What is the common difference for the sequence shown? coordinate plane showing the points 1 comma 4, 4 comma 3, and 7 comma 2 a −3 b −one third c one third d 3

The correct condition for  Trignometric expressions having exactly two solutions is option (B) b > a. This means that b must be greater than a.

To have exactly two solutions for the equation a sinθ = b in the interval 0 ≤ θ < 2π, the condition that needs to be satisfied is (B) b > a.

Let's analyze the options:

(A) a = b: If a = b, then the equation becomes a sinθ = a. This equation simplifies to sinθ = 1. However, in the interval 0 ≤ θ < 2π, the equation sinθ = 1 has only one solution, which is θ = π/2. Therefore, option (A) does not guarantee two solutions.

(C) a = -b: If a = -b, then the equation becomes a sinθ = -a. This equation simplifies to sinθ = -1. However, in the interval 0 ≤ θ < 2π, the equation sinθ = -1 has only one solution, which is θ = 3π/2. Therefore, option (C) does not guarantee two solutions.

(D) a > b > -a: This option does not provide a definite condition regarding the number of solutions. It only specifies a relationship between a and b but does not guarantee two solutions.

Learn more about Trignometry here:

brainly.com/question/22986150

#SPJ11

Answer: 6

Step-by-step explanation:

The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

Learn more about the difference quotient:

https://brainly.com/question/24922801

#SPJ1

The driver's percent value-added time is approximately 18.57%.

The percent value-added time, we need to consider the total time spent in non-value-added activities (waiting in line, eyes tested, and photograph taken) compared to the total time spent, including value-added activities.

Total time spent = Time in line + Time for eyes test + Time for photograph = 57 minutes + 9 minutes + 4 minutes = 70 minutes

Value-added time = Time for eyes test + Time for photograph = 9 minutes + 4 minutes = 13 minutes

Percent value-added time = (Value-added time / Total time spent) * 100

= (13 minutes / 70 minutes) * 100

≈ 18.57%

To learn more about value-added time refer here:

https://brainly.com/question/29340992#

#SPJ11

The Noise is actually coming from a real beast, and the situation is much more serious than Francisco initially thought.

In the short story "Katie's Beast," Francisco assumes that Katie is making the growling noise at first because he believes it to be coming from her direction and she is the only person around. Katie and Francisco are walking through the woods together to get to the school bus. Francisco believes Katie is making the growling noise to scare him because she has been known to play practical jokes on him before. He becomes angry and frustrated with her, insisting that she stop making the noise and that he isn't scared.

However, after a while, Francisco realizes that the growling noise is coming from an actual beast, and he becomes frightened. He and Katie take cover behind a tree as they try to figure out how to get away from the beast.

They eventually realize that the beast is injured and in pain, and they come up with a plan to help it by getting the school bus driver to take them to the vet with the beast.

Katie and Francisco's assumptions about the growling noise at the beginning of the story highlight the theme of appearances can be deceiving.

Francisco assumes that the noise is coming from Katie, who he believes to be playing a practical joke.

However, the noise is actually coming from a real beast, and the situation is much more serious than Francisco initially thought.

For more questions on Noise.

https://brainly.com/question/31367534

#SPJ8

Answer:

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be  0  or  1  for each of its variables. In this case, the degree of variable  y  is  1  and the degree of variable  x  is  5 .

Therefore, it is not linear.

Follow these procedures to calculate the mean absolute deviation.

1. Determine the data's mean by adding all of the values and dividing by the number of values in the data set.

2. Subtract the mean from each of the data points.

3. Make each difference a good one.

4. Add up all of the positive differences.

5. Subtract this total from the amount of data values in the collection.

This is the  mean absolute deviation.

A data set's average absolute deviation is the sum of its absolute departures from a central point. It is a statistical dispersion or variability summary statistic.

The average distance between the values in a data collection and the set's mean is described by mean absolute deviation. A data collection with a mean average deviation of 3.2, for example, has values that are 3.2 units away from the mean on average.

Learn more about mean absolute deviation:
https://brainly.com/question/10528201
#SPJ1

To find the Cartesian products of three sets: A = {a, b}, B = {1, 2}, and C = {2, 3}, you need to form all possible ordered pairs from the given sets.

1. A x B: This is the set of all ordered pairs with the first element from set A and the second element from set B.
A x B = {(a, 1), (a, 2), (b, 1), (b, 2)}

2. A x C: This is the set of all ordered pairs with the first element from set A and the second element from set C.
A x C = {(a, 2), (a, 3), (b, 2), (b, 3)}

3. B x C: This is the set of all ordered pairs with the first element from set B and the second element from set C.
B x C = {(1, 2), (1, 3), (2, 2), (2, 3)}

These are the Cartesian products of the sets A, B, and C.

To learn more about cartesian products visit:

brainly.com/question/30821564

#SPJ11

Answer:

Isang Kilong Pako

Step-by-step explanation:

Ang pako po ay metal at ang bigas po ay grain lang kung ikukumpara mo sa isang butil ng bigas at pako, diba pako po ang mas mabigat, kung isang kilo pa po ehh mas mabigat na po iyon kaysa sa bigas.

Thank you Please mark as Brainliest :>

Answer:

Step-by-step explanation:

The problem as stated asks for the limit as x approaches 2 of (0/x) -2.

As written, the limit is (0/2) -2 = -2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/x -2 is defined as -2 everywhere except x=0. So, the value at x=2 is 0/2 -2 = -2.

__

If you mean (f(2) -f(x))/(x -2), that limit is the limit of 0/(x-2) = 0 as x approaches 2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/(x-2) is zero everywhere except at x=2. The left limit and right limit are both 0 as x approaches 2. Since these limits agree, the limit is said to be 0.

__

If you mean f(x) = ln(x) and you want the limit of (f(2) -f(x))/(x -2), that value will be -1/2.

Explanation: The value of the ratio is 0/0 at x=2, so we can find the limit using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim = (-1/x)/(1)

The value is -1/2 at x=2.

The partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned.

The given water wave function is graphed as z = 1 + sin(x - y) using Mathematica. The crests and troughs of the wave are aligned in the direction of zero change in the height function, which can be determined by analyzing the partial derivatives. The steepest descent from a crest to a trough corresponds to the direction perpendicular to the alignment of crests and troughs. These conclusions are consistent with the graph of the wave.

The water wave function z = 1 + sin(x - y) represents a snapshot of a frozen water wave. To graph this function using Mathematica, the x and y coordinates are assigned appropriate ranges, and the resulting z-values are plotted.

To determine the alignment of the crests and troughs, we examine the rate of change of the height function. Taking the partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned. Setting dz/dx = 0 gives cos(x - y) = 0, which implies x - y = (2n + 1)π/2, where n is an integer. This equation represents lines in the xy-plane along which the crests and troughs are aligned.  

For the steepest descent from a crest to a trough, we need to find the direction of maximum decrease in the height function. This direction corresponds to the negative gradient of the height function, which can be obtained by taking the partial derivatives dz/dx and dz/dy and forming the vector (-dz/dx, -dz/dy). Simplifying this vector, we get (-cos(x - y), cos(x - y)), which represents the direction perpendicular to the alignment of crests and troughs.    

Upon examining the graph of the wave, we can observe that the lines of alignment for the crests and troughs match the lines where the height function has zero change, confirming our conclusion from part (b). Similarly, the direction of steepest descent from a crest to a trough, indicated by the negative gradient, aligns with the steepest downward slopes on the graph.

Learn more about partial derivatives here:

https://brainly.com/question/29652032

#SPJ11

Answer:

Step-by-step explanation:

Here u go

Answer:

256

Step-by-step explanation:

4 to the exponent of 4 = 256

Answer:

$88 in total

Step-by-step explanation:

x = number of hours

y = total cost to rent the snowboard.

$25 is already guaranteed

25 + 15.75x = y

since it is 4 hours from 8:30 a.m. to 12:30 a.m. you put 4 into x.

25+15.75(4) = y

88 = y

Answer:2

Step-by-step explanation:i did it

Answer:

THE ANSWER IS 3×2-5×+6

Step-by-step explanation:

HERE IS A PIC OF THE WORK

Answer:

\(\displaystyle y=14\cdot x\)

Step-by-step explanation:

Directly Proportion

It's said that y varies directly proportional as x, if:

\(y=k\cdot x\)

Where k is a constant of proportionality.

We know that y=7 when x=1/2.

Using the above condition, we can find the value of k:

\(\displaystyle 7=k\cdot \frac{1}{2}\)

Solving for k:

k=14

Thus, the equation is:

\(\boxed{\displaystyle y=14\cdot x}\)

About 50% of Americans households have a tv except  who live in low-income, single-parent, or disadvantaged homes

Proportion: Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole

Virtually all American households have at least one tv except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of American households have at least one tv. More than 50% of American households have at least one tv.

however, about 50% of Americans households have a tv

to learn more about Proportion visit:

brainly.com/question/24232216

#SPJ4

We know that the volume of a rectangular box is given by length times width times height. So, we have:

V = x * (x - 5) * (x + 2) = 180

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

We can use this equation to find the length of the box.

Expanding the equation:

x^3 - 5x^2 + 2x = 180

Solving for x using a calculator or an algebraic equation solver we can find that x = 9.52

So the length of the box is 9.52 inches.

The answer is B. 9.52 in

Learn more about rectangle

brainly.com/question/2607596

#SPJ1

Answer:

Shape 1: 197.04

Shape 2: 125.44

Shape 3: 62.72

Step-by-step explanation:

For shape 1, you first need to find the radius to then find the area of a circle. Which is 394.08. Since this isn't a full circle, you will need to divide it by 2 to get 197.04. For shape 2(Easiest to find) You do 11.2*11.2 to get the answer of 125.44. And lastly for shape 3, you can basically do the same as what you did for shape 2. But since it is a triangle, you divide your answer by 2, to get the answer of 62.72.

Answer:

yes

Step-by-step explanation:

Let the first number be x and y be the second.

Then we habe:

I) x - 4 = 2y

II) x*y = 30

We can rewrite equation I as:

x = 2y + 4

Applying this result on equation II, we have:

(2y + 4)*y = 30

2y² + 4y = 30

2y² + 4y - 30 = 0

y² + 2y - 15 = 0

The second root is negative and don't satisfy equations I and II, then we can discard it.

Replacing y with 5 in equation I, we have:

x - 4 = 2*5

x = 2*5 + 4

x = 14

Step-by-step explanation:

.............,.,.,.,.,.,.,.,

The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

Learn more about average

brainly.com/question/24057012

#SPJ11

Answer:

36π

Step-by-step explanation:

2πR= 12π so R=6

S= πR^2=36π

Answer:

E

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

( unit 1 ) multiplied by ( unit 2 )

(5.9*10^12) multiplied by 8.9
52.51*10^12 or 5.251*10^13 or 52,510,000,000,000

Answer:

25 width and 125 length

Step-by-step explanation:

50+50+100+100 is equal to 25+25+125+125

but 50 x 100 is not equal to 25 x 125

there are many other ways you could have written it as well

Answer:

Length: 40 yd, Width: 130 yd

Dimension's of parking lot: 70 × 100

For this perimeter:   2(L + W) = 2(70 + 100) = 340 yd

For this area:             L × W = 70 × 100 = 7000 yd²

To find dimensions producing same perimeter but smaller area. One dimension has to be too small and one too big.

Possible lengths (all of them applicable):

(a) 40 wide and 130 long

(b) 20 wide and 150 long

(c) 45 wide and 125 long

Answer:

y=-2x

Step-by-step explanation:

should look like a straight line, that is going up to the left. crossing (0,0) and (1,-2)