TRUE/FALSE. most trigonometric equations have unique solutions

Answer:

(3,-4)

Step-by-step explanation:

Point (0,7) moves 2 left to -2, and 2 down to 5. So (5,-2) left 2 and down 2 gets (3,-4).. Right?

Answer:

1/6

Explain:

The reciprocal of the slope is its perpendicular.

6/1 --> 1/6

The surface area is increasing at a rate of approximately 2513.274 square centimeters per second.

The problem provides us with the rate of change of the radius, which is 2 cm/sec. We are asked to find how fast the surface area is increasing when the radius is 10 cm.

To find the rate at which the surface area is increasing, we can use the formula for the surface area of a sphere, which is 4πr^2.

First, we differentiate the formula with respect to time (t) to find the rate of change of the surface area, which is dA/dt:

dA/dt = d/dt(4πr^2)

Next, we substitute the given rate of change of the radius into the equation:

dA/dt = d/dt(4π(10)^2)

Simplifying further:

dA/dt = d/dt(400π)

Since the radius is increasing at a constant rate, its derivative is simply the constant rate itself, which is 2 cm/sec.

Therefore:

dA/dt = 2(400π)

Simplifying the expression:

dA/dt = 800π

Rounding to the nearest thousandths:

dA/dt ≈ 2513.274

So, when the radius of the sphere is 10 cm, the surface area is increasing at a rate of approximately 2513.274 square centimeters per second.

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Answer:

-0.03125

Step-by-step explanation:

Answer:

\(-\frac{1}{32}\) or -0.03125

Skills needed: Exponents

Step-by-step explanation:

1) Negative exponent means 1 over if it was positive:

\(2^{-2} = \frac{1}{2^2}\)

In this case: \(-2^{-5}=\frac{1}{(-2)^5}\)

2) Let's expand the \((-2)^5\) part:

Remember that the exponent (the smaller number in the top-right) shows how many times the base (bigger number) is multiplied by itself.

In this case:

\((-2)^5\) = \(-2*-2*-2*-2*-2\)

We know that: \(-2*-2=4\)

So the above simplifies into: \(4 * 4 * -2\) = \(16*-2\) = \(-32\)

3) That is the denominator in the fraction:

\(\frac{1}{-32}\) which is \(-\frac{1}{32}\)

Answer:

1 + 492008 = 492009

Step-by-step explanation:

OR

200009 + 292000 = 492009

Answer:

20% loss.

Step-by-step explanation:

Suppose the cost of each banana is $1

Then cost of 12 = $12.

You sell 15 bananas for  $12, therefore the price of each banana is 12/15

= $0.80.

So the loss percent is  (1 - 0.80) * 100

= 20%.

Answer:

xy=5

Step-by-step explanation:

from the question, y varies directly with x and y

Then y ∝ xy

If we introduce proportionality sign we have

y=r xy

Where r= proportionality constant

Then if we substitute the given values

y = 25 when r = 5.

We have

y=r xy

25=5xy

Divide both sides by 5

xy=25/5

xy=5

Hence, equation that models the statement is xy=5

==============================================================

Explanation:

Select any two points from the diagonal line. I'll pick (0,-10) and (2,-4).

Use these points in the slope formula

m = (y2 - y1)/(x2 - x1)

m = (-4 - (-10))/(2 - 0)

m = (-4 + 10)/(2 - 0)

m = 6/2

m = 3

The slope is 3.

The y intercept is b = -10 since this is the location where the diagonal line crosses the vertical y axis.

The values m = 3 and b = -10 have us go from y = mx+b to y = 3x-10

The cosine model is y = - 7 + 10 · cos (π · x/30 - π).

The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).

Sinusoidal functions are periodic trascendent expressions which involves trigonometric functions. There are two kinds of sinusoidal functions:

\(y = A \cdot \cos (B\cdot x + C) + D\)     (1)

\(y = A\cdot \sin (B\cdot x + C) + D\)      (2)

Where:

First, we find the amplitude and the midpoint:

A = [3 - (- 17)]/2

A = 10

D = [3 + (- 17)]/2

D = - 7

Now we find the angular phase and the angular frequency for each model:

Cosine model (x, y) = (0, - 17), (x, y) = (30, 3)

- 17 = 10 · cos C - 7     (3)

3 = 10 · cos (30 · B + C) - 7      (4)

By (3):

- 10 = 10 · cos C

cos C = - 1

C = acos(- 1)

C = - π

And by (4):

3 = 10 · cos (30 · B - π) - 7

10 = 10 · cos (30 · B - π)

cos (30 · B - π) = 1

30 · B - π = acos 1

30 · B - π = 0

30 · B = π

B = π/30

The cosine model is y = - 7 + 10 · cos (π · x/30 - π).

Sine model

Obtain the sine model by using trigonometric expressions:

cos θ = sin (θ + π/2)     (5)

By (5):

y = - 7 + 10 · sin (π · x/30 - π + π/2)

y = - 7 + 10 · sin (π · x/30 - π/2)

The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).

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The statement about the given expression is described below.

A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.

Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2

Thus, given expression has two factors which consist 3 terms.

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To find f(6), we will follow the steps given in the prompt:

(1) Evaluate the integral ∫ f(x) (f(x))² dx using the u-substitution method.

Let u = f(x), then du = f'(x) dx.

The integral becomes ∫ u u² du = ∫ u³ du = (1/4)u⁴ + C.

Since f(4) = 1, we have u = f(4) = 1.

Substituting u = 1 in the integral, we get:

(1/4)(1⁴) + C = 1/4 + C.

(2) Consider the integral ∫ dx / (x^2)(f(x))^2.

Using the assumption that f(x) ≠ 0 on the interval, we can rewrite the integral as:

∫ (f'(x))^2 / (f(x))^2 dx.

Let r be a real number.

∫ (f'(x))^2 / (f(x))^2 dx = ∫ (f'(x) / f(x))^2 dx

= ∫ (2r)^2 dx

= 4r²x + D.

(3) Pick r.

Since the integral ∫ (f'(x))^2 / (f(x))^2 dx is nonnegative, if it equals zero, the integrand must be zero.

Therefore, (f'(x) / f(x))^2 = 0, which implies f'(x) = 0.

(4) Solve the separable differential equation df / dx = 0.

Integrating both sides, we get f(x) = C, where C is a constant.

Using the given information, we can use f(4) = 1 to find C:

f(4) = C = 1.

So, the solution to the differential equation is f(x) = 1.

(5) Evaluate f(6).

f(6) = 1.

Therefore, f(6) = 1.

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Given

Large necklace sells for a $4.30

Small necklace sells for $4.10

4 large

1 small

Procedure

Total

The answer would be $21.30

 In the standard normal distribution. the mean is always ZERO and the standard deviation is always ONE .

We have to know about the normal distribution. It is a bell-shaped, symmetrical distribution in which the mean, median and mode are all equal. It also consists another important keywords like...

1.Z scores which are also known as standard scores. The number of standard deviations that a given raw score falls above or below the mean

2.Standard normal distribution is a normal distribution represented in z scores. The standard normal distribution always has a mean of zero and a standard deviation of one.

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The maximum value of the data in the box-and-whisker plot is 75.

A box-and-whisker plot is a standardized representation of statistical data on a plot using a rectangle drawn to represent the distribution of data under five summaries: “minimum”, first quartile [Q1], median, third quartile [Q3], and “maximum.”

The inside vertical line indicates the median value while the lower and upper quartiles are horizontal lines on either side of the rectangle.

Minimum value = 10
Median = 35

Maximum value = 75

Thus, the maximum value, which shows the end of the line, of the data distribution of this box-and-whisker plot is 75.

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Each side of the square room is 9 feet long.

A square is a two-dimensional geometric shape with four equal sides and four equal angles of 90 degrees each. It is a type of rectangle, but it has the additional property that all its sides are of equal length.

Since the room is square and the floor tiles are also square, the number of tiles required to cover the floor is equal to the area of the room divided by the area of each tile.

Let's assume that each side of the square room is "x" feet long. Then, the area of the room can be expressed as x² square feet. If each floor tile measures "y" feet on each side, then the area of each tile can be expressed as y² square feet.

Given that 81 tiles are required to cover the floor, we can set up the following equation:

x² / y² = 81

To solve for "x", we need to first determine the value of "y". Since each floor tile is a square, we can assume that y is the length of one side of a tile. Let's suppose that each tile measures 1 foot on each side. Then, the area of each tile is y² = 1² = 1 square foot.

Substituting y = 1 in the above equation, we get:

x² / 1² = 81

x² = 81

x = √(81)

x = 9

Therefore, each side of the square room is 9 feet long.

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For the given equations of the demand and supply of goods , the elasticity of supply will be (a) 5/4 .

The Elasticity of supply is defined as a measure of responsiveness of the quantity of a good or service supplied to changes in its price. It is the degree to which the quantity supplied of a product or service changes when there is a change in its price.

We know that the elasticity of supply curve is the same as the slope of supply curve because it represents the proportion of change in price that will change the quantity supplied.

The equation for the supply curve is given to be :  S = -5 + (5/4)p ,

So , the slope of Supply curve is given in the equation is 5/4 .

Therefore , The  Elasticity Of Supply is 5/4 , the correct option is (a) .

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The given question is incomplete , the complete question is

Suppose that the supply and demand of a good are given by the following equations:

Demand = 75 - (3/4)p and Supply = -5 + (5/4)p ,

What is the elasticity of supply?

(a) 5/4

(b) 10/9

(c) 3/4

(d) 11/8

The statement is true; given a bounded sequence (sn), there exists a monotonic subsequence whose limit is the limit superior (lim sup) of (sn).

To prove this, consider the set A of all subsequential limits of (sn), denoted as {x: x is a subsequential limit of (sn)}. Since (sn) is bounded, A is also bounded. By the Bolzano-Weierstrass theorem, A contains at least one accumulation point, which we denote as L.

Now, construct a subsequence (sk) such that for each k, sk is the element of (sn) that is closest to L among the elements not yet chosen. By construction, (sk) is a monotonic subsequence.

To show that lim sk = L, we consider any ε > 0. Since L is an accumulation point of A, there exists an element snk in (sn) such that |snk - L| < ε. As (sk) consists of elements that are closest to L, we have |sk - L| ≤ |snk - L| < ε. Thus, lim sk = L, which proves the existence of a monotonic subsequence whose limit is lim sup sn.

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The fraction which is equivalent to 6/12 is 1/2

What does a fraction mean?

In the first place, fraction is a numerical quantity or relationship where one number is expressed in terms of another.

In order to determine the equivalence of 6/12 in fraction , we need reduce 6/12 to the lowest term, since 6 is common to 6 and 12 and that 6 divided by gives 1 and 12/6 gives 2, which means that we are left 1/2

The correct fraction which is equivalent to 6/12 is 1/2

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Full question:

A group of 12 students goes on a school field trip, 6 are in third grade. which fraction is equivalent to 6/12?

(A) 1/3

(B)1/4

(C) 1/6

(D) 1/2

Answer:

B

Step-by-step explanation:

We can't see the answer choices?

Option E should be chosen, which is to explore the assignable causes because the second, fourth, and fifth samples are above the mean.

In an x-bar chart, the control limits (UCL and LCL) are based on the process variability and are used to determine if the process is in control. The central line represents the mean of the process.

Looking at the given sample means of 18, 23, 17, 21, 24, and 16, we can see that the second, fourth, and fifth samples are above the mean of 20. This suggests a potential shift or deviation from the expected process mean.

In an x-bar chart, if any sample mean falls outside the control limits or exhibits a non-random pattern, it indicates the presence of assignable causes, which are factors that can be identified and addressed to improve the process. Since the second, fourth, and fifth samples are above the mean, it is advisable to explore the assignable causes, as stated in option E.

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Answer:

-3.3

Step-by-step explanation:

-2.3 - (4.5-3.5)

-2.3 - (1.)

-3.3

False. A line graph typically shows the relationship between two variables.

It is a useful visualization tool for displaying trends or patterns in data over time or across different categories. The x-axis represents the independent variable or the variable being manipulated or controlled, while the y-axis represents the dependent variable or the variable being measured or observed. Each point on the line graph represents the value of the dependent variable corresponding to a specific value of the independent variable.

However, a line graph cannot directly represent the relationship between three variables.

Therefore, the given statement is false. A line graph typically shows the relationship between two variables.

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Complete question is below

A line graph shows the relationship between three variables true or false

It sounds like you may be experiencing a bug with your Alexa device. This is likely due to a software update or miscommunication between the device and the server.

To resolve this issue, you may need to restart your device by unplugging it from the power source and plugging it back in. You can also try clearing the cache of your device. Additionally, you may need to update the software of your device by visiting the Amazon website and downloading the most recent version of the software. If the issue persists, you may need to contact Amazon customer service for further assistance.

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Answer: It’s adjacent I’ll draw what vertical is. And M is 180-106 which is 74. Adjacent means next to...

Step-by-step explanation:

By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.

To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.

Since a van can ferry a maximum of 12 people, we can write the inequality as:

12v ≥ 80

Now, let's solve for "v":

Divide both sides of the inequality by 12.
v ≥ 80/12

Simplify the inequality.
v ≥ 6.67

Since we cannot have a fraction of a van, we need to round up to the nearest whole number:

v ≥ 7

Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.

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Answer:

its 1.5

Step-by-step explanation:

Answer:

18/12 or 3/2 or 1.5

Step-by-step explanation:

Answer:

looks like it might be 4 but I'm not a 100% sure

Answer:

56

Step-by-step explanation:

2x2x2=8 so 7x8=56