Plz HELP with a and b I WILL MARK AS A BRAINLIEST IF YOU CAN HELP ME WITH BOTH A AND B PLZZ

The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.

1. Identify the exact differential equation.

2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).

3. Multiply the integrating factor with the equation to make it exact.

4. Integrate both sides of the equation to obtain the general solution.

5. Check the solution by differentiating it to confirm that it satisfies the original equation.

6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.

The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.

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To determine the size of carpets that will maximize the company's revenue, we need to find the dimensions that will generate the highest total sales. Let's analyze the situation step by step.

We know that the company can sell 200 carpets per week when the size is 3ft by 3ft. Beyond this size, for each additional foot of length and width, the number sold decreases by 4.

Let's denote the additional length and width beyond 3ft as x. Therefore, the dimensions of the carpets will be (3 + x) ft by (3 + x) ft.

Now, we need to determine the relationship between the number of carpets sold and the dimensions. We can observe that for each additional foot of length and width, the number sold decreases by 4. So, the number of carpets sold can be expressed as:

Number of Carpets Sold = 200 - 4x

Next, we need to calculate the revenue generated from selling these carpets. The price per square foot is $5, and the area of the carpet is (3 + x) ft by (3 + x) ft, which gives us:

Revenue = Price per Square Foot * Area

= $5 * (3 + x) * (3 + x)

= $5 * (9 + 6x + \(x^2)\)

= $45 + $30x + $5\(x^2\)

Now, we can determine the dimensions that will maximize the revenue by finding the vertex of the quadratic function. The x-coordinate of the vertex gives us the optimal value of x.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a = $5 and b = $30.

x = -30 / (2 * 5)

x = -30 / 10

x = -3

Since we are dealing with dimensions, we take the absolute value of x, which gives us x = 3.

Therefore, the additional length and width beyond 3ft that will maximize the revenue is 3ft.

The dimensions of the carpets that the company should sell to maximize its revenue are 6ft by 6ft.

To calculate the maximum weekly revenue, we substitute x = 3 into the revenue function:

Revenue = $45 + $30x + $\(5x^2\)

= $45 + $30(3) + $5(\(3^2)\)

= $45 + $90 + $45

= $180

Hence, the maximum weekly revenue for the company is $180.

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SOLUTION

Since the house decreased by 15%, the value of this in dollars becomes

Which is

Hence the house value decreased by $39,150

The current value of the house becomes

Hence the current value is $221,850

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

1) y=1/8x+2

2) y=1/35x+100

Step-by-step explanation:

Answer: 15/2

Step-by-step explanation: -5/2 + 1/4W = -5/8

-    1/4W = -5/8 + 5/2

-    1/4W = 15/8

-     W = 15/8 × 4

-      W = 15/2

The required area of the shaded perimeter is given as 28 square units.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
As shown in the figure the shaded part is a parallelogram,
The area of the parallelogram is given as = base × height
Substitute the value in the above equation,
Area = 4sin45 × 7 / sin45  [since base / 4 = sin45 and 7 / height = sin45]
Area = 4/√2 × 7 / [1 / √2]
Area = 28

Thus, the shaded perimeter's needed area is specified as 28 square units.

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A sufficient estimator is the distributions of exponential.The correct answer to this question is (c) exponential.

An estimator is a rule or procedure that is used to determine an estimate of a parameter based on observed data. A statistic is used to estimate a parameter, and it is computed from the observed data. An estimator is a random variable that computes a statistic from the data.

The following distributions have a sufficient estimator:

Poisson Distribution with parameters λ and x is a Poisson distribution.

The rate of the occurrence is λ.

Exponential Distribution with parameters λ and x is an exponential distribution.

The mean waiting time is 1/λ.

Bernoulli The Bernoulli distribution is not sufficient for an estimator, but the binomial distribution, which generalizes the Bernoulli distribution, is. In the context of the binomial distribution, p is a parameter Exponential

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, such as the amount of time until the next vehicle arrives at a traffic intersection or the amount of time a particular component lasts in a manufacturing process.

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Answer:

k = -3

Step-by-step explanation:

f(x) = x + 4

g(x) = -3x - 12

Plug this in for g(x) = k*f(x)

[NOTE: the dot *  is a multiplication sign]

-3x -12 = k(x+4)        divide by x-4 on both sides

-3 = k                        we're done!

I think it’s z=1 hope this helps

Answer:

z=-1

Step-by-step explanation:

-2(4z-4)=10-6z

First, distribute the -2 into the parenthesis to get:

-8z+8=10-6z

Then, add 8z to each side to eliminate it from the left side to get:

8=10+8z-6z

Simplify the right side and combine the z's:

8=10+2z

Subtract 10 from BOTH sides to get:

-2=2z

Finally, to get z alone, divide everything by 2 to get:

-1=z or z=-1

Answer:

24 / 3

8 x 50

53 x 7

Answer:

2:5 is the ratio in this situations

Step-by-step explanation:

There are 2 blueberry bars, and 5 cherry.

Answer:

Step-by-step explanation:

Answer:

30c + 6 i believe

Step-by-step explanation:

Step-by-step explanation:

It is so simple Hope u understand

Answer:

Step-by-step explanation:

Sum = -5

Product = 2*(-3) = -6

Factors = -6 , 1   {-6 + 1 = -5  & -6 *1 = -6}

2m² - 5m -3 = 0

2m² - 6m + m -3 = 0

2m(m - 3) + (m -3) = 0

(m -3)(2m + 1) = 0

m - 3 =  0    or 2m + 1 = 0

    m = 3      or 2m = -1

                          m = -1/2

Ans: m = 3 , (-1/2)

Answer:

Step-by-step explanation:

1) 2.094  <  2.702

2) 10.09 < 10.9

5) 24.552 = 24.522

6) 21.337 > 21.31

The surface area of one slipcover for the topiary, excluding the base, is approximately 2.4 square meters when x = 0.75 meters.

To approximate the surface area of one slipcover, we need to consider the shape and dimensions of the topiary. Without specific information about the shape of the topiary, we can assume a simplified shape, such as a cylinder or cone.

Given that the slipcover does not cover the base of the topiary, we can assume that the slipcover covers the sides only. If we consider the shape as a cylinder, the surface area of the slipcover would be the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height.

Since the information provided only mentions x = 0.75 meters, it is not clear which dimension represents the radius or height. However, assuming x represents the height of the topiary, we can estimate the radius as x/2. Therefore, the surface area would be approximately 2π(x/2)(x) = πx^2.

Plugging in x = 0.75 meters, the surface area of one slipcover would be approximately 3.14 * (0.75)^2 = 2.65 square meters. Rounded to the nearest tenth, the approximate surface area of one slipcover would be 2.4 square meters.

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Average number of goals = 2.8

From the question, we have

Average  =  total number of matches/ total number of goals

​=(4×0+10×1+5×2+9×3+7×4+5×5+6×1+7×2)/43

​=120/43

=2.79=2.8

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.

This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

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we have the equation of the line

y=3x+1

Create a table of values

assume different values of x and calculate the value of y

Step-by-step explanation:

since they are in order points p and q are in the middle and points O and R are on the end so they say that OR=36 since you don't know the exact lengths of all of the lengths in the middle from O to R then you multiply 5,6 and 1 by x and add

5x+6x+1x=12x

so then the whole length is equal to the ratio of 12x and also 36 so set those to equal each other

12x=36

x=3

so that is just the ratio and since they are asking for the length of O to Q that means that it is just 5x+6x=OQ

11x=OQ

insert x=3

33=OQ

Hope that helps :)

The planet that has the larger mass is the planet B and the measurements in standard forms are

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

Planet A = 5*10^26 kilograms

Planet B = 2*10^28 kilograms

Rewrite the masses properly

So, we have

Planet A = 5*10²⁶ kilograms

Planet B = 2*10²⁸ kilograms

The exponent 28 is greater than the exponent 26

This means that

2*10²⁸ is greater than 5*10²⁶

So, we have

Planet B has the larger mass

When the measurements are expressed in standard forms, we have

Planet A = 500000000000000000000000000 kilograms

Planet B = 20000000000000000000000000000 kilograms

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Minimum sample size to satisfy manufacturer requirements is 2401.

The sample size is defined as the number of observations used for determining the estimations of a given population. The size of the sample has been drawn from the population. The number of entities in a subset of a population is selected for analysis.

Given,

Margin of error m = 0.02

for Confidence interval = 95% , Z - value = 1.96

Sample size n = Z²p(1 – p)/m²

p is the proportion of population (generally taken as 0.5),

m is the margin of error.

n = (1.96)²× 0.5(1 - 0.5)/(0.02)²

n = (1.96)²× 0.5(0.5)/(0.02)²

n = 2401

Hence, 2401 is the smallest sample size.

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Answer:

Step-by-step explanation:

98°,100°

Answer:

a. 43

Step-by-step explanation:

This question is asking how much candy he had initially.

This means that t = 0 days

Thus anything to the power of 0 is just 1.

Hence: 43 x 1 = 43 candies

Answer:

Step-by-step explanation:

Let's call the angle of elevation of the sun "θ". We want to find the value of θ.

First, we can find the length of the part of the flagpole that is casting the shadow by using trigonometry. We can define:

h = height of the flagpole above the ground

d = length of the shadow

α = angle of inclination of the flagpole (which is the same as the angle between the ground and the sun's rays, since the flagpole is vertical)

Then, we can use the tangent function to relate these variables:

tan(α) = h/d

Rearranging, we get:

h = d tan(α)

We know that the height of the flagpole is 25 feet, and the length of the shadow is 12 feet. So:

25 = 12 tan(α)

Solving for tan(α), we get:

tan(α) = 25/12

Now we can use the inverse tangent function (also called arctangent) to find α:

α = tan^(-1)(25/12)

α ≈ 65.14 degrees

This is the angle between the ground and the sun's rays, as seen from the flagpole. To find the angle of elevation of the sun, we need to subtract α from 90 degrees (since the sun's rays are perpendicular to the ground). So:

θ = 90 - α

θ ≈ 24.86 degrees

Therefore, the angle of elevation of the sun is approximately 24.86 degrees.

The maximum walking speed of a giraffe with a leg of 6 feet is approximately 1.41 times greater than that of a hippopotamus with a leg of 3 feet.

The equation given in the problem, S= square root of gL, represents the maximum walking speed S of an animal with a leg of length L. To find the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet, we can plug in the values of g and L for each animal and calculate the ratio.

For the giraffe: S = √(g6) = √(326) ≈ 9.8 ft/sec

For the hippopotamus: S = √(g3) = √(323) ≈ 5.7 ft/sec

So the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet is approximately 9.8/5.7 ≈ 1.72 or 1.41 to the nearest hundredth.

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