If cosθ = 0.2, find the value of
cosθ + cos (θ + 2π) + cos (θ + 4π)

The exact values of x and y in the triangles are calculated and listed below

Figure 7

Here, we have

y = √(6² + 1²) --- pythagorean theorem

This gives

y = √37

And, we have

x = √(10² - 6²) --- pythagorean theorem

x = 8

Figure 8

Here, we have

x = 1/2 * 10 --- midsegment of equilateral triangle

This gives

x = 5

And, we have

y = √(10² - 5²) --- pythagorean theorem

y = 5√5

Figure 10

Here, we have

2x = √(6² + 8²) --- pythagorean theorem

2x = 10

x = 5

So, we have

x = y = 5

Figure 11

Here, we have

y = 5

And we have

x = √(13² - 5²) --- pythagorean theorem

x = 12

Figure 13

By similar triangles, we have

x/5 = (x + y)/10

This gives

x = y

So, we have

x = y = 3

Figure 14

By similar triangles, we have

x = 6/3 * 4

x = 8

And then, we have

y = √(6² + 8²) --- pythagorean theorem

y = 10

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We can conjecture that the value of the instantaneous velocity at t=3 is  81.6.

To find the average velocity over an interval, we use the formula:

average velocity = (change in distance)/(change in time)

Using the position function s(t) = -16t^2 + 100t, we can find the change in distance over an interval [a, b] by subtracting the value of s(a) from the value of s(b):

change in distance = s(b) - s(a)

change in distance = [-16(b^2) + 100b] - [-16(a^2) + 100a]

change in distance= -16(b^2 - a^2) + 100(b - a)

Similarly, we can find the change in time over the same interval by subtracting a from b:

change in time = b - a

Using these formulas, we can complete the table as follows:

Time Interval | Average Velocity

[2,3] | 84

[2.9,3] | 82

[2.99,3] | 81.6

[2.999, 3] | 81.6

[2.9999,3] | 81.6

Based on these results, we can make a conjecture about the value of the instantaneous velocity at t = 3.

From the table, the average velocity over smaller and smaller intervals around t=3 is approaching a value of 81.6.

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If a rectangle has a perimeter of 48 in. the length and width are scaled by a factor of 2.5, the perimeter of the resulting rectangle is 225 inches.

Let L be the length of the original rectangle and W be the width. Then, the perimeter of the original rectangle is P = 2L + 2W = 48 inches.

If we scale the length and width by a factor of 2.5, we get a new length of 2.5L and a new width of 2.5W. The perimeter of the new rectangle would be:

P' = 2(2.5L) + 2(2.5W)

= 5L + 5W

To find the new perimeter, we need to find the new values of L and W. Since the length and width are scaled by the same factor, we can write:

2.5L = kL

2.5W = kW

where k is the scaling factor.

Since the new rectangle is scaled by a factor of 2.5, k = 2.5. Therefore:

L' = 2.5L = 2.5(12) = 30 inches

W' = 2.5W = 2.5(6) = 15 inches

The new perimeter is:

P' = 5L' + 5W'

= 5(30) + 5(15)

= 225 inches

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84cm³

V= 12 x 7 = 84

volume is always cubed btw

Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

The exponential function that represents the net value of the antique desk is: f(x) = -37 × [tex]0.7027^{x}[/tex]

The exponential function is a mathematical function denoted as "exp(x)" or "[tex]e^x[/tex]", where "e" is Euler's number (a mathematical constant approximately equal to 2.71828) and "x" is the input variable. The exponential function is a special type of mathematical function that grows or decays rapidly as the input value changes.

"Net value" typically refers to the residual value or worth of something after all relevant expenses, debts, or liabilities have been subtracted from its total value or assets.

The table provides values of f(x) for x = 0, 1, 2, 3, 4, and 5. The corresponding values of f(x) are -37, -26, -13, 0, 15, and 32, respectively.

Using the given data, we can create the following exponential function in the form f(x) = a × [tex]b^{x}[/tex], where a and b are constants to be determined:

f(0) = a ×[tex]b^{0}[/tex] = -37

f(1) = a × b¹= -26

f(2) = a × b² = -13

f(3) = a × b³ = 0

f(4) = a × b⁴ = 15

f(5) = a × b⁵ = 32

To find the values of a and b, we can use a system of equations. We can divide the equations f(1) = a × b¹ = -26 by f(0) = a ×b⁰ = -37 to eliminate a:

(-26) / (-37) = b¹ / b⁰

0.7027 ≈ b

Substituting the value of b back into any of the equations, we can solve for a. Using f(0) = a ×b⁰ = -37:

-37 = a × 1

a = -37

So, the exponential function that represents the net value of the antique desk is:

f(x) = -37 × [tex]0.7027^{x}[/tex]

The values are rounded to the nearest whole dollar.

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Answer:

During the first three years Trevor owned the desk, the resale value was less than the cost. Then it exceeded the cost after year 3.

Step-by-step explanation:

See attachment

The surface area is about 157.08 square feet. use formula for the surface area of a right cylinder  to get answer .

what is surface area ?

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object. Surface area is usually measured in square units

In the given question,

The formula for the surface area of a right cylinder is:

S = 2πr² + 2πrh

where r is the radius of the cylinder, h is its height, and π is a mathematical constant approximately equal to 3.14159.

Substituting the given values, we get:

S = 2π(2.5)² + 2π(2.5)(7.5)

S ≈ 2π(6.25) + 2π(18.75)

S ≈ 39.27 + 117.81

S ≈ 157.08

Rounding this to the nearest hundredth, we get:

The surface area is about 157.08 square feet.

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The doubling time of a bank account balance is the amount of time it takes for the balance to double. In this case, the doubling time is 10 years, which means that the balance will double every 10 years.

Let's say the initial balance in the bank account is B. After 10 years, the balance will have doubled to 2B. After another 10 years (i.e., 20 years from the initial balance), the balance will have doubled again to 4B. Finally, after another 10 years (i.e., 30 years from the initial balance), the balance will have doubled one more time to 8B.

Therefore, after 30 years, the balance in the bank account will have grown by a factor of 8B/B, which simplifies to just 8. This means that the balance in the bank account will be 8 times the initial balance after 30 years.

To summarize, the balance in the bank account will double every 10 years due to the given doubling time. After 30 years, it will have doubled three times, resulting in a growth factor of 2 x 2 x 2 = 8, which means the balance will be 8 times the initial balance.

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Answer: it is reflected by y-axis

Step-by-step explanation: as we know when point (x,y) reflected  by y axis the value of y remains the same and the sign of x will be changed since the image is rotated horizontaly

Answer:

y-axis

Step-by-step explanation:

When a point is reflected over the y-axis, the x-coordinate of the point becomes the additive inverse of the original number.

Here, (8, -15) became (-8, -15). The only change in value of the coordinates is the value of the x-coordinate, 8, which became its additive inverse, -8.

Answer: y-axis

Answer: it is reflected by y-axis

Step-by-step explanation: as we know when point (x,y) reflected  by y axis the value of y remains the same and the sign of x will be changed since the image is rotated horizontaly

Answer:

y-axis

Step-by-step explanation:

When a point is reflected over the y-axis, the x-coordinate of the point becomes the additive inverse of the original number.

Here, (8, -15) became (-8, -15). The only change in value of the coordinates is the value of the x-coordinate, 8, which became its additive inverse, -8.

Answer: y-axis

The range of h(x)=-4x^2-6x-4 is  (∞, -13).

Using the vertex notion, find the range of the function h(x)=-4x2-6x-4.

The function's vertex is at x = -b/2a,

where a and b are the coefficients of x2 and x, respectively.

Because a = -4 and b = -6 in this situation, the vertex is at x = -(-6)/(2*(-4)) = 3/4.

To find the vertex's y-coordinate, enter x = 3/4 into the function:

h(3/4) = -4(3/4)^2 - 6(3/4) - 4 = -13

As a result, the function's vertex is at (3/4, -13).

Hence, the function's range is (∞, -13).

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Answer:

B

Step-by-step explanation:

If you take any set of the values and divide the cost (y) by the gummy worms (x) you get 8.4

Answer:

First, we need to put the equation in standard form, which is ax^2 + bx + c = 0. So, we have 2x^2 + 6x + 3 = 0.

Using the Quadratic Formula, x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can plug in the values for a, b, and c:

x = (-6 ± sqrt(6^2 - 4(2)(3))) / 2(2)

x = (-6 ± sqrt(36 - 24)) / 4

x = (-6 ± sqrt(12)) / 4

Simplifying further, we have:

x = (-6 ± 2sqrt(3)) / 4

x = (-3 ± sqrt(3)) / 2

To the nearest hundredth, the solutions are:

A. 2.37 and 0.63

The transformation rule used for the diagram is: Shift by 3 units upwards and a shift by 5 units to the left.

There are different methods of transformation such as:

Reflection

Dilation

Rotation

Translation

Now, from the given graph, we see that both objects remain the same size and the object on the right was first if all shifted by 3 units upwards.

Now, the transformed image in the left is the exact copy and not a mirrored copy and so there was not reflection but only another translation which was by 5 units to the left

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Answer:

1) 26

2) 118

3) 144

4) 58

5) 38

6) 96

7) 84

8) 156

9) 240

Step-by-step explanation:

Draw a Venn diagram to confirm my answers.

35% of the 240 students were interested in athletics, so .35 × 240 = 84 students were interested in athletics. Since 26 students were interested in both athletics and academic clubs, 84 - 26 = 58 students were interested in athletics only.

3/5 of the 240 students were interested in academic clubs, so 3/5 × 240 = 144 students were interested in academic clubs. Since 26 students were interested in both athletics and academic clubs,

144 - 26 = 118 students were interested in academic clubs only. From this information, you should be able to complete the two-way table.

Step-by-step explanation:

Using the distance formula, we know that the distance between points A and B is:

sqrt((3 - 0)^2 + (a - 4)^2) = 5

Simplifying:

sqrt(9 + (a - 4)^2) = 5

Squaring both sides:

9 + (a - 4)^2 = 25

Simplifying:

(a - 4)^2 = 16

Taking the square root of both sides (note that we can take the positive or negative square root since both will satisfy the equation):

a - 4 = ±4

Solving for a:

a - 4 = 4 or a - 4 = -4

a = 8 or a = 0

However, we need to check that these values of a actually make sense based on the given information. If a = 0, then the distance between A and B is:

sqrt((3 - 0)^2 + (0 - 4)^2) = sqrt(9 + 16) = 5

So a = 0 is a valid solution. If a = 8, then the distance between A and B is:

sqrt((3 - 0)^2 + (8 - 4)^2) = sqrt(9 + 16) = 5

So a = 8 is also a valid solution.

Therefore, the possible values of a are a = 0 or a = 8.

The value of a can be 0 or 8 if the distance between the given points is 5.

A straight line drawn between two points is the shortest distance between the two points. We can calculate the shortest distance by the distance formula.

Let A(0,4) = (x1,y1)

     B(3,a) = (x2,y2)

Using distance formula,

[tex]D = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

As distance = 5 units

Therefore,

[tex]\sqrt{(x2-x1)^2 + (y2-y1)^2} = 5[/tex]

[tex]\sqrt{(3-0)^2 + ((a-4)^2} = 5[/tex]

[tex]\sqrt{(3)^2 + (a^2 + 16 + - 8a)} = 5[/tex]

[tex]\(9 + 16 + a^2 - 8a = 25[/tex]

[tex]25 + a^2 -8a = 25[/tex]

[tex]a^2 - 8a = 0[/tex]

[tex]a(a-8) = 0[/tex]

a = 0 and a = 8

Therefore, the answer is 0 or 8.

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The zeros of the function are:

-¹/₂ ± √((3)/2) i, 1/3 and - 2

We want to find the Zeros of the polynomial:

f(x) = 3x⁴ + 8x³ + 6x² + 3x - 2

By the rational root theorem, we know that any rational zeros of f(x) must be expressible in the form p/q for integers p,q with p a divisor of the constant term −2 and q a divisor of the coefficient 3 of the leading term.

Therefore, the only possible rational zeros are:

±¹/₃, ±²/₃, ±1, ±2

Let's check x = 1/3 to get:

f(¹/₃) = 3(¹/₃)⁴ + 8(¹/₃)³ + 6(¹/₃)² + 3(¹/₃) - 2 = 0

f(-2) = 3(-2)⁴ + 8(-2)³ + 6(-2)² + 3(-2) - 2 = 0

Thus, x = 1/3 and - 2 are zeros of the function and (3x - 1) and (x + 2) are factors.

Using these factors and using the polynomial to divide them, we have that the remaining factor is: x² + x + 1

The zeros of x² + x + 1 are the Complex cube roots of 1, since

(x - 1)(x² + x + 1) = x³ - 1

using the quadratic formula, we have:

x = -¹/₂ ± √((3)/2) i

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Answer:

For y = tan(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.

For y = cot(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.

Answer:

8

Step-by-step explanation:

12 ÷ 3 = 4

2 x 4 = 8

Hope I could help :)

In the cylinder , height of the water tank is 5.5 feet.

What is volume?

The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Given that,

A cubic foot contains roughly 7.48 liquid gallons.

We have to find what is roughly the height of a cylindrical water tank with a capacity of 1,500 liquid gallons and a radius of 3.4 feet.

We know that,

7.48 liquid gallons are contained in one cubic foot.

The cylindrical water tank's radius is 3.4 feet.

1,500 liquid gallons are the maximum capacity.

The cylindrical water tank's volume is calculated to hold 1500 liquid gallons ,

= [tex]\frac{1500}{7.48}[/tex]

= 200.53 ft³

Volume of the cylinder= πr²h

=> 200.53= 3.14 ×3.4×3.4×h

=> 200.53 = 3.14 × 11.56 × h

=> 200.53 = 36.29 × h

=> h= 5.5

=> h= 5.5 feet (Approximately)

Therefore, height of the water tank is 5.5 feet.

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The margin of error is given as 4.22 mph

Margin of Error = t * (sample standard deviation / √(sample size))

degrees of freedom (df), which is calculated as:

df = n - 1 = 13 - 1 = 12

95% confidence level with 12 degrees of freedom = 2.179.

Margin of Error = t * (s / √n)

Margin of Error = 2.179 * (7 / √13)

Margin of Error ≈ 2.179 * (7 / 3.606)

Margin of Error ≈ 2.179 * 1.939

Margin of Error ≈ 4.22 mph

The margin of error is given as 4.22 mph

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For the given quadratic equation, the value of constant abc is 45/8.

We need to rewrite the given quadratic equation in the form of a(x+b)²+c, where a, b, and c are constants, and then find the product abc. To do this, we'll complete the square.

Given quadratic equation: 2x² -10x+8

Follow these steps to determine the product:

1: Divide the entire equation by the leading coefficient 2:

x² -5x+4

2: Add and subtract the square of half the linear coefficient inside the parentheses. Half of 5 is 5/2, and (5/2)² is 25/4:

x² - 5x + 25/4 - 25/4 + 4

3: Combine the terms and rewrite the equation in the form a(x+b)²+c:

(1)(x - 5/2)² - 9/4

4: Now, we can see that a = 1, b = -5/2, and c = -9/4. So the product abc is:

abc = (1)(-5/2)(-9/4) = (45/8)

Therefore, the value of abc is 45/8.

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What is proration?

It's when you only pay for part of something you used.

Like if you only use half of a month of a service, you only pay for half of the monthly cost.y cost.

When is proration used?

When you sign up for a service that you don't use for a full month.

When you change your service in the middle of a billing cycle.

Why is proration used?

To make sure people only pay for what they use.

To be fair and not overcharge people for services they didn't fully use.

chatgpt

The probability of picking a card with an 'E' is 2/6 and not picking an E is 4/6

From the question, we have the following parameters that can be used in our computation:

REFLEX

In the above, we have

Letters = 6

E = 2

So, we have

P(E) = 2/6

This also means that

P(Not E)  = 1 - 2/6

P(Not E)  = 4/6

Hence, the letters are

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The decision rule is Reject the null hypothesis if the calculated z-value is greater than 2.33.

To determine the decision rule, we need to perform a hypothesis test to see if the sample mean of 4.6 pounds/square inch is significantly different from the population mean of 4.4 pounds/square inch.

Null hypothesis: The population mean pressure is equal to 4.4 pounds/square inch.

Alternative hypothesis: The population mean pressure is greater than 4.4 pounds/square inch.

We will use a one-tailed z-test with a level of significance of 0.01. Since the standard deviation is known, we can use the z-test formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we get:

z = (4.6 - 4.4) / (0.8 / √110) = 2.75

The critical value for a one-tailed test with a level of significance of 0.01 is 2.33 (obtained from a standard normal distribution table). Since our calculated z-value of 2.75 is greater than the critical value of 2.33, we reject the null hypothesis.

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The domain and range of this sine function y = sinx include the following:

C. Domain: All real numbers

D. Range: -1 ≤ y ≤ 1

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞}, x|x ∈ R, or all real numbers.

Range = {-1, 1}, y ≥ or -1 ≤ y ≤ 1.

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Answer:

China's fiscal stimulus increases global aggregate demand because it increases China's GDP and imports, which increases other countries' exports to China. This fiscal stimulus might have lost some of its force because it decreases China's government budget surplus and raises the world real interest rate.

Step-by-step explanation:

hope this helps

Answer:

To determine the fluid replacement rate for a burn patient in the first 8 hours, we can use the Parkland formula:

Fluid (in liters) = 4 mL × body weight in kg × % total body surface area (TBSA) burned

First, we need to calculate the TBSA burned. We can use the Rule of Nines to estimate this:

Head: 9%

Left Arm: 9%

Right Arm: 9%

Upper Front Torso: 0%

Upper Back Torso: 0%

Lower Front Torso: 18%

Lower Back Torso: 18%

Upper Left Leg: 0%

Upper Right Leg: 0%

Lower Left Leg: 0%

Lower Right Leg: 9%

Total TBSA burned = 9 + 9 + 9 + 18 + 18 + 9 = 72%

Now we can plug in the values into the Parkland formula:

Fluid (in liters) = 4 mL × 50.9 kg × 72% = 14,694.72 mL

To convert mL to liters, we divide by 1000:

Fluid (in liters) = 14,694.72 mL ÷ 1000 = 14.69 L

This is the total amount of fluid the patient needs in the first 8 hours. To determine the hourly rate, we divide by 8:

Hourly fluid rate = 14.69 L ÷ 8 = 1.84 L/hour

Therefore, the patient should receive approximately 1.84 liters of fluid per hour in the first 8 hours of their care.

Answer:

(x+10)/(x+8).

Step-by-step explanation:

(x+5)/(x+8) = (x+5)/(x+8) + (x+5)/(x+1)

= (x+5) + (x+5)/(x+1)

= (x+10)