The function y=sin x + cos x is a solution to which differential equation a. Y+dy/dx =2sinx, b. Y+dy/dx=2cosx or c. dy/dx-y=-2sinx?

Answer:

1/2 + 1/4 = 2/4 + 1/4 = 3/ 4

first box = 2

last box= 3/4

Answer:

For every gallon of gas added to the tank, the buyer is charged $2.35

The constant of proportionality of the given equation y = 2.35x will be 2.35.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Let's x ∝ y

Then x = ky where k will be constant of proportional.

k = x/y which means when two variables are divided which were in proportion it will create a constant proportional.

So,

y /x = 2.35 will be constant of propotional.

Hence "The constant of proportionality of the given equation y = 2.35x will be 2.35".

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Answer: If you like your best friend, you should explain to him/her that you like him/her. If you don’t want to do this, then keep a close eye on them and detect whether they like you back like if they treat you with more kindness than you usually receive.

Step-by-step explanation: Activity: Give them different topics and see if they answer in a way that is different from how they would answer someone else.

Answer:B.Sample space

Step-by-step explanation:

Answer:

To find the input (value of x) for which the output is 20, we need to solve the given equation: -3 + 5x = 4x - 5.

Let's solve this equation step by step:

-3 + 5x = 4x - 5

To isolate the x terms on one side, we can subtract 4x from both sides:

-3 + 5x - 4x = 4x - 4x - 5

Simplifying:

x - 3 = -5

Now, to isolate x, we can add 3 to both sides:

x - 3 + 3 = -5 + 3

Simplifying:

x = -2

Therefore, the input (value of x) for which the output is 20 is x = -2.

None of the options provided (A. 55, B. -15, C. -5, D. 35) match the solution x = -2. It seems that the given options do not include the correct answer. I recommend discussing this discrepancy with your teacher or referring to the textbook/materials for further clarification.

Answer:

A = 64 pi

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

The radius is 8

A = pi * 8^2

A = 64 pi

The standard deviation of a numerical data set measures the variability of the data. It is a widely used measure in statistics that helps to determine how spread out the values are within a given data set.

By calculating the standard deviation, we can better understand the range and distribution of values in the data set, as well as identify potential outliers. This measure is particularly important in fields such as finance, science, and engineering, where understanding the variability in data can be crucial for making informed decisions and predictions. So, the most appropriate term that makes the statement true is D: variability.

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Answer:

10

Step-by-step explanation:

plz mark as brainliest

Answer:

10

Step-by-step explanation:

Given:

The two sides of a triangle are 2 and 6.

To find:

The side length that would NOT work to make a triangle with the two slide lengths of 2 and 6.

Solution:

For a triangle, the sum of two smaller sides must be greater than the largest side.

Let x be the third side.

Case 1: x is the largest side, then

\(2+6>x\)

\(8>x\)              ...(i)

Case 2: x is not the largest side, then

\(2+x>6\)

\(x>6-2\)

\(x>4\)              ...(ii)

From (i) and (ii), we get

\(4<x<8\)

Here, 4 and 8 are not included.

6, 5, 7 are included in the above interval, but 4 is not included in the above interval. It means 4 would NOT work to make a triangle with the two slide lengths of 2 and 6.

Therefore, the correct option is D.

Therefore, the derivative of the function y = e * tan(θ) is y\(' = (e^tan(θ)) * (sec^2(θ)).\)

To find the derivative of the function y = e * tan(θ), we can use the chain rule.

Let u = tan(θ), and \(v = e^u.\) Then, the function can be rewritten as y = v.

Now, let's find the derivatives of u and v with respect to θ:

\(du/dθ = sec^2(θ)\)

\(dv/du = e^u\)

Next, we can apply the chain rule:

dy/dθ = (dv/du) * (du/dθ)

Substituting the expressions for du/dθ and dv/du:

\(dy/dθ = (e^u) * (sec^2(θ))\)

Since u = tan(θ), we can substitute back:

\(dy/dθ = (e^tan(θ)) * (sec^2(θ))\)

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We have shown that \(\(S^2/n\)\) is an unbiased estimator of the variance of the sample mean when\(\(X_i\)\) are independent and identically distributed (i.i.d.) with mean \(\(\mu\) and variance \(\sigma^2\).\)

To show that \(\(S^2/n\)\)is an unbiased estimator of the variance of the sample mean when\(\(X_i\)\) are independent and identically distributed (i.i.d.) with mean\(\(\mu\)\) and variance \(\(\sigma^2\),\) we need to demonstrate that the expected value of \(\(S^2/n\)\) is equal to \(\(\sigma^2\).\)

The sample variance, \(S^2\), is defined as:

\(\[S^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})^2\]\)

where\(\(\bar{X}\\)) is the sample mean.

To begin, let's calculate the expected value of \(\(S^2/n\):\)

\(\[\begin{aligned}E\left(\frac{S^2}{n}\right) &= E\left(\frac{1}{n} \sum_{i=1}^{n} (X_i - \bar{X})^2\right)\end{aligned}\]\)

Using the linearity of expectation, we can rewrite the expression:

\(\[\begin{aligned}E\left(\frac{S^2}{n}\right) &= \frac{1}{n} E\left(\sum_{i=1}^{n} (X_i - \bar{X})^2\right)\end{aligned}\]\)

Expanding the sum:

\(\[\begin{aligned}E\left(\frac{S^2}{n}\right) &= \frac{1}{n} E\left(\sum_{i=1}^{n} (X_i^2 - 2X_i\bar{X} + \bar{X}^2)\right)\end{aligned}\]\)

Since \(\(X_i\) and \(\bar{X}\)\) are independent, we can further simplify:

\(\[\begin{aligned}E\left(\frac{S^2}{n}\right) &= \frac{1}{n} E\left(\sum_{i=1}^{n} X_i^2 - 2\sum_{i=1}^{n} X_i\bar{X} + \sum_{i=1}^{n} \bar{X}^2\right)\end{aligned}\]\)

Next, let's focus on each term separately. Using the properties of expectation:

\(\[\begin{aligned}E(X_i^2) &= \text{Var}(X_i) + E(X_i)^2 \\&= \sigma^2 + \mu^2 \\&= \sigma^2 + \frac{1}{n} \sum_{i=1}^{n} \mu^2 \\&= \sigma^2 + \frac{1}{n} n \mu^2 \\&= \sigma^2 + \frac{1}{n} n \mu^2 \\&= \sigma^2 + \frac{1}{n} \sum_{i=1}^{n} \mu^2 \\&= \sigma^2 + \frac{1}{n} \sum_{i=1}^{n} \mu^2 \\&= \sigma^2 + \mu^2\end{aligned}\]\)

Since\(\(\bar{X}\)\)is the average of \(\(X_i\)\), we have:

\(\[\begin{aligned}\bar{X} &= \frac{1}{n} \sum_{i=1}^{n} X_i\end{aligned}\]\)

Thus, \(\(\sum_{i=1}^{n} X_i = n\bar{X}\)\), and substit

uting this into the expression:

\(\[\begin{aligned}E\left(\frac{S^2}{n}\right) &= \frac{1}{n} E\left(\sum_{i=1}^{n} X_i^2 - 2n\bar{X}^2 + n\bar{X}^2\right) \\&= \frac{1}{n} E\left(n \sigma^2 + n \mu^2 - 2n \bar{X}^2 + n \bar{X}^2\right) \\&= \frac{1}{n} (n \sigma^2 + n \mu^2 - n \sigma^2) \\&= \frac{1}{n} (n \mu^2) \\&= \mu^2\end{aligned}\]\)

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Answer: 3.69

Step-by-step explanation: by multiplying 24.60 by 0.15 for the tip the tip is 3.69

The magnitude of the resultant force is approximately 119.89 pounds, and the direction angle is approximately S12.2°W.

To solve the problem, we can use vector addition.

Let F1 be the vector representing the first force, and F2 be the vector representing the second force. Then, we can find the resultant force R by adding the two vectors:

R = F1 + F2

To add two vectors, we need to resolve them into their x and y components. Let's do that first.

For F1:

Magnitude = 80 pounds

Direction = S58°E

To resolve F1 into its x and y components, we can use trigonometry:

Fx1 = 80 cos 58° = 42.57 pounds (east)

Fy1 = 80 sin 58° = 68.13 pounds (south)

For F2:

Magnitude = 50 pounds

Direction = N76°E

To resolve F2 into its x and y components, we can again use trigonometry:

Fx2 = 50 cos (180° - 76°) = -16.92 pounds (east)

Fy2 = 50 sin (180° - 76°) = 48.76 pounds (north)

Note that we used (180° - 76°) for the angle because the direction is N76°E, which means it is 76° east of due north.

Now we can add the x and y components separately:

Rx = Fx1 + Fx2 = 42.57 - 16.92 = 25.65 pounds (east)

Ry = Fy1 + Fy2 = 68.13 + 48.76 = 116.89 pounds (south)

To find the magnitude and direction of the resultant force, we can use trigonometry again:

Magnitude = sqrt(Rx^2 + Ry^2) = sqrt(25.65^2 + 116.89^2) = 119.89 pounds (rounded to the nearest hundredth)

Direction angle = atan(Rx/Ry) = atan(25.65/116.89) = 12.2° (rounded to the nearest tenth)

The direction angle is approximately S12.2°W, and the resultant force has a magnitude of about 119.89 pounds.

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Answer:

Step-by-step explanation:

Given:

Solution

As per midpoint formula;

Converting 7π/21 to degrees will be 60°.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees. Although it is not a SI unit—the radian is the SI unit of angular measure—it is mentioned as an accepted unit in the SI brochure.

Angles are measured in terms of radians. Angles are measured using the degree and radian units. In calculus and the majority of other branches of mathematics, angles are typically or generally measured in radians.

It should be noted that in order to convert radians yo degrees, you've to multiply by 180/π since a full circle is 360°.

This will be illustrated as:

= 7π / 21 × 180 / π

= 7/21 × 180

= 60°

The value is 60°.

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Answer:

5000

Step-by-step explanation:

100 × 50

5000

Answer:

1 , 2

Step-by-step explanation:

Since 0.506 is a decimal, any whole number would be greater.

Answer- 33

We are told that A=6, there for we can right out our equation fully.

(5 x 6)+3. Our multiplication sentence with go in parentheses ( ) so we know to do that part of our equation first.  5 times 6 is 30. After we multiply we add our outside number(s). 30 plus 3 is 33. Which means the solution to the equation is 33.

5a +3= 33 or (5x6) +3 = 33

Hope this helps! and GOOD LUCK.

If the length of a rectangle is nine inches more than its width and its area is 442 square inches, the width of the rectangle is 17 inches and its length is 26 inches.

Let's denote the width of the rectangle as "w" and its length as "l". From the problem statement, we know that:

l = w + 9 (since the length is nine inches more than the width)

The area of the rectangle is given by the formula:

A = l * w

Substituting in the expression for "l" in terms of "w", we get:

A = (w+9) * w

Simplifying, we get a quadratic equation:

w^2 + 9w - 442 = 0

We can solve this equation by factoring or using the quadratic formula. Factoring gives:

(w+26)(w-17) = 0

Therefore, the possible values for "w" are -26 and 17. However, since the width of the rectangle cannot be negative, we can eliminate -26 as a possible value. Thus, the width of the rectangle is 17 inches.

Using the expression for "l" in terms of "w", we can find the length:

l = w + 9 = 17 + 9 = 26 inches

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Answer:

33 pi

Step-by-step explanation:

113.1/2 = 56.55

56.55 + 47.12 = 103.67

103.67/ pi = 33

Answer:

1. 12

2. 0

3. 9

Step-by-step explanation:

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

3/12 = 2/8

Step-by-step explanation:

The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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Answer:

I can't see it the picture is not clean or close enough but it's in the bottom left

Answer:

No solutions.

Step-by-step explanation:

Problem:

Solve y−4x=−3;y=4x+7

Steps:

I will solve your system by substitution.

y=4x+7;−4x+y=−3

Step: Solve y=4x+7 for y:

Step: Substitute 4x+7 for y in −4x+y=−3:

−4x+y=−3

−4x+4x+7=−3

7=−3(Simplify both sides of the equation)

7+−7=−3+−7(Add -7 to both sides)

0=−10

Answer:

No solutions.

Answer:

  No solutions

Step-by-step explanation:

It is easiest to determine whether the equations are consistent by putting both of them in the same form.

The equation on the left is in "standard form." The one on the right is in "slope-intercept form." We can rewrite either one of them to put it into the other form.

Rewriting the left equation to slope-intercept form, we have ...

  y = 4x -3 . . . . . . . add 4x to both sides

Comparing this to the right equation ...

  y = 4x +7

we see that the slopes are the same, and the intercepts are different. These equations describe parallel lines. Parallel lines can never meet, so cannot have any point in common. The equations are inconsistent and have no solution.

Rewriting the right equation to standard form, we have ...

  y -4x = 7 . . . . . . . subtract 4x from both sides

Comparing this to the left equation ...

  y -4x = -3

we see that the coefficients are the same, but the constants are different. There can be no values of x and y that will satisfy both equations. Any values that make the terms have one sum cannot also make them have a different sum.

There are no solutions.

The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

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The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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