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The two solutions of the equation sin(theta) = 0.5 within the range of 0 to 2pi radians are approximately 0.524 radians and 6.166 radians.

To find two solutions of an equation, we need to solve the equation for the given range of theta. Since the question specifies that theta should be in radians and between 0 and 2pi, we will find two solutions within this range.
Let's consider an example equation to demonstrate the steps. Suppose we have the equation:
sin(theta) = 0.5
1: Identify the equation and the trigonometric function involved. In this case, the equation is sin(theta) = 0.5, and the trigonometric function is sine.

2: Solve for theta algebraically. To solve the equation, we need to find the values of theta that make the equation true. In this example, we can use the inverse sine function (also known as arcsin) to solve for theta. Applying the inverse sine function to both sides of the equation, we get:
theta = arcsin(0.5)

3: Calculate the value of theta using the inverse sine function. The inverse sine function gives us the angle whose sine is equal to 0.5. In this example, the inverse sine of 0.5 is approximately 0.524 radians (or 30 degrees).

4: Find a second solution within the given range. To find a second solution, we can add the period of the sine function to the first solution. The period of the sine function is 2pi radians. Adding 2pi to the first solution, we get:
theta = 0.524 + 2pi
Simplifying, we find that the second solution is approximately 6.166 radians (or 354 degrees).

Therefore, the two solutions of the equation sin(theta) = 0.5, within the range of 0 to 2pi radians, are approximately 0.524 radians (or 30 degrees) and 6.166 radians (or 354 degrees).

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(a) The equilibrium point is approximately (26, 26) where quantity (x) and price (P) are both 26.

(b) Consumer surplus ≈ 434

(c) 434 dotars (d)  -1155 dotars.

To calculate the deadweight loss, we need to find the area between the supply and demand curves from the equilibrium quantity to the quantity \(x_C\).

To find the equilibrium point, we need to set the demand and supply functions equal to each other and solve for the quantity.

Demand function: D(x) = 61 - x
Supply function: S(x) = 22 + 0.5x

Setting D(x) equal to S(x):
61 - x = 22 + 0.5x

Simplifying the equation:
1.5x = 39
x = 39 / 1.5
x ≈ 26

(a) The equilibrium point is approximately (26, 26) where quantity (x) and price (P) are both 26.

To find the point (\(x_C\), \(P_C\)) where the price ceiling is enforced, we substitute the given price ceiling value into the demand function:

P_C = $30
D(\(x_C\)) = 61 - \(x_C\)

Setting D(\(x_C\)) equal to \(P_C\):
61 - \(x_C\) = 30

Solving for \(x_C\):
\(x_C\) = 61 - 30
\(x_C\) = 31

(b) The point (\(x_C\), \(P_C\)) is (31, $30).

To calculate the new consumer surplus, we need to integrate the area under the demand curve up to the quantity \(x_C\) and subtract the area of the triangle formed by the price ceiling.

Consumer surplus

\(=\int[0,x_C] D(x) dx - (P_C - D(x_C)) * x_C\\=\int [0,x_C] (61 - x) dx - (30 - (61 - x_C)) * x_C\\=\int [0,31] (61 - x) dx - (30 - 31) * 31[61x - (x^2/2)]\)
evaluated from

0 to 31 - 31[(61*31 - (31²/2)) - (61*0 - (0²/2))] - 31[1891 - (961/2)] - 311891 - 961/2 - 311891 - 961/2 - 62/2(1891 - 961 - 62) / 2868/2
Consumer surplus ≈ 434

(c) The new consumer surplus is approximately 434 dotars.

To calculate the new producer surplus, we need to integrate the area above the supply curve up to the quantity \(x_C\).

Producer surplus \(= (P_C - S(x_C)) * x_C - \int[0,x_C] S(x) dx(30 - (22 + 0.5x_C)) * x_C - \int[0,31] (22 + 0.5x) dx(30 - (22 + 0.5*31)) * 31 - [(22x + (0.5x^2/2))]\)
evaluated from 0 to 31(30 - 37.5) * 31 - [(22*31 + (0.5*31²/2)) - (22*0 + (0.5*0²/2))](-7.5) * 31 - [682 + 240.5 - 0](-232.5) - (682 + 240.5)(-232.5) - 922.5-1155
(d) The new producer surplus is -1155 dotars. (This implies a loss for producers due to the price ceiling.)

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Answer:

a -8 power

Step-by-step explanation:

yes you do that the same way

Answer:

I needed thisssss ! Thanks for the points and you too<3

Step-by-step explanation:

Answer:

Yes! You get it, fellow human!

Step-by-step explanation:

Thank you so much! You made my day :))))) <3<3<3

Answer: When x=2 and z = 1, then the value of y =4.

Step-by-step explanation:

Given: y varies directly as x and z i.e. \(y\ \alpha \ xz\)

\(y=k(xz)\)      (i) , where k is the proportionality constant.

Put  Y=40 ,x =5 and z = 4, then we get

\(40=k(5\times4)\\\\\Rightarrow\ k=\dfrac{40}{20}\\\\\Rightarrow\ k=2\)

Required equation: \(y=2(xz)\)  [Put value of k in (i)]

Now put x=2 and z = 1, then we get

\(y=2(2\times1)=2(2)=4\\\\\Rightarrow\ y=4\)

Hence, when x=2 and z = 1, then the value of y =4.

7 but the one is 4 because 7×4=28 then + 4= 32

Answer:there are 20

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

True.

Let's say A = 5, and B = 10.

We need to swap the contents of A and B, so A will end up with 10 and B will end up with 5.

A = 5

B = 10

Introduce variable C.

C = A (now C contains 5)

A = B (now A contains 10)

B = C (now B contains 5)

In the last two steps above, you see that the values of A and B were swapped.

Answer:

13 with a remander of 1

Step-by-step explanation:

Step-by-step explanation:

Here :-

\(\begin{gathered}\end{gathered}\)

Let the cost price of one ball is ₹1. So ;-

↝ Here the selling price of 25 balls is equal to the cost of 15 balls. It means C.P of 15 balls = S.P of 25 balls. So, the selling price of 25 balls is ₹15.

\(\begin{gathered}\end{gathered}\)

Firstly, finding the loss :-

\({\dashrightarrow{\sf{Loss = Cost \: Price - Selling \: Price}}}\)

\({\dashrightarrow{\sf{Loss = 25 - 15}}}\)

\({\dashrightarrow{\sf{\underline{\red{Loss =Rs.10}}}}}\)

∴ The loss is Rs.10.

\(\begin{gathered}\end{gathered}\)

Now, finding the loss percentage :-

\({\dashrightarrow{\sf{Loss\: \%= \dfrac{Loss }{Cost \: Price} \times 100}}}\)

\({\dashrightarrow{\sf{Loss\: \%= \dfrac{10 }{25} \times 100}}}\)

\({\dashrightarrow{\sf{Loss\: \%= \dfrac{10 \times 100 }{25}}}}\)

\({\dashrightarrow{\sf{Loss\: \%= \dfrac{1000 }{25}}}}\)

\({\dashrightarrow{\sf{Loss\: \%=\cancel{\dfrac{1000 }{25}}}}}\)

\({\dashrightarrow{\sf{\underline{\red{Loss\: \%=40 \: \%}}}}}\)

∴ The loss percent is 40%.

\(\underline{\rule{200pt}{2.5pt}}\)

The answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

The equation x3 + y3 = 9 is a cubic equation and is a non-linear equation. As such, it does not have any tangent lines that are horizontal. A tangent line is a line that just touches a point on a curve and has the same slope as the curve at that point. Since the equation is non-linear, the slope of the curve changes at each point, meaning that there cannot be any horizontal tangent lines.

To calculate the slope of the curve at any point (x,y), we use the formula m = (dy/dx) or m = 3*(x2/y2). At these points, the slope of the curve will not be zero, meaning that there is no horizontal tangent line at any point on the curve.

Therefore, the answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

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Answer:

\(\frac{55}{14}\)

Step-by-step explanation:

First, we convert the mixed numbers into improper fractions: \(1\frac{3}{7} =\frac{10}{7}\), and \(2\frac{3}{4}=\frac{11}{4}\). Now, we multiply the fraction using the multiplication rule, \(\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\): \(\frac{10}{7} \times \frac{11}{4} = \frac{110}{28} = \frac{55}{14}\).

Thus, the product of the two given fractions is 55/14.

• We are required to find Z so that the area is to the right, this means that the area is to be positive .

• 88 % can be converted to 88/100 = 0.88

• z = 1-0.88 = 0.12

The value tha corresponds with 0.12 = 0.04775

= 0.048

using the cumulative standard normal z score of 0.12 = 0.5478

Answer:

c

Step-by-step explanation:

Answer:

cccc

Step-by-step explanation:

The answers that  best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.

The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.

To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.

Therefore the correct option is C.

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Answer:

190

Step-by-step explanation:

Surface Area of Rectangular Prism:

S = 2(lw + lh + wh)

Answer:

190

Step-by-step explanation:

The formula surface area of a rectangular prism is 2(wl+hl+hw)

Hope this helped :)

Dilated version will be larger than the original version

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle PQR and its dilated form P'Q'R'.

The dilated version will be larger than the original version as the scale factor k is greater than 1.

Therefore, dilated version will be larger than the original version.

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Step-by-step explanation:

we don't see all answer options.

but I am sure it must be b.

simply because the right graph shows that the curve goes through

(4, 0) and (-4, 0)

and

(0, 3) and (0, -3)

but if I am mistaken about b showing that, please pick the graph that shows this.

the reason is to think when is the x term being 1, when y = 0, and when is the y term being 1, when x = 0.

these are some "cornerstones" for the graph based on the functional definition.

and the answers are the points listed above.

The trinomial for the rectangular rug is 3x² + 5x - 2

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.

A trinomial is a polynomial with three terms.

The area of a rectangle = length * width

Area of rectangle = (x + 2) * (3x - 1) = 3x² + 6x - x - 2

Area of rectangle = 3x² + 5x - 2

The trinomial for the rectangular rug is 3x² + 5x - 2

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Answer:

30

Step-by-step explanation:

130+20=150. 180-150=30

Answer:

Number of terms = 3

Degree = 6

Step-by-step explanation:

A polynomial is a mathematical expression that gives the detailed combination of variables with their coefficients, their positive exponential, and other variables using the operations of subtraction, addition, and multiplication

The number of terms in a polynomial is the number of different powers of added or subtracted in the expression

Therefore, the number of terms in the expression -3·s⁶ + 2·s⁴ + 3·s³ is 3 terms

Number of terms = 3

The degree of a polynomial is given by the highest power of the variables in the polynomial. Therefore, the degree of the given polynomial is 6

Degree = 6

Answer:

18.

Step-by-step explanation:

3 x 6 = 18. He eats 3 slices every 5 minutes so 5 minutes x 6 is half an hour. so 18 is your answer.

If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

The Linear equation in one variable is an algebraic equation of degree one.

it can be expressed in the form of Ax +B = 0 where x is a variable, and A and B are two integers.

Takaya can eat three slices of pizza in five minutes.

for half an hour it would be 6 times five minutes.

So, in half an hour Takaya can eat 3 × 6 = 18

Therefore, If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

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Answer:

The transformation was the function went up 5 units, right two units, and a vertical stretch of 2.

Step-by-step explanation: