What is the slope of the line?

The second additional Polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

We have a point in polar coordinates (3,-π/6) and we have to find two additional polar representations of this point. Let's recall the formula for converting from Cartesian to polar coordinates :x = rcosθy = rsinθAnd

the formula for converting from polar to Cartesian coordinates :r = √(x²+y²)θ = arctan(y/x)So, we can use the second formula to convert (3,-π/6) to Cartesian coordinates:$$x=3\cos(-\frac{\pi}{6})=3\cdot \frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{2}$$$$y=3\sin(-\frac{\pi}{6})=3\cdot \frac{-1}{2}=-\frac{3}{2}$$

Now we can use the first formula to convert back to polar coordinates:$$r=\sqrt{(\frac{3\sqrt{3}}{2})^2+(-\frac{3}{2})^2}=\frac{3\sqrt{6}}{2}$$$$\theta=\arctan(-\frac{3}{3\sqrt{3}})=-\frac{\pi}{3}$$

So, the first additional polar representation of the point (3,-π/6) is ($\frac{3\sqrt{6}}{2}$, $-\frac{\pi}{3}$).To find the second polar representation,

we need to add or subtract multiples of π to the angle until it is in the range [-2π, 2π].$$-\frac{\pi}{3}+2\pi=\frac{5\pi}{3}$$$$-\frac{\pi}{3}-2\pi=-\frac{7\pi}{3}$$

So, the second additional polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

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Answer:

(a) \(C(x) = 12 + 5x\)

(b) \(C(x) = 8x\)

(c) Tables

(d) See attachment for graph

(e) Banner newspaper

(f) Free press newspaper

Free Press

\(\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}\)

Banner

\(\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}\)

Step-by-step explanation:

Given

Free Press

\(Initial = 12\)

\(Rate =5\)

Banner

\(Initial=0\)

\(Rate =8\)

Solving (a): Free Press Equation

This is calculated as:

\(C(x) = Initial + Rate * x\)

Where

\(x \to\) days

So, we have:

\(C(x) = 12 + 5x\)

Solving (b): Banner Equation

This is calculated as:

\(C(x) = Initial + Rate * x\)

Where

\(x \to\) days

So, we have:

\(C(x) = 0 + 8x\)

\(C(x) = 8x\)

Solving (c): Table of values

For free press, we have:

\(\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}\)

C(x) is calculated as:

\(x = 1;\ C(1) = 12 + 5* 1 =17\)

\(x = 2;\ C(2) = 12 + 5* 2 =22\)

..

\(x = 5;\ C(5) = 12 + 5* 5 =37\)

For banner, we have:

\(\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}\)

C(x) is calculated as:

\(x = 1;\ C(1) = 8* 1 =8\)

\(x = 2;\ C(2) = 8* 2 =16\)

..

\(x = 5;\ C(5) = 8* 5 =40\)

Solving (d): Graph of both using rapidtable

See attachment

Solving (e) Newspaper to use for 1 day

From the graph, when \(x = 1\)

\(Free\ press = 17\)

\(Banner = 8\)

So, we use Banner newspaper because it is cheaper

Solving (f) Newspaper to use for 12 days

From the graph, when \(x = 12\)

\(Free\ press = 72\)

\(Banner = 96\)

So, we use free press newspaper because it is cheaper

Hi ;-)

Calculate

\(6-(-11)=6+11=\boxed{17}\)

Answer:

17

Step-by-step explanation:

6-(-11)

Subtracting a negative is like adding

6+11

17

The volume of the solid of revolution is \(\frac{16\pi}{3}\) cubic units.

First, we determine the limits between the two curves. (\(f(x) = 4\cdot x -2\), \(g(x) = x^{2}+1\))

\(f(x) = g(x)\) (1)

\(4\cdot x - 2 = x^{2}+1\)

\(x^{2}-4\cdot x +3 = 0\)

\((x-1)\cdot (x-3) = 0\)

The lower and upper bounds are 1 and 3, respectively. It is to notice that \(f(x) > g(x)\) for \(x \in (1, 3)\). Thus, we determine the volume of the solid of revolution by shell method, that is to say:

\(V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx\) (2)

If we know that \(a = 3\), \(b = 1\), \(f(x) = 4\cdot x - 2\) and \(g(x) = x^{2}+1\), then the volume of the solid of revolution is:

\(V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx\)

\(V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx\)

\(V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx\)

\(V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)\)

\(V = \frac{208\pi}{3} - 40\pi -24\pi\)

\(V = \frac{16\pi}{3}\)

The volume of the solid of revolution is \(\frac{16\pi}{3}\) cubic units.

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Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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By using trigonometry, it can be calculated that- sin 23º = \(\frac{5}{13}\)

What is Trigonometry?

Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles. It is used to calculate the lengths of sides, the measures of angles, and the relationships between the two. Trigonometry is important for understanding many areas in mathematics, such as calculus and engineering. Trigonometric functions are used to model and analyze phenomena in many areas, such as sound waves, light waves, and ocean tides. Trigonometric identities allow us to simplify equations and solve problems. Trigonometry is a fundamental tool in many scientific and engineering disciplines.

There are six trigonometrical functions. They are

\(sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta\)

\(sin\theta = \frac{perpendicular}{hypotenuse}\\cos\theta = \frac{baser}{hypotenuse}\\tan\theta = \frac{perpendicular}{base}\\cot\theta = \frac{base}{perpendicular}\\sec\theta = \frac{hypotenuse}{base}\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\)

Trigonometry is a very important tool in mathematics.

For an angle of 23º,

Perpendicular is 5, base is 12 and hypotenuse is 13

sin 23º = \(\frac{5}{13}\)

First option is correct.

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Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

Answer:

A. $1389.69

Step-by-step explanation:

To calculate the new monthly mortgage payment that Carissa will start paying going forward, we use the formula for calculating monthly mortgage payments.

The formula is:- M = P { [r ( 1+ r)^n] ÷ [ ( (1+r)^n) -1] }

Here, M is the monthly mortgage payment.

P is the principal

r is the monthly interest rate calculated by dividing your annual interest rate by 12

n is the number of payments(the number of months you will be paying the loan).

Hence, the new principal that Carissa must payback is $231,905.47¢.

The annual interest rate has been reduced to 5.25% from 5.75%.

Therefore, the new monthly interest rate will be obtained by dividing the new annual interest rate by 12

= 5.25%/2

= 0.438%

This is the new monthly interest rate.

Since she has been paying her mortgage loan diligently for 5 complete years. It means she now has just 25 years to complete the payment. If 12 months make up one year, then there are - 12 × 25 = 300 more months to go.

300 is, therefore "n" that is required for the calculation.

All the terms needed for the calculation of her new monthly mortgage are now complete.

P = $231,905.47¢

r = 0.4375%

n = 300

M = 231,905.47 { [0.004375 (1+0.004375) ^300] ÷ [ ( (1+0.004375) ^ 300 ) - 1] }

= 231,905.47 { [ 0.004375 (3.7048) ] ÷ (2.7048) }

= 231,905.47 × 0.005992

M = $1,389.69

Therefore her new monthly mortgage payment will become $1,389.69

Answer: $1389.69

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

We Know

You buy 4 5/8 blue fabric and 2 1/8 green fabric .

4 5/8 = 37/8 = 4.625 blue fabric

2 1/8 = 17/8 = 2.125 green fabric

How much blue than green did you buy?

We Take

4.625 - 2.125 = 2.5

So, you buy 2.5 blue more than green.

Answer:

47 and 49

Step-by-step explanation:

Answer:

2303

Step-by-step explanation:

Let the smaller of the two odd integers be x.

Then the next odd integer is x + 2.

Since the sum of these 2 integers is 96, we may write x + (x + 2) = 96

Now solving for x we obtain:

2x = 94

x = 47

To find the next value we can subtract 47 from 96, which is 49.

Hence, the required two integers are 47 and 49. Multiplying them, we get a product of 2303.

hope this helps!

R= 10 + 3X

then for 8 hours

Rent R = 10 + 3•8= 34

Answer is $34 dollars

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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The value of each digit in a number is known as the place value. The value of the 5 in the number 40.52 is 10 times the value of the 5 in 115.78.

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

The value of 5 in the given numbers can be written as,

Now, we can write the value of the two numbers as,

5 = 0.5 × x

x = 5/0.5

x = 10

Hence, the value of the 5 in the number 40.52 is 10 times the value of the 5 in 115.78.

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Answer:

You will have saved $69,612 after five years.

Step-by-step explanation:

This can be calculated using the for formula for calculating the future value of a growing annuity as follows:

FV = C * (((1 + r)^n - (1 + g)^n) / (r - g)) ……………………………………… (1)

Where;

FW = future value or amount you will have saved after five years = ?

C = first deposit = $1,000

r = periodic monthly interest rate of = 0.4%, or 0.004

g = growth rate of contribution = 0.1%, or 0.001

n = number of months = 5 years * 12 = 60

Substituting all the values into equation (1), we have:

FV = $1,000 * (((1 + 0.004)^60 - (1 + 0.001)^60) / (0.004 - 0.001))

FV = $1,000 * 69.612001854052

FV = $69,612.00

Therefore, you will have saved $69,612 after five years.

Answer:

mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra

Step-by-step explanation:

formula :

a² - b² = ( a + b )(a - b )

Answer:

|2x+1|=0 has one solutions

2|x+1|=-2 has no solution

|x+21|=2 has two solution

Step-by-step explanation:

\( \: \: \: \: \large\bf\implies \: 4.32\)

\( \longrightarrow \bf \: 1.42 - ( - 2.9) \\ \longrightarrow \bf \: 1.42 + 2.9 \\ \longrightarrow \bf \: 4.32\)

First of all we know that to do this type of question that is ↓

The angle by which turns counterclockwise about point P to coincide with is 180 degree angle

What is 180 degree angle?

The angle which forms a straight line is called the 180-degree angle. A 180-degree angle is a straight angle and it is exactly half of a revolution. The two arms of the angle which are making 180-degree are just opposite to each other from the common vertex.

The points D, P and C forms a straight line.

So, if it turns clockwise about Point P, it would make an angle of 180 degree.

as the point D and C are of equal lengths and opposite to each other, the angle from P turning clockwise makes 180 degree angle.

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Answer:

100

80

Step-by-step explanation:

plato

Answer:

7 schools have fewer than 50 classrooms.

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

=x^2+7x+10

Step-by-step explanation:

Simplify: xx+5x+2x+2.5: x+7x+10

Add similar elements: 5x+2x= 7x

=xx+7x+2.5

xx=x2

2.5=10

=x+7x+10

Answer: =x^2+7x+10

Hope this helps.

Answer:

30°

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.

In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:

short leglong leg​=13​​

short leg93​​=13​​

Cross-multiplying and solving for the short leg, we get:

short leg=3​93​×1​=9

Similarly, we can use another proportion to find the hypotenuse:

long leghypotenuse​=3​2​

93​hypotenuse​=3​2​

Cross-multiplying and solving for the hypotenuse, we get:

hypotenuse=3​2×93​​=18

Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer:

Table B is proportional since y = 1.5x:

4.5 ÷ 3 = 1.5

7.5 ÷ 5 = 1.5

10.5 ÷ 7 = 1.5

Answer:

2253.75

Step-by-step explanation:

It would have a decimal because these numbers are not equal :D

Answer:

5 equation matches the table

Answer:

207775

Step-by-step explanation:

because I know it true

Answer:

Step-by-step explanation:

You want the values among those listed that satisfy the inequality -m > 4.

Multiplying the given inequality by -1 gives an equivalent inequality with a positive coefficient for m:

  m < -4

This means you need to choose the numbers that are less than -4 from those in the answer choices. The appropriate values are ...

  {-9, -5, -4.1}