help me pls ASAP I need it in 5mins​

y(t) = 2t^2 - 12t + 16 for 0 ≤ t ≤ 2, and y(t) = 0 otherwise, using both methods of integrating the convolution.

To determine and plot y(t) = x(t) * h(t), where * represents convolution, using the given waveforms, we can use two methods: (a) integrating the convolution analytically and (b) integrating the convolution graphically.

(a) Integrating the convolution analytically:

The convolution of two functions f(t) and g(t) is given by the integral of the product of the two functions over all possible values of the variable t:

f(t) * g(t) = ∫ f(τ)g(t-τ) dτ

where τ is a dummy variable of integration.

Using this formula, we can compute y(t) = x(t) * h(t) as follows:

y(t) = ∫ x(τ)h(t-τ) dτ

= ∫ x(τ)h(2-t-τ) dτ (since h(t) is non-zero only for 0 ≤ t ≤ 2)

= ∫ x(τ)h(2-t)h(τ-t+2) dτ (using the time reversal property of h(t))

= h(2-t) ∫ x(τ)h(τ-t+2) dτ (since h(2-t) is constant w.r.t τ)

= 2(2-t) ∫ 2(τ-t+2) dτ (since x(t) is constant w.r.t τ and h(τ-t+2) is zero outside the interval [t-2, t])

= (2-t) [τ^2-2tτ+8τ] from τ=0 to τ=2-t

= 2t^2 - 12t + 16 for 0 ≤ t ≤ 2

= 0 otherwise

(b) Integrating the convolution graphically:

To integrate the convolution graphically, we can plot x(t) and h(t) on the same graph and slide h(t) along the t-axis, multiplying it with x(t) at each value of t and adding up the products to obtain y(t).

From the given waveforms, we can plot x(t) and h(t) on the same graph as follows:

x(t) is a rectangular pulse of width 1 and amplitude 2, centered at t=0.5.

h(t) is a triangular pulse of base width 2 and peak amplitude 1, centered at t=1.

Now, we slide h(t) along the t-axis and multiply it with x(t) at each value of t as shown in the attached image. At t=0, h(t) and x(t) do not overlap, so their product is zero.

At t=1, h(t) and x(t) overlap partially, so we multiply x(t) with the overlapping part of h(t) and obtain a trapezoidal pulse of amplitude 2.

At t=2, h(t) and x(t) overlap completely, so we multiply x(t) with h(t) and obtain a triangular pulse of amplitude 2.

Adding up the products at each value of t, we obtain y(t) as shown in the attached image. The resulting waveform is a piecewise linear function of t, with maximum amplitude 4 and zero outside the interval [0, 2].

In summary, we have obtained the same result, y(t) = 2t^2 - 12t + 16 for 0 ≤ t ≤ 2, and y(t) = 0 otherwise, using both methods of integrating the convolution.

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Answer:

m<ADC = 107

Step-by-step explanation:

You need to know three things to solve this problem.

1) Opposite angles of an inscribed quadrilateral are supplementary.

2) The measure of an inscribed angle is half the measure of its subtended arc.

3) The sum of the measures of all the arcs of a circle is 360 deg.

From 1) we get:

m<A + m<C = 180

72 + m<C = 180

m<C = 108

From 2) we get:

m<C = (1/2)m(arc)BAD

108 = (1/2)[m(arc)AB + m(arc)AD]

216 = m(arc)AB + 122

m(arc)AB = 94

From 3) we get:

m(arc)AB + m(arc)BC + m(arc)CD + m(arc)DA = 360

94 + 120 + m(arc)CD + 122 = 360

m(arc)CD = 24

From 2) we get:

m<ADC = (1/2)m(arc)ABC

m<ADC = (1/2)[m(arc)AB + m(arc)BC]

m<ADC = (1/2)[94 + 120]

m<ADC = 107

Note that if the pattern (arithmetic progression) continues, in the 6th diagram there will be 64 crosses. (Option C)

Each term in the   sequence is obtained by multiplying the previous term   by 2.

The expression   for the nth term of this arithmetic progression canbe written as  -

aₙ = a₁ * r⁽ⁿ⁻¹⁾

Where  -

aₙ is the nth term

a₁ is the first term (2 in this case)

r is the common ratio (2 in this case)

n is the position of the term in the sequence

So, the expression for the nth term in this progression is:

aₙ = 2 * 2⁽ⁿ⁻¹⁾

For n = 6, substituting the value into the expression

a₆ = 2 * 2⁽⁶⁻¹⁾

= 2 * 2⁵

= 2 * 32

= 64

Therefore, the number of crosses in the 6th diagram is 64. (Option C)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

No

Step-by-step explanation:

By multiplying each ratio by the second number of the other ratio, you can determine if they are equivalent.

Answer:

7x(3c)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

7 more then, start with +7. 3 multiplied by c is 3c. Therefore, it would be 7+3c

Answer:

D

Step-by-step explanation:

as you can see its decreasing

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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There is no unique combination of x₁w₁ + x₂w₂ + x₃w₃ that gives the zero vector with x1 = 1. The vectors w1, w2, and w3 are linearly independent.

The three vectors lie in a three-dimensional space (3D). The matrix W with these three columns is not invertible because it has linearly dependent columns, which means its determinant is zero.

To find a combination of the vectors that gives the zero vector, we can set up the following equation:

\(x₁w₁ + x₂w₂ + x₃w₃ = 0\)

Given that x1 = 1, we can rewrite the equation as:

\(1 × [1 2 3] + x₂ × [4 5 6] + x₃ × [7 8 9] = 0\)

Expanding the equation, we get:

\([1 2 3] + x₂ × [4 5 6] + x₃ × [7 8 9] = [0 0 0]\)

This equation can be expressed as three separate equations:

\(1 + 4x₂ + 7x₃ = 0 ---- (Equation 1)\\2 + 5x₂ + 8x₃ = 0 ---- (Equation 2)\\3 + 6x₂ + 9x₃ = 0 ---- (Equation 3)\)

To determine the values of x₂ and x₃, we can solve this system of linear equations. Let's solve it using the method of elimination:

Subtracting Equation 1 from Equation 2, we get:

\((2 + 5x₂ + 8x₃) - (1 + 4x₂ + 7x) = 0\)

Simplifying, we have:

1 + x₂ + x₃ = 0 ---- (Equation 4)

Now, subtracting Equation 1 from Equation 3:

\((3 + 6x₂ + 9x₃) - (1 + 4x₂ + 7x₃) = 0\)

Simplifying, we have:

2 + 2x₂ + 2x₃ = 0 ---- (Equation 5)

We have obtained a system of two equations:

Equation 4: 1 + x₂ + x₃ = 0

Equation 5: 2 + 2x₂ + 2x₃ = 0

Let's solve this system:

From Equation 4, we can express x₃ in terms of x₂:

x₃ = -1 - x₂

Substituting this into Equation 5:

\(2 + 2x₂ + 2(-1 - x₂) = 0\)

Simplifying:

\(2 + 2x₂ - 2 - 2x₂ = 0\\0 = 0\)

The equation 0 = 0 is always true, which means there are infinitely many solutions for x₂ and x₃.

Therefore, there is no unique combination of x₁w₁ + x₂w₂ + x₃w₃ that gives the zero vector with x₁ = 1. The vectors w₁, w₂, and w₃ are linearly independent.

The three vectors lie in a three-dimensional space (3D). The matrix W with these three columns is not invertible because it has linearly dependent columns, which means its determinant is zero.

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The complete question goes thus:

Find a combination x1w1 + x2w2 + x3w3 that gives the zero vector with x1 = 1:

w1 = [1 2 3], w2 = [4 5 6], w3 = [7 8 9]

Those vectors are (independent) (dependent). The three vectors lie in a _____. The matrix W with those three columns is not invertible.

To view the representation of graph of check the attached image.

Given that ;

Stewart's overdue assignment = 36

Per day he complete 4 overdue assignments.

To find : In how many days he complete all the overdue assignments

To complete 36 overdue assignments = 36/4

                                                                = 9 days

Therefore, In 9 days he complete all the overdue assignments

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Answer:  650 miles

Step-by-step explanation:

If it takes 5 hours to go from Paris to Geneva and a train is travelling at 130 miles per hour then multiply the total number of miles per hour by 5 to find how many miles you will have to travel from Paris to Geneva.

130 * 5 =  650

Explanation:

A quadrilateral has four sides, and each side is a straight line.

Quad = 4

Lateral = side

This means we go for choices A and C.

Choice B is ruled out because of the curved side on the right.

Choice D is ruled out because it has 5 sides instead of 4.

Answer:

c + s = 12

or

11c + 15s = 148

where c is the number of new york cheese sold and s is the number of strawberry cheesecake sold

Step-by-step explanation:

We want to give one equation that we can get from the information above

Let the number of the new york cheese cake be c while the number of the strawberry cheese cake sold be s

A total 12 was sold:

So:

c + s = 12

Let’s now work with the prices;

11c + 15s = 148

The flux of the vector field F = -xz i - yz j + z² k through the surface S, which is the cone z = √(x² + y²) for 0 ≤ z ≤ 9, oriented upward, can be computed by evaluating the double integral:

Flux = ∫[0,2π]∫[0,9] (r² cos(u) + r² sin(u) + r³) r dr du.

To compute the flux of the vector field F = -xz i - yz j + z² k through the surface S, which is the cone

z = √(x² + y²) for 0 ≤ z ≤ 9, oriented upward, we can use the surface integral formula:

Flux = ∬S F · dS

where F is the vector field, dS is the outward-pointing unit normal vector to the surface S, and ∬S represents the surface integral over S.

To proceed with the calculation, we first need to parameterize the surface S in terms of two variables, typically denoted as u and v. In this case, we can use cylindrical coordinates:

x = r cos(u)

y = r sin(u)

z = r

where r is the radius, and u varies from 0 to 2π.

Next, we calculate the partial derivatives of x, y, and z with respect to u and v:

∂x/∂u = -r sin(u)

∂y/∂u = r cos(u)

∂z/∂u = 0

∂x/∂v = 0

∂y/∂v = 0

∂z/∂v = 1

Now, we can calculate the cross product of the partial derivatives ∂r/∂u and ∂r/∂v:

∂r/∂u x ∂r/∂v = (-r sin(u) i + r cos(u) j) x k

                = -r sin(u) i x k + r cos(u) j x k

                 = -r cos(u) i - r sin(u) j

The magnitude of this cross product is √(r² cos²(u) + r² sin²(u)) = r.

Now, we calculate the dot product F · (∂r/∂u x ∂r/∂v):

F · (∂r/∂u x ∂r/∂v) = (-xz i - yz j + z² k) · (-r cos(u) i - r sin(u) j)

                     = xr cos(u) + yr sin(u) + z² r

Since z = r, we can simplify further:

Flux = ∬S F · dS = ∬S xr cos(u) + yr sin(u) + r³ dA

To evaluate this integral, we integrate over the surface S with respect to the parameters u and r:

Flux = ∫[0,2π]∫[0,9] (r² cos(u) + r² sin(u) + r³) r dr du

Integrating this expression will yield the flux of the vector field F through the surface S.

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Answer:

25.71 (2 d.p)

Step-by-step explanation:

\(.\)

Answer:

Step-by-step explanation:

12,787

a. ^p^ represents the proportion of adults who chose chocolate pie, ^q^ represents the proportion of adults who did not choose chocolate pie, n represents the sample size, E represents the margin of error, and p represents the population proportion.

b. The value of α for a 99.99% confidence level is 0.0001.

a. ^p^ represents the sample proportion of adults who chose chocolate pie, ^q^ represents the proportion of adults who did not choose chocolate pie (1 - ^p^), n represents the sample size of 1500, E represents the margin of error of ±3 percentage points (0.03), and p represents the population proportion of adults who choose chocolate pie.

b. To find the value of α for a 99.99% confidence level, we need to subtract the confidence level from 100% to get the level of significance, which is 0.0001. This means that there is a 0.0001 probability of rejecting the null hypothesis when it is actually true.

The level of significance (α) is used to determine the critical value for the test statistic, which is then used to determine whether or not to reject the null hypothesis.

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Answer: 14 cars.

Step-by-step explanation:

A car can be washed with : 100/11 oz.

1 gallon=128 oz.

Hence,

\(\displaystyle\\\frac{128}{\frac{100}{11} } =\frac{128*11}{100} =\frac{1408}{100} =14,08\ (cars).\)

The total number of cars that can be washed with 1 gallon of soap if 100oz Can wash 11 cars would be given as 14 cars

To determine how many cars can be washed with 1 gallon of soap, we need to find the ratio between the amount of soap used and the number of cars washed.

Given that 100 oz of soap can wash 11 cars, we can set up the following proportion:

100 oz soap / 11 cars = 1 gallon soap / x cars

I gallon is given as 128 OZ

Such that we have

128 x 100 / 11

= 14.08 cars

Hence the total number of cars would be given as 14 cars

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Hey there!

5x - 6y - 3a

= 5(-2) - 6(3) - 3(-4)

= -10 - 18 - 12

= -28 - (-12)

= -28 + 12

= -16

Therefore, your answer is: -16

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The expression of (f+g)(x) from the functions  f(x)=−2x2+4x and g(x)=3x+3 is (f+g)(x) = (-2x^3+7x^2 +3x ).

From the question we were given the functions that is expected to be simplified as :

f(x)=−2x^2+4x

g(x)=3x+3

And we were told to find the function  (f+g)(x) which can be written as :

(f+g)(x) = [(−2x^2+4x )+(3x+3)]x

This can be further expressed as :

(f+g)(x) = (-2x^2+4x +3x+3 )x

This can be further simplified as :

(f+g)(x) = (-2x^2+7x+3 )x

This can be further simplified as :

(f+g)(x) = (-2x^3+7x^2 +3x )

Therefore, the expression of the function (f+g)(x) is (f+g)(x) = (-2x^3+7x^2 +3x ).

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The missing part:

Find (f+g)(x).

Answer:

x = -72

Step-by-step explanation:

-72 + 8 = -64

The third square root of -64 is -4

Answer:

I am not sure but

Step-by-step explanation:

try to use to website https://www.symbolab.com/solver/pre-algebra-calculator

you can chose what your learning and it gives you the right answer. make sure you put the numbers in correctly. if you don't it will mess every thing up for that problem. That one reason I have a B in math cuz i use that site for my math. and it shows you how to do it with steps

please give me a heart if the site really helps you guys :)

The best definition of SST is:

(C) The total amount of variation in the y variable.

The total sum of squares (SST) is a measure of the total variation in a data set. It represents the total amount of deviation of each data point from the mean of the data set.

The total sum of squares can be broken down into two components: explained variation and unexplained variation. The explained variation is the part of the total sum of squares that can be attributed to the influence of one or more variables on the response variable.

The sum of squares total, denoted SST, is the squared differences between the observed dependent variable and its mean. You can think of this as the dispersion of the observed variables around the mean – much like the variance in descriptive statistics.

The correct option is (C)

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Answer:

\(3x^2+7x+4\)

Step-by-step explanation:

Using FOIL (First, outer, inner, last)

First, we multiply 3x and x to get \(3x^2\) (First)

We then multiply 3x and 1 to get \(3x\) (outer)

Then 4 and x to get \(4x\) (Inner)

Then multiply 1 and 4 to get \(4\) (last)

Since the quadratics are all positive, we add all the terms together to get:

\(3x^2+3x+4x+4\). Since 3x and 4x are like terms, we add them together and simplify to get:

\(3x^2+7x+4\)

And since we can't simplify any further, that's our answer!

Hope this helps :D

Answer:

\(3x^{2} +7x+4\)

Step-by-step explanation:

To simplify the double bracket, you can use a Foil method ( you can search it to see detailed explanation )

(3x + 4 )( x + 1)

\(3x^{2} +7x+4\)

Hope that is right, ask any questions if unsure :)

The graph that represents the function f(x) = 4[x] is option C.

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4 [x]

[x] is the greatest integer function.

We see that,

f(0) = 4 [0] = 0

f(0.5) = 4 [0.5] = 4 x 0 = 0

f(x) = 0 for 0 ≤ x < 1

f(1) = 4 [1] = 4

f(1.5) = 4 [1.5] = 4 x 1 = 4

f(x) = 4 for 1 ≤ x < 2

f(2) = 4 [2] = 4 x 2 = 8

f(2.5) = 4 [2.5] = 4 x 2 = 8

f(x) = 8 for 2 ≤ x < 2

Thus,

The graph on option C has the required coordinates.

f(x) = 0 for 0 ≤ x < 1

f(x) = 4 for 1 ≤ x < 2

f(x) = 0 for 2 ≤ x < 2

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Answer:

8.277

Step-by-step explanation:

Pretty simple, just add up the values but convert the word form into decimals.

\(6+2.2+0.033+0.044=8.277\)

Also, your question said 33 thousandths, so it is what I answered.

Answer:

8.277

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

37 = 96 %

x  = 100%

\(x =\frac{37(100)}{96} =38.54= 39\)

\(\huge\boxed{39\ \text{students}}\)

Note: The numbers in this problem are a little weird and don't work out perfectly. I'll demonstrate at the end of this answer how something seems a little off in the problem, but we'll get as close as possible.

We know from the problem that 37 students are equal to 96% of the class.

Let's write this as an equation:

\(37=0.96x\)

Divide both sides of the equation by \(0.96\) to isolate \(x\).

\(38.54\approx x\)

We'll round this to \(39\) as the final answer.

It's important to note that you can't have partial students, only whole numbers.

If we do the math here, 37 out of 39 students is about 95%.
Also, 37 out of 38 is about 97%.

I'm not sure how the original writer of the question got 96%, but I suppose 39 is the best answer with what's been given.

The third option is the correct option.

The equation in slope point form is given as y-1= -1(x-4).

A equation which is satisfied by every point on the line is known as equation of the line. There are various method to find the equation of lines, such as two point form, slope point form, slope intercept form.

We are given two points (4,1) (-2,7)

We first find the slope of the line which is the ratio of change in y to the change in x

Slope = (7-1)/-2-4)

Slope = 6/-6

Slope = -1

Hence the equation can be given as

y - = m(x-)

Substituting the values, we get the equation as

y - 1 = -1(x-4)

The third option is the correct option

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The recursive rule for the sequence in the graph is aₙ = aₙ₊₁ + 4

Recursive rule are the rules that continually takes a previous number and changes it to get to a next number.

It gives first term or terms of sequence and describes how term is related to previous term with an equation.

Looking at the graph ,

taking first two point  ,n = 1 and n = 2

At n = 1 , a(n) = 13

At n = 2 , a(n) = 9

so , 9 = 13 - 4

we can write it as,

a₂ = a₁ - 4

Hence , recursive formula for sequence :

aₙ₊₁ = aₙ - 4

bring aₙ to the left

=>  aₙ = aₙ₊₁ + 4 is required recursive formula

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Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

In hypothesis testing, if the null hypothesis is rejected, it means that there is sufficient evidence to support the alternative hypothesis. A null hypothesis is a statement that there is no significant difference or relationship between variables, while the alternative hypothesis states that there is a significant difference or relationship. To determine if the null hypothesis is true or not, we conduct a statistical test and calculate the p-value. If the p-value is less than the level of significance, usually set at 0.05, we reject the null hypothesis and accept the alternative hypothesis. Therefore, the correct answer is that the evidence supports the alternative hypothesis. This means that we have found significant results that support our research hypothesis.
Keep in mind that rejecting the null hypothesis does not prove the alternative hypothesis, but it does suggest that it's more plausible based on the data collected.

Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

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