PLEASE HELP WILL GIVE 30 POINTS

The solution to the initial value problem y" + 4y + 13y = 0, with initial conditions y(π/2) = 0 and y'(π/2) = 6, is y(t) = 3sin(2t) + 2cos(2t). As t approaches infinity, the solution oscillates with decreasing amplitude.

To find the solution of the initial value problem y" + 4y + 13y = 0, we can assume a solution of the form y(t) = e^(rt) and substitute it into the equation. This leads to the characteristic equation r^2 + 4r + 13 = 0. Solving this quadratic equation, we find that the roots are complex numbers: r = -2 ± 3i.

Since the roots are complex, the general solution is of the form \(y(t) = e^{-2t}(c_{1} cos(3t) + c_{2} sin(3t))\)

. Applying the initial conditions y(π/2) = 0 and y'(π/2) = 6, we can solve for the coefficients c1 and c2.

By substituting the given values, we find that c1 = 2 and c2 = 3. Therefore, the solution to the initial value problem is y(t) = 3sin(2t) + 2cos(2t).

As t approaches infinity, the solution oscillates with decreasing amplitude. This is because the exponential term e^(-2t) approaches zero, while the trigonometric terms sin(2t) and cos(2t) continue to oscillate but with decreasing magnitude. Hence, the solution approaches a constant value, exhibiting exponential decay to a constant.

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Credit To: "lublana" On Brainly For This Answer

Answer:

Given that one time charge of appartment "a" = $100

Given that monthly rent of appartment "a" = $400

say the number of months = x

then total cost of the rent for apartment "a" = 100+400x

Given that one time charge of appartment "b" = $500

Given that monthly rent of appartment "b" = $350

then total cost of the rent for apartment "b" = 500+350x

Now we have to make an inequality so that number of months it would take for the total paid to be less for apartment b.

that means 100+400x is less than 500+350x

Hence required inequality is 100+400x<500+350x.

Now we have to solve this inequality.

400x-350x<500-100

50x<400

divide both side by 50

x<8

hence final answer is number of months should be less than 8.

Answer:

True

Step-by-step explanation:

false

Step-by-step explanation:

Answer:

i think B

Step-by-step explanation:

because if we think logically...the price have to more than 10-28.All answer except B are illogical for me i think

hope its help

Answer:

it's the 2md option

_

because if you would calculate them and solve it would be something greater than 10

Gretal paid $7680 on tax in 2018.

"A percentage is a ratio of a number to 100. The symbol % is used to indicate a percentage."

Given

Earning = 32000

Tax paid = 24%

Amount paid on tax = \(32000\) × \(\frac{24}{100}\)

= $7680

Hence, she paid $7680 on tax.

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Answer:

Step-by-step explanation:

Given a transversal crossing parallel lines and supplementary angles (x+8°) and (2x-5°), you want to find the measures of angles L and O, supplementary to each of these.

Where a transversal crosses parallel lines, consecutive interior angles are supplementary. Using the given expressions, this means ...

  (x +8°) +(2x -5°) = 180°

  3x +3° = 180° . . . . . . . . . simplify

  x +1° = 60° . . . . . . . divide by 3

  x = 59°  . . . . . . subtract 1°

Then the acute angle is ...

  x+8° = 59° +8° = 67°

and the obtuse angle is ...

  2x -5° = 2(59°) -5° = 113°

Angle L corresponds to angle (2x-5°), so is congruent:

  ∠L = 113°

Angle O is an alternate interior angle with respect to angle (x+8°), so is congruent:

  ∠O = 67°

Answer:

decimal 0.13

percent is 13

Step-by-step explanation:

Answer:

Decimal: 13

Percent: 13%

Step-by-step explanation:

Sorry if it wrong

The coordinates of the image of triangle P'Q'R' after a rotation, translation, and reflection are (-4, -1), (-3, -3), and (-2, 0).

In Mathematics, rotating a point 90° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (y, -x).

By applying a rotation of 90° clockwise to triangle PQR, the coordinate of the image of triangle P'Q'R' is given by:

(x, y)                           →               (y, -x)

Points at P = (-4, 4)   →  Points at P' = (4, -(-4)) = (4, 4)

Points at Q = (-2, 3)   →  Points at Q' = (3, -(-2)) = (3, 2).

Points at R = (-5, 2)   →  Points at R' = (2, -(-5)) = (2, 5).

Next, we would translate the coordinates of the image of triangle P'Q'R' 5 units down:

Points at P' = (4, 4) = (4, (4 - 5)) = (4, -1)

Points at Q' = (3, 2) = (3, (2 - 5)) = (3, -3)

Points at R' = (2, 5) = (2, (5 - 5) = (2, 0).

Lastly, we would reflect the coordinates of the image of triangle P'Q'R' across the y-axis:

(x, y)                  →       (-x, y)

Points at P' = (4, -1) = (-4, -1)

Points at Q' = (3, -3) = (-3, -3)

Points at R' = (2, 0) = (-2, 0).

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Complete question :

Select the correct answer from each drop-down menu.

Use the given expression to complete the statements.

5x - 8(3y + 13) - 1

In the first term, 5 is a

In the second term (3y + 13) is a

In the third term. -1 is a

Answer:

Kindly check explanation

Step-by-step explanation:

Given the expression : 5x - 8(3y + 13) - 1

In the first term :

5 a Coefficient, which is the numerical value which exists before and multiplying a variable usually in an algebraic expression. Hence since 5 exists before the variable x, then 5 is the Coefficient of x.

(3y + 13) is a factor in the expression 8(3y + 13), it was used to get a simplified form of the initial expression 24y + 104

-1 is a constant term in the algebraic expression as it has no variable attached to it

Given expression to complete the statements.

Given the expression : 5x - 8(3y + 13) - 1

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Answer:

c

Step-by-step explanation:

Answer:3/10

Step-by-step explanation:

x is 1/6 so 3 * x is 3/6. 3/6 - 1/5 is 15/30 - 6/30 = 9/30. then simplify so the answer is 3/10.

Answer: C. It illustrates the resistance of the median.

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Step-by-step explanation:

The line representing the equation 7x1 + 4x2 = 28 goes through the points (4,0) and (0,7).

The value of k for the function f(x+3) = f((x-3) + 3) is 2 by simplifying the function and substituting the values.

Let's substitute x-3 for x in the given function: f(x+3) = f((x-3) + 3) = f(x).

Then, we can rewrite the given function as f(x) = (x-3)² + k(x-3) - 21.

To find the value of k, we can set x=0 and solve for k: f(0) = (0-3)^2 + k(0-3) - 21 = -12 + 3k - 21 = 3k - 33.

We know that f(0) = f(3-3) = f(-3), so we can also calculate f(-3) using the given function:

f(-3+3) = f(0) = 0² + k(0) - 21 = -21.

Setting f(-3) = -21, we get:

-21 = (-3)² + k(-3) - 21, which simplifies to k = 2.

Therefore, the value of k is 2.

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The given expression is sec cot csc tan.

To find the simplest form of this expression, let's break down each trigonometric function:

1. sec(theta) is equal to 1/cos(theta).
2. cot(theta) is equal to 1/tan(theta), which is the same as cos(theta)/sin(theta).
3. csc(theta) is equal to 1/sin(theta).
4. tan(theta) is equal to sin(theta)/cos(theta).

Now, substituting these values into the original expression, we get:

sec cot csc tan = (1/cos(theta)) * (cos(theta)/sin(theta)) * (1/sin(theta)) * (sin(theta)/cos(theta))

We can simplify this expression by canceling out common factors. The cos(theta) in the numerator of the second term and the denominator of the fourth term cancel out, as do the sin(theta) in the denominator of the second term and the numerator of the third term.

After canceling out these common factors, we are left with:

sec cot csc tan = 1/sin(theta)

So, the simplest form of the expression sec cot csc tan is 1/sin(theta).

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What is the simplest form of the expression below? cot(theta) cos(theta)/sin(theta)*tan(theta) divided by sin(theta)/cos(theta) tan(theta)

Given the image of the situation: Image text: A person is standing at point A looking up to the top of a radar tower located at point B. The distance from point A to point B is 150 feet. Angle 4 is formed by the horizontal line and the line from the person to the top of the radar tower.

Angle 4 is also formed by the horizontal line and the line from the top of the radar tower to the person. What is the description of angle 4 as it relates to the situation below?

The description of angle 4 as it relates to the situation below is: angle 4 is the angle of elevation from the person to the radar tower (a).Explanation: An angle of elevation is the angle formed by a horizontal line and a line of sight that is directed upward.

Therefore, in this situation, Angle 4 is the angle of elevation from the person to the radar tower. Angle 4 is the angle between the line of sight from the person to the top of the radar tower and the horizontal line drawn through the person.

Hence, the answer is option (a). Therefore, option (a) is the correct description of angle 4 as it relates to the situation in the given image.

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The solution for question a is -2.00. The solution for question b is  0.6687. The solution for question c is 10 students. We can show the working in the following manner.

a. What is the probability of completing the exam in one hour or less (to 4 decimals)?

To answer this question, we need to convert the time of one hour (60 minutes) to a z-score using the mean and standard deviation provided. We have:

z = (60 - 80) / 10 = -2.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in one hour or less is approximately 0.0228, rounded to 4 decimal places.

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?

To answer this question, we need to find the probability of completing the exam in less than 75 minutes and subtract the probability of completing the exam in less than 60 minutes. We have:

z1 = (60 - 80) / 10 = -2.00

z2 = (75 - 80) / 10 = -0.50

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in less than 75 minutes is approximately 0.6915 and the probability of completing the exam in less than 60 minutes is approximately 0.0228, as calculated in part a.

So, the probability of completing the exam in more than 60 minutes but less than 75 minutes is approximately:

0.6915 - 0.0228 = 0.6687, rounded to 4 decimal places.

c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

To answer this question, we need to find the number of students whose exam time is greater than 90 minutes, which is the maximum time allowed. We can use the normal distribution with the given mean and standard deviation to calculate this.

First, we need to find the z-score corresponding to a time of 90 minutes:

z = (90 - 80) / 10 = 1.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in more than 90 minutes is approximately 0.1587.

Therefore, the expected number of students who will be unable to complete the exam in the allotted time is:

60 x 0.1587 = 9.52, which rounds up to 10 students (to the next whole number).

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No, the maximum demand for bracelets will not be met if the store produces the optimal number of bracelets and necklaces. This is because the optimal solution is determined by the store’s profit, which is contingent on the cost of production and the demand for the product.

The optimal number of bracelets and necklaces produced is the point where the cost of production is minimized while the demand for the product is maximized. In this case, the optimal solution will not be enough to meet the maximum demand for bracelets.

If the store does not produce any bracelets, the resulting profit from the necklaces will depend on the demand for necklaces. If the demand is high enough, the store could make a higher profit from necklaces than if it were to produce bracelets.

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Answer:

by using the formula hypotension(h) is ? base(b) is 8 and perpendicular(p) is15

h=rootunder( p²+b²)

h=(8)²+(15)²

h=289

Yes, the expression; y = x³ is a function because it passes the vertical line test.

Discussion:

By definition, a function from a set x to a set y assigns to each element of x exactly one element of y.

On this note, the set containing all possible values of x is called the domain of the function and the set y is called the co-domain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

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George needs to sail close to 3.7 miles from Paradise Island to reach Shipwreck Rock.

Applying  the law of cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where:

c = the unknown distance

a = 3.7 miles (distance from the dock at the mainland to Paradise Island)

b = 5.6 miles (distance from the dock at the mainland to Shipwreck Rock)

C = 72 degrees (angle formed between the dock at the mainland and Shipwreck Rock)

The we convert the angle from degrees to radians:

72 degrees = (72/360) * 2π radians = 1.2566 radians (approx.)

Substituting  the values into the formula and solving  for c:

c^2 = 3.7^2 + 5.6^2 - 2(3.7)(5.6)cos(1.2566)

c^2 = 13.69

c ≈ 3.7 miles

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Answer:

Step-by-step explanation:

First of all cross multiply

That's

g( wd + f ) = a + bc

Multiply the terms at the left side of the equation

We have

gwd + fg = a + bc

Send fg to the right side of the equation

That's

gwd = a + bc - fg

Divide both sides by dg to make W stand alone

We have the final answer as

Hope this helps you

Answer:

2.0

Step-by-step explanation:

This question has 3 parts: subject (distance), and numbers (5.1 and 3.1).

Distance means subtraction. Between means to 5.1 and 3.1 .

So 5.1 - 3.1 = 2.0

Answer:

difference is 12 units

Step-by-step explanation:

line shown has a y-intercept of -4

now find y-intercept of f(x) by first finding its slope:

(-2,0) and (2,-32)

m = (0+32)/(-2-2)

m = 32/-4

m = -8 (slope)

Now find the y-intercept (or 'b') from substituting into 'y=mx+b':

0 = (-2)(-8) + b

0 = 16 + b

-16 = b (y-intercept)

-16 - (-4) = -12

The expression for y" is (-x/7y) multiplied by (7x² - 7y²) / (49y³).

We start by differentiating both sides of the equation x² + 7y² = 7 with respect to x using the chain rule.

On the left-hand side, we have:

d/dx(x²) + d/dx(7y²) = d/dx(7)

The derivative of x² is 2x. To differentiate 7y², we use the chain rule and get:

d/dx(7y²) = 7 * 2y * dy/dx

The derivative of a constant is zero, so the right-hand side is simply zero. Therefore, our equation becomes:

2x + 14y(dy/dx) = 0

Next, we can use algebraic manipulation to solve for dy/dx, which represents the first derivative of y with respect to x:

dy/dx = -2x/14y = -x/7y

Finally, we differentiate this expression with respect to x to find the second derivative of y:

d/dx(dy/dx) = d/dx(-x/7y)

Using the quotient rule, we get:

d/dx(dy/dx) = [(7y)(-1) - (-x)(dy/dx)(1)] / (7y)²

Substituting our expression for dy/dx, we get:

d/dx(dy/dx) = [(7y)(-1) - (-x)(-x/7y)(1)] / (7y)²

Simplifying this expression, we get:

d/dx(dy/dx) = (7x² - 7y²) / (49y³)

This is the expression for the second derivative of y with respect to x, or y".

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Complete Question:

Find Y" By Implicit Differentiation. Simplify Where Possible. x^2 + 7y^2 = 7

y" = -x/7y

Answer:

A.

Step-by-step explanation:

The formula for trying to find the area of a circle is Area= r^2

Sooo:

Area=3.14 x 18 x 18

18 x 18 is the first part of the equation

=324

Then:

3.14(pi) x 324 = 1017.36 = 1017 ft2