let y=x2 2x. compute δy and dy at x=3 if dx=0.2. what is the difference between δy and dy? that is, what is δy−dy?

The value of the integral is [tex](137/2) \sqrt(\pi).[/tex]

To determine the convergence of the integral, we can use the limit comparison test. We compare the given integral with the integral of a known function that has the same behavior for large values of x.

Let's choose the function [tex]f(x) = e^(^-^x^2).[/tex]

Then we have:

∫ from -∞ to ∞ 137x [tex]e^(^-^x^2)[/tex]dx ≤ ∫ from -∞ to ∞ [tex]e^-^x^2 dx[/tex]

To evaluate the integral on the right-hand side, we can use the fact that:

∫ from -∞ to ∞ [tex]e^-^x^2 dx[/tex] = [tex]\sqrt(\pi)[/tex]

Therefore, we have:

∫ from -∞ to ∞ 137x [tex]e^-^x^2 dx[/tex] ≤ [tex]\sqrt(\pi)[/tex]

Since [tex]\sqrt(\pi)[/tex] is a finite constant, the given integral is convergent.

To evaluate the integral, we can use integration by parts.

Let u = x and dv = 137 [tex]e^-^x^2 dx[/tex], so that du/dx = 1 and v = (-137/2) [tex]e^-^x^2 dx[/tex].

Then we have:

∫ from -∞ to ∞ 137x [tex]e^-^x^2 dx[/tex] = [-137x [tex]e^-^x^2^/^2 dx[/tex]] from -∞ to ∞ + ∫ from -∞ to ∞ (137/2) [tex]e^-^x^2 dx[/tex]

The first term evaluates to zero because [tex]e^-^x^2[/tex] goes to zero faster than x as x approaches infinity. Therefore, we have:

∫ from -∞ to ∞ 137x [tex]e^-^x^2dx[/tex] = (137/2)∫ from -∞ to ∞ [tex]e^-^x^2 dx[/tex]= [tex](137/2) \sqrt(\pi)[/tex]

Therefore, the value of the integral is [tex](137/2) \sqrt(\pi).[/tex]

Learn more about integral

brainly.com/question/30900582

#SPJ11

The area of the region is approximately 0.0204 square units.

To find the area of the region that is bounded by the curve r = e−θ/14 and lies in the sector between θ = 0 and θ = π/2, we need to integrate the equation for the area.

The equation for the area of a sector is A = 1/2 [tex]r^2[/tex] θ, where r is the radius and θ is the central angle in radians.

In this case, the radius r is given by r = e−θ/14 and the central angle θ is π/2 - 0 = π/2.

Therefore, the area of the region is:

A = 1/2 (e−π/28[tex])^2[/tex] π/2
A ≈ 0.0204 square units

So the area of the region bounded by the given curve and lying in the specified sector is approximately 0.0204 square units.

Learn more about area of curved region

brainly.com/question/31038846

#SPJ11

The value of the lograithm expression log(56) is 1.7482

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

log(56)

Applying the law of logarithm, we have the following equation

log(56) = log(56)/log(10)

Using a calculator in the above equation, so, we have the following representation

log(56) = 1.7482/1

Evaluate the quotient of 1.7482 and 1

So, we have the following representation

log(56) = 1.7482

Hence, the approximation is 1.7482

Read more about log at

brainly.com/question/28041634

#SPJ1

Answer:

880 square feet

Step-by-step explanation:

ik its not an option but i tried and got 880

If  f(x,y)=2/(x^2 + y^2) and u is the unit vector in the direction of 〈−2,0〉, then

(a) ∇f(x,y) = <-4x/(x^2+y^2)^2, -4y/(x^2+y^2)^2>

(b) ∇f(4,3) = <-16/169, -12/169>

(c) Duf(4,3) = 16/169.

(a) To find the gradient of f(x,y), we take the partial derivatives of f(x,y) with respect to x and y

∂f/∂x = -4x/(x^2+y^2)^2

∂f/∂y = -4y/(x^2+y^2)^2

Therefore, the gradient of f(x,y) is

∇f(x,y) = <∂f/∂x, ∂f/∂y> = <-4x/(x^2+y^2)^2, -4y/(x^2+y^2)^2>

(b) To find ∇f(4,3), we plug in x=4 and y=3 into the expression for ∇f(x,y) from part (a)

∇f(4,3) = <-4(4)/(4^2+3^2)^2, -4(3)/(4^2+3^2)^2> = <-16/169, -12/169>

(c) To find Duf(4,3), we need to take the directional derivative of f(x,y) in the direction of u=<-2,0>. The formula for the directional derivative is

Duf(4,3) = ∇f(4,3) · u

where · denotes the dot product. We already know ∇f(4,3) from part (b), so we just need to find the unit vector in the direction of u

|u| = sqrt((-2)^2 + 0^2) = 2

u-hat = u/|u| = <-2/2, 0/2> = <-1, 0>

Now we can compute the dot product

∇f(4,3) · u-hat = <-16/169, -12/169> · <-1, 0> = (-16/169) × (-1) + (-12/169) × 0 = 16/169

Therefore, Duf(4,3) = 16/169.

Learn more about directional derivative here

brainly.com/question/30365299

#SPJ4

I have solved the question in general, as the given question is incomplete.

The complete question is:

Suppose f(x,y)=2/(x^2 + y^2) and u is the unit vector in the direction of 〈−2,0〉. Then,

(a) ∇f(x,y)=

(b) ∇f(4,3)=

(c) Duf(4,3)=

Answer:

6 cars

Step-by-step explanation:

Each car wash=15$

Jake raised 90$, so the amount of cars he washed would be 90/15=6

Hope this helps!

Answer:

6

Step-by-step explanation:

this is because

if one car=$15

then how many cars would be=$90.

this will result us in ratio and proportion

if more then less divide ,

and we will get

90\15 × 1= 6

therefore Jake wash 6 cars for $90

To know about the product of symmetric matrices. I will provide proof for both the 2x2 and nxn cases.

Proof:
a) 2x2 symmetric matrices A and B:
Let A = |a, b|
         |b, c|
   B = |p, q|
         |q, r|
AB = |ap+bq, aq+br|
       |bp+cq, bq+cr|
BA = |ap+pq, bp+rq|
       |aq+bq, bq+cr|

To prove that AB is symmetric, we need to show (AB)ij = (AB)ji, where i and j are indices.
(AB)12 = aq+br and (AB)21 = bp+cq
(AB)12 = (AB)21 if aq+br = bp+cq
This is equivalent to AB=BA, which is the condition given.

b) nxn symmetric matrices A and B:

To prove that the product AB is symmetric, we need to show (AB)ij = (AB)ji.
(AB)ij = Σ Aik * Bkj (summing from k=1 to n)
(AB)ji = Σ Ajk * Bki (summing from k=1 to n)

Now, since A and B are symmetric matrices, we have Aik=Aki and Bkj=Bjk.
(AB)ij = Σ Aki * Bjk
(AB)ji = Σ Aki * Bjk

As we can see, (AB)ij = (AB)ji if and only if AB = BA.

In conclusion, for both the 2x2 and nxn cases, the product of two symmetric matrices A and B is a symmetric matrix if and only if AB = BA.

To learn more about “matrices” refer to the https://brainly.com/question/11989522

#SPJ11

The possible numbers of minutes Maria could add water is,

⇒ t > 5

We have to given that;

Maria's fish tank has 18 liters of water in it.

And, She plans to add 6 liters per minute until the tank has more than 48 liters.

Now, Let t represent the number of minutes.

Hence, We get;

⇒ 18 + 6t > 48

Solve for t;

⇒ 6t > 48 - 18

⇒ 6t > 30

⇒ t > 5

Thus, The possible numbers of minutes Maria could add water is,

⇒ t > 5

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ1

Rounding to the nearest whole number, we can estimate that approximately 308 students will score between 48 and 62.

To determine the number of students that are expected to score between 48 and 62, we first need to find the z-scores for these values using the formula:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

For x = 48:

z = (48 - 50) / 10 = -0.2

For x = 62:

z = (62 - 50) / 10 = 1.2

Using a standard normal distribution table, we can find the probability of a z-score between -0.2 and 1.2, which is 0.3849.

Finally, we can calculate the approximate number of students that will score between 48 and 62 by multiplying the probability by the total number of students:

Number of students = 0.3849 x 800 = 307.92

To learn more about distribution click on,

https://brainly.com/question/4573045

#SPJ4

Answer:

round

Step-by-step explanation:

its goes up then down like 2 halves of a circle in a 2d plane

Learn the unit circle to understand better, but basically its just a reformed circle that goes up and down on an  y = ? line on a graph.

Answer:

A C E are the correct statements.

A. The domain of log, is > 0

C. The range of log, is (-0, +00)

E. log 1-10

consider giving me an 5star of rating <3 and thanks if this helps u!

135

135 and 125 are odd numbers however, only 135 is a multiple of 3 and 5.

Answer:

(5 × 7 × 13) + (6 × 7 × 3) = 455 + 126

= 581 cubic cm

The first measurement, Response to treatment coded as 1=no response, 2=minor improvement, 3=major improvement, 4=complete recovery, is classified as ordinal. The second measurement is classified as continuous. The third measurement is classified as continuous. The fourth measurement is classified as ordinal. The fifth measurement is classified as categorical.

1. Classify this measurement as continuous, ordinal, or categorical: Response to treatment coded as 1=no response, 2=minor improvement, 3=major improvement, 4=complete recovery.
The correct option is B. ordinal

2. Classify this measurement as continuous, ordinal, or categorical: Annual income (pre-tax dollars).
The correct option is A. continuous

3. Classify this measurement as continuous, ordinal, or categorical: Body temperature (degrees Celsius).
The correct option is A. continuous

4. Classify this measurement as continuous, ordinal, or categorical: Grade in a course code: A, D, B, D, or F.
The correct option is B. ordinal

5. Classify this measurement as continuous, ordinal, or categorical: Course credit (pass or fail).
The correct option is C. Categorical

You can learn more about measurement at: brainly.com/question/30087426

#SPJ11

Due to chance variation, there is a significant difference between the section's average and the whole class's average. The number of tickets in the null box is 900, but the observed difference is too large to be attributed to chance alone.

To answer this question, we will perform a hypothesis test to determine if the low average of the TA's section is due to chance variation or if there is a significant difference between the section's average and the whole class's average.

Step 1: Define the null and alternative hypotheses
- Null hypothesis (H0): The TA's section's low average is due to chance variation.
- Alternative hypothesis (H1): The section's average is too low to be due to chance variation.

Step 2: Calculate the test statistic
In this case, we have the following data:
- Whole class average: 62
- Whole class standard deviation (SD): 18
- Section's average: 54
- Number of students in the section: 30

The test statistic (z-score) = (Section's average - Whole class average) / (SD / √Number of students)
z = (54 - 62) / (18 / √30) ≈ -2.49

Step 3: Determine the number of tickets in the null box
In the problem, it is mentioned that there are 900 tickets in the null box. To assess the null hypothesis, we will compare the z-score to the critical value corresponding to a significance level (e.g., α = 0.05).

Step 4: Compare the test statistic to the critical value
For a two-tailed test with α = 0.05, the critical value is approximately ±1.96. Since the calculated z-score (-2.49) is beyond the critical value, we reject the null hypothesis.

Learn more about Average:

brainly.com/question/24057012

#SPJ11

For a normally distributed random variable X with mean μ = 84 and standard deviation σ = 4, the probability P(X < 86) is 0.6915 or 69.15%.

To find the probability P(X < 86) for a normally distributed random variable X with mean μ = 84 and standard deviation σ = 4, we'll follow these steps:

Step 1: Standardize the variable
We need to convert the given value of X (86) into a standardized value called a z-score. The z-score represents how many standard deviations away from the mean the value is. Use the formula:
z = (X - μ) / σ
z = (86 - 84) / 4
z = 2 / 4
z = 0.5

Step 2: Use the z-score to find the probability
Now, we'll use a standard normal distribution table (Z-table) or a calculator with a built-in normal distribution function to find the probability corresponding to the z-score. The table or calculator will provide the probability P(Z < z) for a standard normal distribution with mean 0 and standard deviation 1.

Looking up the z-score of 0.5 in a Z-table or using a calculator, we get the probability:
P(Z < 0.5) = 0.6915

Step 3: Interpret the result
The probability P(X < 86) is the same as P(Z < 0.5), which we found to be 0.6915. This means that there is a 69.15% chance that a randomly selected value from the distribution will be less than 86.

In summary, for a normally distributed random variable X with mean μ = 84 and standard deviation σ = 4, the probability P(X < 86) is 0.6915 or 69.15%.

To know more about standard deviation refer here:

https://brainly.com/question/12402189

#SPJ11

The equation that provides evidence of determining the best spot to build a fire station, illustrated by taking into account the towns and cities within 5 miles, would be: b. (x+3)² + (y+1)² = 25

This equation shapes a circle with a size of five units in radius with its center nestled at coordinates (-3,-1).

Postulating any city situated in or tantalizingly near this circumference would remain within the five-mile distance from the fire department. The others equations do not portray circles that have central points providing maximum coverage of settlements located within a 5-unit range.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

Each spoonful holds 500 milligrams of cocoa.

To find the amount of cocoa in each spoonful, we can divide the total amount of extra cocoa added (4 grams) by the number of spoonfuls used (8):

4 grams / 8 spoonfuls = 0.5 grams per spoonful

To convert this to milligrams, we can multiply by 1000:

0.5 grams * 1000 = 500 milligrams

Therefore, each spoonful holds 500 milligrams of cocoa.

Read more on unit rate here https://brainly.com/question/4895463

#SPJ1

An increase in the cost of a variable input shifts the​ average total cost curve upward. The correct answer is B. Only i is correct.

An increase in the cost of a variable input, such as labor or raw materials, will cause an increase in the marginal cost (MC) of producing each additional unit of output, because more money is needed to purchase the inputs required to produce each unit.

This increase in marginal cost will not, by itself, shift the marginal cost curve upward, since it only represents a movement along the curve.

However, this increase in marginal cost will cause the average total cost (ATC) curve to shift upward. The reason for this is that average total cost is calculated as total cost divided by the quantity produced.

As the marginal cost of each unit increases, the total cost of producing each unit also increases. This causes a higher total cost to be divided among the same quantity produced, leading to a higher average total cost.

Thus, an increase in the cost of a variable input shifts the average total cost curve upward, but does not shift the marginal cost curve.

The correct answer is B. Only i is correct.

To learn more about cost curve click on,

https://brainly.com/question/14244662

#SPJ4

The sine function for this problem is given as follows:

y = 2sin(x) - 2.

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The function varies between -4 and 0, for a difference of 4, hence the amplitude is given as follows:

A = 4/2

A = 2.

The function varies between -4 and 0, instead of between -2 and 2, for a vertical shift of -2, hence the coefficient C is given as follows:

C = -2.

The period of the function is of 2π, which is the shortest distance between consecutive repetitions of the function, hence the coefficient B is given as follows:

B = 1.

Thus the function is:

y = 2sin(x) - 2.

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The general solution to the given differential equation is:

y = [tex]9xe^x[/tex]+ [tex]Ce^x[/tex], where C is a constant.

The given differential equation is:

y' - y = [tex]9e^x[/tex]

This is a linear first-order differential equation. We can solve it using the method of integrating factors.

First, we find the integrating factor:

μ(x) = [tex]e^∫(-1)[/tex]dx = [tex]e^(^-^x^)[/tex]

Multiplying both sides of the equation by μ(x), we get:

[tex]e^(^-^x^)y' - e^(^-^x^)y[/tex] = 9

The left side is the product rule of ([tex]e^(^-^x^)[/tex]y):

d/dx ([tex]e^(^-^x^)[/tex]y) = 9

Integrating both sides with respect to x, we get:

[tex]e^(^-^x^)[/tex]y = 9x + C

where C is the constant of integration.

Multiplying both sides by [tex]e^x[/tex], we get:

y = [tex]9xe^x[/tex] + [tex]Ce^x[/tex]

Therefore, the general solution to the given differential equation is:

y = [tex]9xe^x[/tex]+ [tex]Ce^x[/tex], where C is a constant.

Learn more about Differential equation

brainly.com/question/14620493

#SPJ11

The number of minutes that it will take to remove all at the same time is: 60 minutes

Given that:

- The scones bake for 15 minutes, the muffins bake  for 12 minutes, and the cookies bake for 10 minutes.

Here we need to find out how many minutes after Caylan puts the trays in the oven will he first remove the scones, muffins, and cookies at the same time.

Based on the above information, the calculation is as follows:

Here we have to determine the L.C.M of each number:

12 = 2 * 2 * 3

15 = 3 * 5

20 = 2 * 2 * 5

Final LCM = 2 * 2 * 3 * 5 = 60

Therefore we can conclude that He will remove all trays at every 60 minutes interval.

Read more about Algebra Word Problems at: https://brainly.com/question/21405634

#SPJ1

Answer:

Step-by-step explanation:

1256cm^2

Formula. Binomial theorem:

[tex](x + y)^ n = C(n,0) x^{ny}^{0} + C(n,1)x^{(n-1)} \ \ y + C(n,2)x^{(n-2)} \ y^2 + ...+ C(n,n+1)xy^{(n-1)} + C(n,n)x^{0y}^n[/tex]

So, for n = 5:

[tex](x + 2)^5 = C(5,0)x^5 + C(5,1)x^4 \ . \ 2 + C(5,2) x^3 \ . \ 2^2 + C(5,3)x^2 \ . \ 2^3 + C(5,4)x \ . \ 2^4 + C(5,5) \ . \ 2^5[/tex]

So, the third term is [tex]\bold{C(5,2)x^3 2^2}[/tex]

The lateral surface area of the prism is 144 in².

The lateral surface area of the prism is calculated by applying the following formula as shown below;

L.S.A = (S₁ + S₂ + S₃)l

where;

The lateral surface area of the prism is calculated as;

The missing length of triangular face is calculated;

s₁ = √(5² - 4²)

s₁ = 3 in

L.S.A = ( 3 + 5 + 4) x 8

L.S.A = 144 in²

Learn more about lateral surface area here: https://brainly.com/question/12506372

#SPJ1

s is a basis for p3.

First, we check for linear independence by setting a linear combination of the vectors in s equal to the zero vector and solving for the coefficients:

c1(6 − t) + c2t3 + c3(4t2) + c4(9t + t3) + c5(−16t) = 0

Rearranging and collecting like terms:

(−c1 + c4)t3 + (4c3 + 9c4 − 16c5)t2 + (−c1)t + (9c4) = 0

For this equation to hold for all values of t, we must have:

-c1 + c4 = 0

4c3 + 9c4 - 16c5 = 0

-c1 = 0

9c4 = 0

From the first and fourth equations, we have c1 = c4 = 0. Substituting into the second equation, we get 4c3 - 16c5 = 0, or c3 - 4c5 = 0. Finally, from the third equation, we have c1 = 0.

Putting everything together, we have:

c1 = 0

c2 is arbitrary

c3 = 4c5

c4 = 0

c5 is arbitrary

Therefore, the only solution to the equation c1(6 − t) + c2t3 + c3(4t2) + c4(9t + t3) + c5(−16t) = 0 is the trivial solution, which means that s is linearly independent.

Next, we need to check whether s spans p3. Since p3 is the vector space of polynomials of degree at most 3, we can write any polynomial in p3 as:

p(t) = a0 + a1t + a2t2 + a3t3

To show that s spans p3, we need to show that we can write any polynomial in p3 as a linear combination of the vectors in s. That is, for any polynomial p(t) in p3, we need to find coefficients c1, c2, c3, c4, and c5 such that:

p(t) = c1(6 − t) + c2t3 + c3(4t2) + c4(9t + t3) + c5(−16t)

Expanding the right-hand side and comparing coefficients with the left-hand side, we get the following system of equations:

c1 = a0

c2 = a3

4c3 + 9c4 - 16c5 = a2

-c1 + c4 = a1

9c4 = 0

Since the fifth equation implies that c4 = 0, the fourth equation simplifies to c1 = a1, which means that we can choose c1 = a1 without loss of generality. Then, we can solve for c2, c3, and c5 in terms of a0, a2, and a3:

c1 = a1

c2 = a3

4c3 - 16c5 = a2

c4 = 0

c5 = 0

Therefore, we can write any polynomial in p3 as a linear combination of the vectors in s, which means that s spans p3. Therefore s is a basis.

To know more about basis, here

brainly.com/question/28194667

#SPJ4

{(a,1), (a,2), (a,3), (b,1), (b,2), (b,3)} ,  {(a,1), (a,2), (b,1), (b,2), (a,2), (b,2), (a,3), (b,3)} , {(a,1), (a,2), (b,1), (b,2), (a,2), (b,2), (a,3), (b,3)},  {} ,{(a,2), (b,2)} Using set roster notation is defined .

(a) Ax(BU C) = {(a,1), (a,2), (a,3), (b,1), (b,2), (b,3)}

(b) (Ax B) U (Ax C) = {(a,1), (a,2), (b,1), (b,2), (a,2), (b,2), (a,3), (b,3)}

(c) Ax(BnC) = {}

(d) (Ax B) n (Ax C) = {(a,2), (b,2)}


(a) A × (B ∪ C)
First, let's find the union of B and C: B ∪ C = {1, 2, 3}
Now, let's compute the Cartesian product A × (B ∪ C): {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}

(b) (A × B) ∪ (A × C)
A × B = {(a, 1), (a, 2), (b, 1), (b, 2)}
A × C = {(a, 2), (a, 3), (b, 2), (b, 3)}
(A × B) ∪ (A × C) = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}

(c) A × (B ∩ C)
B ∩ C = {2}
A × (B ∩ C) = {(a, 2), (b, 2)}

(d) (A × B) ∩ (A × C)
(A × B) ∩ (A × C) = {(a, 2), (b, 2)} defined as separated lists of ordered pairs.

To know more about set roster notation click here:

brainly.com/question/16881144

#SPJ11

The inequality is solved for d as d< 0. Option A

The inequality signs are represented as;

From the information given, we have that;

3 + d < 3 - d

To solve the inequality,

collect the like terms, we get;

d + d < 3 - 3

Add or subtract the values

2d < 0

Divide by the coefficient of d, we get;

d < 0/2

Find the ratio

d< 0

Learn more about inequalities at: https://brainly.com/question/25275758

#SPJ1

The value of a in Quadrilateral BCDE which is a rhombus, would be a = 13°.

In a rhombus, all sides are equal, and opposite angles are equal. Also, diagonals bisect each other at right angles and bisect the angles of the rhombus.

We know m∠BCF = a + 14°, and m∠CDF = 63°. Since ∠CBF and ∠CDF are opposite angles in a rhombus, they are equal:

m∠CBF = m∠CDF = 63°

Now, we can find the value of a:

m∠BCF + m∠CBF = 90°

(a + 14°) + 63° = 90°

a + 77° = 90°

a = 90° - 77°

a = 13°

Find out more on rhombi at https://brainly.com/question/29167679

#SPJ1

The tangential and normal components of the acceleration vector of r(t) = t i + t² j + 5t k are respectively 1 and 10.

To find the tangential and normal components of the acceleration vector, we first need to find the velocity and acceleration vectors. The velocity vector is the first derivative of the position vector:

The acceleration vector is the second derivative of the position vector:

Next, we need to find the unit tangent vector T(t) and unit normal vector N(t):

Finally, we can find the tangential and normal components of the acceleration vector by projecting a(t) onto T(t) and N(t):

Therefore, the tangential and normal components of the acceleration vector are respectively 1 and 10.

Learn more about acceleration vector

https://brainly.com/question/14860101

#SPJ4