HELP HELP HELP HELP I JUST NEED HELP FOR FINDING THE SLOPE

The given differential equation is y'' + 81y = {9t,63,0≤t≤7t>7}, y(0) = 0, y'(0) = 0.

The Laplace  transform of the given differential equation is:L{y''} + 81 L{y} = L{9t}For L{y''}, we haveL{y''} = s² Y(s) - s y(0) - y'(0) = s² Y(s)For L{9t},

we haveL{9t} = 9 L{t} = 9/s²

For the given initial conditions, we have y(0) = 0, y'(0) = 0

Substituting the above values, we get:s² Y(s) + 81 Y(s) = 9/s²Simplifying,

we get the following quadratic equation:s² Y(s) + 81 Y(s) - 9/s² = 0Multiplying by s²,

we get:s⁴ Y(s) + 81 s² Y(s) - 9 = 0

Solving the above quadratic equation for Y(s), we getY(s) = {-81 s² ± [81² + 4 * s⁴ * 9]^(1/2) } / 2s⁴

The solution for Y(s) will depend on the sign of the square root.Using partial fractions,

we can simplify the above expression to express Y(s) in terms of the inverse Laplace transform.

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add it and you will get 24 so pick D

Answer:

Step-by-step explanation:

2 x 36 ÷ 3 + 9 - 4

= 72 ÷ 3 + 9 - 4 (perform multiplication first)

= 24 + 9 - 4 (perform division)

= 29 (perform addition and subtraction)

Therefore, 2x36 ÷ 3 + 9 - 4 = 29.

Answer:

29

Step-by-step explanation:

2×36=72

72/3=24

24+9=33

33-4=29

Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Answer:

18 x 65/100 = 11.7

18 - 11.7 = $6.3

5^(-2) = (1/5)^(2) = 1/25

Answer:

K = -2

Step-by-step explanation:

K represents the y-intercept, which is where the line crosses the y axis. We can see from the y = -4x -2, that -2 is the y-intercept, because in y =  mx + b, b is the y -intercept.

~theLocoCoco

Answer:

X = 0, Y= -2

Step-by-step explanation:

Compare the x and y coordinate values

3x + 2y =-4_______(1)

2x - y = 2 ________(2)

Multiply the (2) with 2

4x - 2y = 4

and add the new equation to (1)

3x + 2y =-4

4x - 2y = 4

____________

7x = 0

X = 0

Substitute x value into (1)

3 *0 + 2y = -4

0 + 2y =-4

2y =-4

Y= -2

The likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%

When dealing with normally distributed data, we use the mean and standard deviation to determine the likelihood of certain events occurring. In this case, the mean weight of bags of cement is 53 with a standard deviation of 2.

To find the likelihood that a randomly selected bag has a weight greater than 50, we need to calculate the z-score for 50. The z-score tells us how many standard deviations away a particular value is from the mean.

z = (X - μ) / σ

where X is the value we're interested in (50), μ is the mean (53), and σ is the standard deviation (2).

z = (50 - 53) / 2 = -1.5

A z-score of -1.5 means that a weight of 50 is 1.5 standard deviations below the mean. To find the likelihood of a bag weighing more than 50, we can use a z-table or a calculator to find the area to the right of this z-score.

Looking up a z-score of -1.5, we find that the area to the left is approximately 0.0668, which means the area to the right (the likelihood of a bag weighing more than 50) is:

1 - 0.0668 = 0.9332

Thus, the likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%.

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Answer:

the expression is equal to 31

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Substitute x and y into the equation to get..

(3×7)-(-5×2)

21- -10

31

Hope this helps :)

Step-by-step explanation:

5u - 8 > 32

5u > 32 + 8

5u > 40

u > 40/5

u > 8

Answer:

f(-3) = -18

Step-by-step explanation:

f(x)=2x^3+4x^2, find f(-3); let's rewrite

f(x) = 2\(x^{3}\) + 4\(x^{2}\); substitute -3 for x

f(-3) = 2\((-3)^{3}\) + 4\((-3)^{2}\); do the exponents

f(-3) = 2(-27) + 4(9); multiply and add

f(-3) = -54 + 36 = -18

The value of the function  f(x) = 2x³ + 4x² at f(-3) is - 18.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 2x³ + 4x².

Now, The value of the function f(-3) can be obtained by replacing

x with - 3.

Therefore, f(-3) = 2(-3)³ + 4(-3)².

f(-3) = 2×-27 + 4×9.

f(-3) = - 54 + 36.

f(-3) = - 18.

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Answer:

m∡BCA = 57°

Step-by-step explanation:

find 'x' by adding all expressions and setting them equal to 360°

9x+1 + tx+12 + 10x-37 = 360

24x = 384

x = 16

Substitute 16 into 10x-37

160 - 37 = 123

m∡BCA is supplemental with 123°, therefore it measures 57°

The 90% confidence interval is (2.76, 4.84).

The standard deviation is a measure of the amount of variation or dispersion of a set of values.  A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation may be abbreviated SD and is most commonly represented in mathematical texts and equations by the lower-case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Mean \($(\overline{\mathbf{x}})\) =3.8, sample standard deviation \($(\mathrm{s})\) =1.8, sample size     \($(\mathrm{n})\) = 10

since population standard deviation \($(\sigma)$\) is unknown and the value of \($\mathrm{n}$\) is less than 30, use. \($\mathrm{t}$\) - distribution

degrees of freedom =10-1=9

for 90% confidence level with degrees of freedom = 9

\($t_{\frac{\alpha}{2}}=1.833\) (from t- table)

formula: confidence interval for population mean. \($\mu=\bar{x} \pm t_{\frac{\alpha}{2}} *\left\{\frac{s}{\sqrt{n}}\right\}$\)

= 3.8 ± 1.833×\(\left\{\frac{1.8}{\sqrt{10}}\right\}$\)

= 3.8 ± 1.04

= (3.8 - 1.04, 3.8 + 1.04)

= (2.76, 4.84)

Therefore, the 90% confidence interval is (2.76, 4.84).

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Answer: Its the last one trust me

Step-by-step explanation:

Answer:

okffxddg you can see the attached file is scanned

The 10(x - x₁) - (y - y₁) - 7(z - z₁) = 0, or 10x - y - 7z = 10x₁ - y₁ - 7z₁. We can write this equation as:10x - y - 7z - 10x₁ + y₁ + 7z₁ = 0or10(x - x₁) - (y - y₁) - 7(z - z₁) = 0Thus, the equation of the plane is 10(x - x₁) - (y - y₁) - 7(z - z₁) = 0, where (x₁, y₁, z₁) is the given point.

Given the line (x - 1) / 10 = y + 5 = (z + 7) / -7, we need to find the equation of the plane passing through a given point and is perpendicular to the line. This line can be written in vector form as r = (1, -5, -7) + t(10, -1, -7).We know that a plane passing through a point (x₁, y₁, z₁) and perpendicular to the line with direction ratios a, b, c has the equation a(x - x₁) + b(y - y₁) + c(z - z₁) = 0.So, let's find the direction ratios of the given line by comparing it with the standard equation of a line. We get:10x - 1 = y + 5 = -7zTherefore, the direction ratios of the line are 10, -1, and -7. Let the point through which the plane passes be (x₁, y₁, z₁). Since we know the direction ratios of the line, the normal to the plane will be the vector n = 10i - j - 7k. The equation of the plane is, therefore, 10(x - x₁) - (y - y₁) - 7(z - z₁) = 0, or 10x - y - 7z = 10x₁ - y₁ - 7z₁. We can write this equation as:10x - y - 7z - 10x₁ + y₁ + 7z₁ = 0or10(x - x₁) - (y - y₁) - 7(z - z₁) = 0Thus, the equation of the plane is 10(x - x₁) - (y - y₁) - 7(z - z₁) = 0, where (x₁, y₁, z₁) is the given point.

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Answer:

1/5

Step-by-step explanation:

Answer:1/2

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

I search it up

Answer:

0.345 thats the answer

Answer:

B. 3.45

I hope it helps you

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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Answer:

C) 115 degrees

Step-by-step explanation:

A line is 180 degrees.

This means that the other side of the line with an angle of 115 degrees will be 180-115=65 degrees.

The angle above that will be 115 and the other will be 65.

Line v is similar to line u. This means that it is 115 degrees because the question mark is at the spot that is 115 degrees in the above angles.

Answer: a

Step-by-step explanation:

i just did the quiz:))

Answer:

Step-by-step explanation:

The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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Answer:

XM = 7

Step-by-step explanation:

M is the midpoint of XY , thus

XM = MY ( given XY is 7 ) , then

XM = 7

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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The circumference and area of a circle with diameter 6 inches are as follows;

Circumference = 18.84 inches.

Area = 28.26 in².

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, we have the following radius;

C = 3.14 × 6

C = 18.84 inches.

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circle = πr²

Area of a circle = 3.14(6/2)²

Area of a circle = 28.26 in².

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To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

d

Step-by-step explanation:

Answer:

b

Step-by-step explanation: