-by-step explanation:

Mathmagic Land had taught me more about math that I never knew before. I learned that everything can be involved with math. It all starts at the Pythagoreans which were the Greek. An example of how math is used today, is by playing billiards.

In billiards, you have to have a good technique of how your going to hit the ball, (good angles,) and you have to have a precise calculation of the angle your going to hit it at.I also learned when you cut shapes like a sphere, it just makes more and more shapes.

This is what I learned watching the Mathmagic Land Video.

Yes,  Donald Duck in Mathmagic Land taught me alot of things I did not know before.

F(5) means replace x with 5 then solve:

3x-4 = 3(5)-4 = 15-4 = 11

F(5) = 11

Answer:

A. B.

Step-by-step explanation:

: D. Chemical energy is transformed to light and thermal energy

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

To learn more about scaling matrix click here : brainly.com/question/16662440

#SPJ11

Answer:

We use percentages to make calculations easier. It is much simpler to work with parts of 100 than thirds, twelfths and so on, especially because quite a lot of fractions do not have an exact (non-recurring) decimal equivalent.

Step-by-step explanation:

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

To learn more about curve parameterization visit:

brainly.com/question/12982907

#SPJ11

1.

Collinear : Points on the same line

Non-collinear: Points not on same line

Line: All points between any two points extending in opposite directions.

Space: Where things exist

Coplaner: Points and lines on the same plane

Geometry: Earth measure

Plane: A flat surface

Non-coplaner: Points and lines not on the same plane

2. EF

3. EGD

4. AD

5. G