8c + c

I need this answer asap​

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

Using exact values from the 30- 60- 90 special triangle

2cos60°sin30°

= 2 × \(\frac{1}{2}\) × \(\frac{1}{2}\) = 1 × \(\frac{1}{2}\) = \(\frac{1}{2}\)

\(2 \cos(60) \sin(30) \)

\( \cos(60) = \frac{1}{2} \)

\( \sin(30) = \frac{1}{2} \)

\(2 \times \frac{1}{2} \times \frac{1}{2} \)

\(2 \times \frac{1}{4} \)

\( \frac{1}{2} \)

Step-by-step explanation:

its true... opposite sides are equal

Answer:

true

Step-by-step explanation:

/■\ <--- that is the shape

Answer:

11.25 pounds of chicken need to be bought

Step-by-step explanation:

Per person will eat:

3/8 * 2 = 3/4 = 0.75 pound

So if one person will eat 0.75 pound.

15 people will eat 15 * 0.75 = 11.25 pounds

Step-by-step explanation:

Cube ...so each side is 5 cm

Diagonal = sqrt ( 5^2 + 5^2 + 5^2 )    <====like Pythagorean theorem in 3-D

        = sqrt (75) = 5 sqrt 3  = 8.66 cm

Answer:

7.071

Step-by-step explanation:

this is sqrt(25+25)

which is 7.071

Brainliest?

It's important to follow the order of operations to ensure accurate calculations. the correct answer to the calculation 5.25 + 41.8 + 34.1 is 81.15.

To perform the calculation using the correct order of operations, we need to follow the rules of precedence, also known as the PEMDAS rule. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the given expression step by step:

5.25 + 41.8 + 34.1

According to the PEMDAS rule, we need to start with any calculations inside parentheses, but there are no parentheses in this expression. Next, we move to addition and subtraction from left to right.

5.25 + 41.8 equals 47.05.

Now we add 34.1 to the result:

47.05 + 34.1 equals 81.15.

Therefore, the correct answer to the calculation 5.25 + 41.8 + 34.1 is 81.15.It's important to follow the order of operations to ensure accurate calculations.

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Answer:

(-1,12)

Step-by-step explanation:

let R be(x,y)

Q(4,5)=midpoint

R(x,y)=(x1,y1)

p(9,-2)=(x2,y2)

now,

(4,5)= x1+x2/2 , y1+y2/2

(4,5)= x+9/2 , y-2/2

so,

x+9/2=4              y-2/2=5

x+9=8                  y-2=10

x= -1                      y=12

therefore, R(x,y)= (-1,12)

The limit of (f(x) + 1) / sin(x) as x approaches 0 is 0, the approximation for f(1/2) using Euler's method with two steps is 19/32 and the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1.

(a) To find the limit of (f(x) + 1) / sin(x) as x approaches 0, we can first rewrite the given differential equation as:

dy / dx = y²  (2x + 2)

Separating variables, we get:

dy / y²  = (2x + 2) dx

Integrating both sides, we have:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side gives:

-1 / y = x²  + 2x + C1

where C1 is the constant of integration.

Since we have the initial condition f(0) = -1, we substitute x = 0 and y = -1 into the above equation:

-1 / (-1) = 0²  + 2(0) + C1

1 = C1

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Now, to find the limit (f(x) + 1) / sin(x) as x approaches 0, we substitute x = 0 into the particular solution equation:

f(0)(0²  + 2(0) + 1) + 1 = 0

-1(0) + 1 = 0

1 = 0

Therefore, the limit of (f(x) + 1) / sin(x) as x approaches 0 is 0.

(b) Using Euler's method, we approximate the value of f(1/2) starting at x = 0 with two steps of equal size. Let's choose the step size h = 1/4.

First step:

x0 = 0, y0 = f(0) = -1

Using the differential equation, we have:

dy / dx = y²  (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (-1)²  (2(0) + 2) (1/4)

Δy ≈ 1/2

Next, we update the values:

x1 = x0 + Δx = 0 + 1/4 = 1/4

y1 = y0 + Δy = -1 + 1/2 = 1/2

Second step:

x0 = 1/4, y0 = 1/2

Using the differential equation again:

dy / dx = y^2 (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (1/2)²  (2(1/4) + 2) (1/4)

Δy ≈ 3/32

Updating the values:

x2 = x1 + Δx = 1/4 + 1/4 = 1/2

y2 = y1 + Δy = 1/2 + 3/32 = 19/32

Therefore, the approximation for f(1/2) using Euler's method with two steps is 19/32.

c)To find the particular solution to the differential equation dy/dx = y^2 (2x + 2) with the initial condition f(0) = -1, we can solve the separable differential equation.

Separating variables, we have:

dy / y² = (2x + 2) dx

Integrating both sides:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side:

-1 / y = x²  + 2x + C

where C is the constant of integration.

To find the particular solution, we substitute the initial condition f(0) = -1:

-1 / (-1) = 0²  + 2(0) + C

1 = C

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Therefore, the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1

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Answer:

24

Step-by-step explanation:

Answer:

14% or 105 students

Step-by-step explanation:

7/50 is equal to 105/750

Answer: 105

Step-by-step explanation: Take 105/750 (which is the answer) and divide that by 1 and you will get 7/50.  

Answer:

3 series I believe

Step-by-step explanation:

7-4=3 this is what I got I believe it's right

The values of w typically vary, on average, from the mean of the distribution about 3.46.

The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

For a geometric(p = 0.25) distribution, the variance is computed here as:

Var(X) = (1 - p)/ p2 = (1 - 0.25) / 0.252 = 12

Therefore, the standard deviation is computed as:

= ✓(12) = 3.46 observations.

This is the standard deviation of the given distribution here.

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\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the concept of growth rate.

Answer is D. 1.002

Since, it has power t for the growth rate to increase.

To find the consumer's and producer's surplus, we need more information about the demand and supply functions or the market equilibrium.

You provided the demand function D(x) = 25, but we require additional details to proceed with the calculations. The consumer's surplus is the difference between the maximum price consumers are willing to pay and the price they actually pay. It represents the benefit or surplus gained by consumers in a market transaction.

The producer's surplus is the difference between the minimum price producers are willing to accept and the price they actually receive. It represents the benefit or surplus gained by producers in a market transaction.

To calculate these surpluses, we typically need information about the supply function, equilibrium price, and equilibrium quantity. These values help determine the areas of the consumer's and producer's surpluses on the supply-demand graph.

Please provide the necessary information about the supply function, equilibrium price, or any other relevant details so that I can assist you in calculating the consumer's and producer's surplus accurately.

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Answer:

(x + 4)^2 + (y - 1)^2 = 61.

Step-by-step explanation:

We need to find the square of the radius and the coordinates of the center.

Center = (-10 + 2)/2 , (-4 + 6)/2

= (-4, 1).

Length of the diameter

=  √((-10-2)^2 + (-4-6)^2)

= √(144 + 100)

=√244

So the radius = √244/2

and r^2 = 244/4 = 61,

So the equation of this circle is:

(x - (-4)^2 + (y - 1)^2 = 61

(x + 4)^2 + (y - 1)^2 = 61.

(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given coordinates of the diameter of circle are  (-10,-4) and (2,6)

Diameter=√(x₂-x₁)²+(y₂-y₁)²

x₂=2,x₁=-10, y₁=-4, y₂=6

Diameter=√(2-(-10))²+(6-(-4))²

=√(12)²+(10)²

=√144+100

=√244

We know that Radius=Diameter/2

R=√244/2

Squaring both sides

R²=244/4

R²=61

So the equation of this circle is:

(x - (-4)² + (y - 1)² = 61

(x + 4)²+ (y - 1)² = 61.

Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)

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The root mean square (RMS) speed of gas molecules is directly proportional to the square root of the Kelvin temperature.

Relationship between temperature (T) and the RMS speed (v) is given by:

v ∝ √T

If the Kelvin temperature doubles (2T), we can determine the change in the RMS speed as follows:

v2/v1 = √(2T1) / √T1

Simplifying:

v2/v1 = √2√T1 / √T1

= √2

Therefore, the ratio of the final RMS speed (v2) to the initial RMS speed (v1) is √2. In other words, when the Kelvin temperature of an ideal gas doubles, the RMS speed of the gas molecules increases by a factor of √2 or approximately 1.414.

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Refer to the photos taken.

The length of the rectangular painting is equal to 76 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of a rectangular painting is 4636 cm². The width of the painting is equal to 61 cm.

The length of the painting is calculated as,

Area of rectangle = Length x Width

4636 = Length x 61

Length = 4636 / 61

Length = 76 cm

The length is 76 cm for the rectangle.

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Answer:

lol......

.

..

............

There are existing infinite solutions for the given equation 12s + 1 = 3 ( 4s + 1) - 2.

Solving the equation,

12s + 1 = 3 ( 4s + 1) - 2

 12s + 1 = 12s + 3 -2

 12s + 1 equals to (=) 12s + 1

Bringing constant to one side of the equation and variables to the other side of the equation so that equation could be solved

+ 12s - 12s   =   +  1 -  1

        0        =      0

This shows that the given equation has infinite solutions because after solving it gives a solution where both sides are equal.

"

Complete question:

How many solutions exist for the given equation 2s + 1 = 3 ( 4s + 1) - 2?

"

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Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

Answer:

25 is the answer.

Step-by-step explanation:

Answer:

25 because 7 squared plus 24 squared is 625 then you find the square root which is 25.

Answer:

B. 14 and 15

hope this helps

have a good day :)

Step-by-step explanation:

the square root of 200 is 14.14213562 so it has to be between 14 and 15

Answer:

10 students love strawberries

Answer:

504.57

Step-by-step explanation:

452.75 + 210.00 - 43.18 - 115.00

I am going to assume "had a debit" means used the debit card.

Answer:

Step-by-step explanation:

20% tip on 52.22 is 10.44

52.22*0.2=10.44

I don't think he has enough to do it though

52.22+10.44=62.664

Answer: He doesn't have enough (2.66 dollars short) Max percentage: 14.9%

Step-by-step explanation:

If Rowan has $60 dollars and wants a 20% tip. He would need to multiply the restaurant bill by 6/5, of if easier 120%

$52.22 x 120% = 62.66 dollars.

62.66 - 60 = 2.66. Therefore, Rowan CANNOT pay off a 20% tip and has $2.66 short.

Now, if we wanted to calculate which percent he can pay at max we look at 60/52.22.

This will give us 1.14898. Because of this, we can determine what percent Rowan can pay at max. 1.14898 - 1 = 0.14898.

Therefore, converting to percent, he can pay 14.9%(rounded)

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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(a) There is no extreme value of A subject to the given constraint,

(b) For x = 0, y + z² ≤ 16.

y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.

For x = ±y, z = 4 - y².

y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.

When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.

Therefore, one should exclude the value of zero from the domain of the function or expression.

In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.

Let's find the partial derivatives of A with respect to x, y, and z.

∂A/∂x = 3

∂A/∂y = 2y - 2 = 2(y - 1)

∂A/∂z = 0

Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.

\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)

Substituting the values of the partial derivatives, we get:

\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)

The second and third equations are contradictory. So, under the given constraint, A has no extreme value.

In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.

Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.

We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.

2x = λ(2x),

2y = λ(1),

2z = λ(2z).

Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.

Substituting the values of x and λ from the first and second equations into the third equation, we get:

z = 4 - y² or z = 0.

Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:

Case 1: x = 0, y + z² ≤ 16.

So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.

Case 2: x = ±y, z = 4 - y².

So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.

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The tip of the shadow is moving at a rate of approximately 1.36 ft/s.

Definition of the rate?

In general terms, rate refers to the measurement of how one quantity changes in relation to another quantity. It quantifies the amount of change per unit of time, distance, volume, or any other relevant unit.

Rate can be expressed as a ratio or a fraction, indicating the relationship between two different quantities. It is often denoted using units, such as miles per hour (mph), meters per second (m/s), gallons per minute (gpm), or dollars per hour ($/hr), depending on the context.

To find the rate at which the tip of the shadow is moving, we can use similar triangles.

Let's denote:

Based on similar triangles, we have the following ratio:

\(\frac{(L + x)}{ x} = \frac{(H + h)}{ H}\)

Substituting the given values, we have:

\(\frac{(L + x)}{ x} = \frac{(6 + 16)}{ 6}=\frac{22}{6}\)

To find the rate at which the tip of the shadow is moving, we need to differentiate this equation with respect to time t:

\(\frac{d}{dt}[\frac{(L + x)}{ x}]= \frac{d}{dt}[\frac{22}{ 6}]\)

To simplify the equation, we assume that L and x are functions of time t.

Let's differentiate the equation with respect to t:

\(\frac{[(\frac{dL}{dt} + \frac{dx}{dt})*x-(\frac{dL}{dt} + \frac{dx}{dt})*(L+x)]}{x^2}=0\)

Simplifying further:

\((\frac{dL}{dt} + \frac{dx}{dt})= (L+x)*\frac{\frac{dx}{dt}}{x}\)

We know that \(\frac{dx}{dt}\) is given as 5 ft/s (the rate at which the man is walking towards the street light)

Now we can solve for \(\frac{dL}{dt}\), which represents the rate at which the tip of the shadow is moving:

\(\frac{dL}{dt}= (L+x)*\frac{\frac{dx}{dt}}{x}- \frac{dx}{dt}\)

Substituting the given values and rearranging the equation, we have:

\(\frac{dL}{dt}= (L+x-x)\frac{\frac{dx}{dt}}{x}\)

Substituting L = 6 feet, \(\frac{dx}{dt}\) = 5 ft/s, and solving for x:

\(x =\frac{22}{6}*L\\ =\frac{22}{6}*6\\ =22\)

Substituting these values into the equation for \(\frac{dL}{dt}\):

\(\frac{dL}{dt}=6*\frac{5}{22}\\=\frac{30}{22}\)

≈ 1.36 ft/s

Therefore, the tip of the shadow is moving at a rate of approximately 1.36 feet per second.

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Answer:

All shapes except the cone with 5in radius and 8in height

Step-by-step explanation:

Volume of the cylinder with radius 5in and height 8in is expressed as;

V = πr²h

V = 3.14*5²*8

V = 3.14*25*8

V = 628 square inches

The volume of the cylinder is greater than 500in³

Volume of the cone with radius 5in and height 24in is expressed as;

V = 1/3πr²h

V = 1/3*3.14*5²*24

V = 3.14*25*8

V = 628 square inches

The volume of the cone is greater than 500in³

Volume of the spheree with radius 5in is expressed as;

V = 4/3πr³

V = 4/3π(5)³

V = 4/3 * 3.14 * 125

V = 523.33 square inches

The volume of the sphere is greater than 500in³