After five practice sessions, some freshmen Cadets in your squad still can't do an about face. They seem to be trying, but just aren't getting it. What supervisory function do you need to exercise more with these Cadets

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

Learn more about intergal here:

https://brainly.com/question/31109342

#SPJ1

Answer:

x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.

Step-by-step explanation:

x+a= b , where a,b are uncertain values. Although both can be solved similarly, the difference is that, in literal equations, the letters representing the amount of a numerical value do not always change; however, in a single-variable equation, the letters representing these can/may vary.

Answer:

Step-by-step explanation:

\(LHS = \frac{1}{m^{2}}-\frac{1}{m^{2}+1}\\\\\\=\frac{1*(m^{2}+1)}{m^{2}*(m^{2}+1)}-\frac{1*m^{2}}{(m^{2}+1)*m^{2}}\\\\\\=\frac{m^{2}+1- m^{2}}{(m^{2}+1)*m^{2}}\\\\\\=\frac{1}{(m^{2}+1)m^{2}}=RHS\)

(a) Laplace(u) = 0, the given function u(x,y) is harmonic ; (b) The required function is \(f(z) = 8xy^3 + 2ix^\)2y^3 + if (y) + c.

Given function is: \(`u(x,y) = -8x'y + 8xy^3`\)

Let's compute first-order partial derivatives of u(x,y) with respect to x and y as follows:

\(u_x = 8y^3, u_y = -8x' + 24xy²\)

Let's compute the second-order partial derivatives of u(x,y) with respect to x and y as follows:

\(u_xx = 0, \\u_yy = -8, \\u_xy = 24x\)

Now, the Laplacian of u(x,y) can be found using the following formula:

Laplace

\((u) = u_xx + u_yy\)

= 0 - 8= -8

Since Laplace(u) = 0, the given function u(x,y) is harmonic.

Hence, part (a) of the problem is proven.

(b) Conjugate of u(x,y) is given by the following equation:

v(x,y) = ∫u_ydx - ∫u_xdy + c

where c is an arbitrary constant of integration.

Integrating u_x and u_y with respect to x and y, we get:

\(u_x = 8y^3\)

⇒\(v(x,y) = 2x^2y^3 + f(y)u_y \\= -8x' + 24xy²\)

⇒ \(v(x,y) = -4xy^2 + g(x)\)

where f(y) and g(x) are arbitrary functions of integration.

Let's write f(z) in terms of v(x,y) and the constant of integration (c) as follows:

f(z) = u(x,y) + iv(x,y) + c

Therefore, substituting \(u(x,y) = -8x'y + 8xy^3\) and\(v(x,y) = 2x^2y^3 + f(y)\)into the above equation, we get:

\(f(z) = 8xy^3 + i(2x^2y^3 + f(y)) + c\)

Hence, the required function is:

\(f(z) = 8xy^3 + 2ix^2y^3 + if(y) + c.\)

Know more about the partial derivatives

https://brainly.com/question/29655602

#SPJ11

If the sales tax in Brian’s area is 8.51%, then Brian pay in total is option (d) $507.96

Brian's credit card has an interest rate of 9.4% compounded monthly, which means that the interest is calculated based on the balance of the credit card at the end of each month. Therefore, the interest will accumulate over time, and Brian will have to pay more than the base price of $435.

Additionally, the sales tax in Brian's area is 8.51%, which means that he needs to pay this percentage of the total cost of his purchase as well.

To calculate how much Brian paid in total, we need to take into account the base price, the interest rate, and the sales tax.

First, let's calculate the total cost of the air conditioning unit including sales tax. The sales tax is 8.51% of the base price, which is:

8.51% x $435 = $37.02

So, the total cost of the air conditioning unit including sales tax is:

$435 + $37.02 = $462.04

Now, let's calculate how much Brian paid in interest. Since the interest rate is compounded monthly, we need to divide the annual rate by 12 to get the monthly rate. Therefore, the monthly interest rate is:

9.4% / 12 = 0.78333% (rounded to five decimal places)

Over a year and a half (or 18 months), the interest accumulated on Brian's credit card balance can be calculated using the following formula:

\(A = P(1 + r/n)^{nt} - P\)

where A is the total amount paid, P is the principal amount (which is the same as the base price of the air conditioning unit), r is the interest rate in decimal form, n is the number of times the interest is compounded per year (which is 12 in this case since the interest is compounded monthly), and t is the time in years (which is 1.5 in this case since Brian made monthly payments for a year and a half).

Substituting the values we have:

A = $435\((1 + 0.0078333)^{12\times1.5}\) - $435 = $45.92

Therefore, the total amount of interest paid by Brian is $45.92.

Finally, to calculate the total amount that Brian paid, we need to add the total cost of the air conditioning unit including sales tax and the total amount of interest paid:

$462.04 + $45.92 = $507.96

So, the correct answer is (d) $507.96, rounded to the nearest cent.

To know more about interest here.

https://brainly.com/question/29335425

#SPJ4

Answer: v=-81.92

Step-by-step explanation:

\(\displaystyle\\7+\frac{v}{8} =-3.24\\\\7+\frac{v}{8}-7 =-3.24-7\\\\\frac{v}{8} =-10.24\\\\\frac{v}{8} =-10.24\)

Multiply both parts of the equation by 8:

\(\displaystyle\\(\frac{v}{8})(8)=(-10.24)(8) \\\\v=-81.92\)

Answer:

does the sugar levels matter just bake the da*n cookies man

Answer:

1 2 3

Step-by-step explanation: 1 times 18, 2 times 9, 3 times 6

Answer:

Your other answers all look good - I think the word in the blank is producer, which means an organism that makes its own food. Green plants do so through photosynthesis.

Answer:

producer

Step-by-step explanation:

Because it makes sense

Answer:

D

Step-by-step explanation:

The correct answer is:

The probability that one event will occur given that the other has already occurred.

The term joint probability refers to a statistical measure that calculates the likelihood of two events occurring together and at the same point in time. Put simply, a joint probability is the probability of event Y occurring at the same time that event X occurs.

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs.

The best description of a joint probability is:

The probability that one event will occur given that the other has already occurred.

Learn more about Probability here:

brainly.com/question/27682397

#SPJ11

The expression that is equivalent to cos3x/sinx cosx is B.

secxcos2x- cscxsin 2x.

How to solve cos3x/sinx cosx?Given an expression cos3x/sinx cosx.

The goal is to simplify it using trigonometric identities.

We know that the quotient identity of tan x is:

tan x = sin x / cos x

We can convert the above equation as:

cos x / sin x = 1 / tan x

Similarly, cot x = cos x / sin x

We can convert the above equation as:

sin x / cos x = 1 / cot x

Now, we can use the above equations to simplify the given equation.

Simplify cos3x/sinx cosx

We have:

cos3x/sinx cosx= cos2x * cosx / sinx cosx

= cos2x / sinx + cos2x / cosx

= cos2x/sinx + cos x

And, we know that

cos 2x =\(1 - 2sin^2x\)

= \(2cos^2x - 1\)

Substituting this value in the above equation, we get:

cos3x/sinx cosx = (\(2cos^2x - 1\)) / sinx + cos x

= secxcos2x- cscxsin 2x

Therefore, the expression that is equivalent to cos3x/sinx cosx is B.

secxcos2x- cscxsin 2x.

To know more about trigonometric visit:

https://brainly.com/question/29156330

#SPJ11

Answer:

14 dance videos

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

<

Step-by-step explanation:

because 42.18 is smaller than 42.7

Answer:

All of them would be under $65

Answer:

D

Step-by-step explanation:

A family-wise inflation of error rate is the increase in the probability that one or more results of a numerous, independently (separately) conducted statistical analyses to become statistically significant, but these results can actually be attributed to random variation or measurement error.

In Statistics, a family-wise inflation of error rate is also referred to as family-wise error rate (FWER) and it can be defined as the probability of making at least one false conclusion or type I errors in numerous, separate statistical analyses or hypothesis tests.

Hence, a family-wise inflation of error rate increases the probability that one or more of the results among groups within an independent data set to be statistically significant, especially due to random variation or measurement error.

Read more: https://brainly.com/question/22851088

usually we'd end up with a system of three variables by using three points to get the quadratic, but in this case since we have some zeros, we shamelessly used (0 , 48) to get one of the variables, so we only ended up with a system of two, not exactly but pretty much.

\({\Large \begin{array}{llll} y=ax^2+bx+c \end{array}} \\\\[-0.35em] ~\dotfill\\\\ (0~~,~~48)\hspace{5em}48=a(0)^2+b(0)+c\implies 48=c \\\\[-0.35em] ~\dotfill\\\\ (1~~,~~40)\hspace{5em}40=a(1)^2+b(1)+c\implies 40=a+b+c \\\\[-0.35em] ~\dotfill\\\\ (2~~,~~0)\hspace{5em}0=a(2)^2+b(2)+c\implies 0=4a+2b+c\)

so from our template above, we get those three fellows, but the first equation gives us 48 = c, so we know what that is already, so let's shamelessly use it in the 2nd equation and then do some substitution

\(\stackrel{\textit{substituting on the 2nd equation}}{40=a+b+(48)}\implies -8=a+b\implies -8-a=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{now doing some substituting on the 3rd equation}}{0=4a+2(-8-a)+(48)}\implies 0=4a-16-2a+48 \\\\\\ 0=2a+32\implies -32=2a\implies \cfrac{-32}{2}=a\implies \boxed{-16=a} \\\\\\ -8-a=b\implies -8-(-16)=b\implies \boxed{8=b}\hspace{5em}\boxed{c=48} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=-16x^2+8x+48 \end{array}} ~\hfill\)

\(y(1.75)=-16(1.75)^2+8(1.75)+48\implies {\Large \begin{array}{llll} y(1.75)=13 \end{array}}\)

Check the picture below.

Answer:

Option (A)

Step-by-step explanation:

The given absolute function is,

f(x) = |-4x + 36|

If the given function f(x) ≥ 0,

(-4x + 36) ≥ 0

4x ≤ 36

x ≤ 9

If the given function f(x) < 0,

(-4x + 36) < 0

4x > 36

x > 9

Therefore, piecewise function that defines the absolute function will be,

f(x) = 4x - 36 if x ≤ 9

        -4x + 36 if x > 9

Option (A) will be the correct option.

Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

Answer:

Step-by-step explanation:

(8 x 6) x 25 =

48 x 25 =

1200 ft2

Make's absolutely no sense. Please rephrase this as a question.

Answer:

Step-by-step explanation:

AAS theorem: If two angles and a non-included side of one triangle are congruent to corresponding two angles and a non-included side of second triangle, then the triangles are congruent.

~~~~~~~~~~~~~

1). ∠N ≅ ∠L   Given

2). JK ≅ MK  Given

3). ∠JKN ≅ ∠MKL   Vertical

4). ΔJKN ≅ ΔMKL   AAS theorem of congruence.

The equation of the tangent line to the curve y = 6sin(x) at the point (π/6, 3) which can be written in the form y = mx + b is:

y = 3√3x - π√3/2 + 3, where m = 3√3 and b = -π√3/2 + 3.

To obtain the equation of the tangent line to the curve y = 6sin(x) at the point (π/6, 3), we need to determine the slope (m) of the tangent line and the y-intercept (b).

The slope of the tangent line is equal to the derivative of the function y = 6sin(x) evaluated at x = π/6.

Let's calculate it:

dy/dx = d/dx(6sin(x))

      = 6 * d/dx(sin(x))

      = 6 * cos(x)

Substituting x = π/6 into the derivative, we get:

m = 6 * cos(π/6)

 = 6 * cos(π/6)

 = 6 * (√3/2)

 = 3√3

Now that we have the slope (m), we can determine the y-intercept (b) using the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Plugging in the point (π/6, 3), we get:

y - 3 = 3√3(x - π/6)

Next, we can simplify and rewrite the equation in the form y = mx + b:

y = 3√3(x - π/6) + 3

 = 3√3x - π√3/2 + 3

To know more about this tangent line refer here:

https://brainly.com/question/31585637#

#SPJ11

Answer:

750 Students

Step-by-step explanation:

1. 1250 / 50 = 25

2. 30 * 25 = 750 Pupils.

Therefore out of the 1,250 Student's, 750 of them work on the weekends.

40 = 5X

X = 10 dollars

Now divide 40/5 = 8

On average, each girl spends $8 dollars

Now write an inequality ,for this situation

5X ≤ 40

(a + b + c + d + e)/5 = 40

Answer:

The equation of the straight line passing through the point ( 3,1 )

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Step-by-step explanation:

Step(i):-

The equation of the straight line passing through the point ( 3,1 )

                      \(\frac{x}{a} + \frac{y}{b} = 1\)

                     \(\frac{3}{a} + \frac{1}{b} = 1\)

                    3b + a = ab ...(i)

Given the difference of length is  4

                      a-b = 4

                       b =  a - 4 ...(ii)

Step(ii):-

substitute b=a-4 in equation (i) , we get

                3( a-4 ) + a = a (a-4)

               3a - 12+ a =  - 4 a + a²  

                 a² - 8 a + 12 =0

Find the factors of 'a'

                 a² - 6a -2a +12 =0

                a (a-6) -2(a-6) =0

             a =2 and a=6

                  we know that a-b =4

             put       a = 2

                          2 - b =4

                            b = -2

The equation of the straight line whose intercepts on the axes

                    \(\frac{x}{a} + \frac{y}{b} = 1\)

                   \(\frac{x}{2} + \frac{y}{-2} = 1\)

The equation of the straight line

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Verification:-

The equation of the straight line passing through the point (3,1)

                      \(\frac{x}{2} + \frac{y}{-2} = 1\)

Put x =3 and y=1

                  \(\frac{3}{2} + \frac{1}{-2} = 1\\\frac{2}{2} =1\\\)

                 1 = 1

∴  The point (3,1) is satisfies the equation

The approximation of the solution using Taylor's method of order two with h = 0.1 is y(1.1) ≈ 0.005. The values of y(1.04) ≈ 0.0006, y(1.55) ≈ 0.0395, and y(1.97) ≈ 0.0163.

To approximate the solution using Taylor's method of order 2 with h = 0.1 and compare with the exact values of y, we can follow the steps below:

Step 1:

The second derivative of y with respect to t is given as follows:

y'' = [(2/t) y + t'² e^t]'

y''= [2y/t - (2/t²) y + 2t'e^t + t'² e^t]'

y''= [(2/t) - (2/t²)]y + [2e^t + 2t'e^t + 2t'e^t + 2t t'e^t]

y''= [(2/t) - (2/t²)]y + [4t'e^t + 2t t'e^t]

y''= [(2/t²) y + (4/t) y] + [4t'e^t + 2t t'e^t]

y''= (2/t²)[ty' + 2y] + 2t'e^t[2 + t]

Step 2:

Using Taylor's method of order two with h = 0.1, we can approximate the solution of the problem as follows:

y(t + h) = y(t) + hy'(t) + (h²/2) y''(t)

y(t + h)= y(t) + h[(2/t)y + t'² e^t] + (h²/2)[(2/t²) y + (4/t) y] + (h²/2) [4t'e^t + 2t t'e^t]

y(t + h)= y(t) + h(2/t)y + h t'² e^t + (h²/t²) y + (2h/t) y + (h²/2) [4t'e^t + 2t t'e^t]

y(t + h)= y(t) + [2h/t + (h²/t²)]y + h t'² e^t + (h²/2) [4t'e^t + 2t t'e^t]where,

y(1) = 0, t = 1, h = 0.1

y(1.1) = y(1) + [2(0.1)/1 + (0.1²/1²)](0) + 0.1 (2/1)(0) + (0.1²/2) [4(0) + 2(1)(0)]

y(1.1) = 0.005

The approximation of the solution using Taylor's method of order two with h = 0.1 is y(1.1) ≈ 0.005.

To find y(1.04), y(1.55), and y(1.97), we will use the linear interpolation method.

Step 3:

The values of y(1.1) and y(1) are used to find the value of y(1.04) as follows:

y(1.04) = y(1) + [(1.04 - 1)/(1.1 - 1)](y(1.1) - y(1))

y(1.04)= 0 + [(1.04 - 1)/(1.1 - 1)](0.005 - 0)

y(1.04)≈ 0.0006

Therefore, y(1.04) ≈ 0.0006.

Step 4:

The values of y(1.1) and y(1.55) are used to find the value of y(1.97) as follows:

y(1.55) = y(1) + [(1.55 - 1)/(1.1 - 1)](y(1.1) - y(1))

y(1.55)= 0 + [(1.55 - 1)/(1.1 - 1)](0.005 - 0)

y(1.55)≈ 0.0395

Similarly, y(1.97) = y(1.55) + [(1.97 - 1.55)/(1.1 - 1.55)](y(1.1) - y(1.55))

y(1.97) = 0.0395 + [(1.97 - 1.55)/(1.1 - 1.55)](0.005 - 0.0395)

y(1.97)≈ 0.0163

Therefore, y(1.04) ≈ 0.0006, y(1.55) ≈ 0.0395, and y(1.97) ≈ 0.0163.

The question should be:

Given the initial value problem y' = (2/t)y+t’²e^t. 1≤t≤2, y(1)=0,  

With exact solution y(t)=t² (e^t – e).

1) Use Taylor's method of order two with h=0.1 to approximate the solution, and compare it with the actual values of y.

2) Use the answers generated in part (1) and linear interpolation to approximate y at the following

I. y(1.04)

II. y(1.55)

III. y(1.97)

To learn more about linear interpolation: https://brainly.com/question/26174353

#SPJ11

The null hypothesis would not be rejected and the researcher would fail to find statistical significance at the chosen alpha level of .05.

If a researcher sets the alpha level at .05 and obtains a p-value of .06, it means that the p-value is greater than the chosen significance level. The alpha level, also known as the significance level, represents the threshold for determining whether the results are statistically significant or not.

In hypothesis testing, the null hypothesis assumes that there is no significant difference or relationship between variables.

If the p-value is less than or equal to the alpha level, it suggests that there is enough evidence to reject the null hypothesis and conclude that there is a significant difference or relationship.

However, if the p-value is greater than the alpha level, as in this case with a p-value of .06, it means that the observed data does not provide sufficient evidence to reject the null hypothesis.

To know more about hypothesis visit:

https://brainly.com/question/32562440

#SPJ11

The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.

The sides of the triangle are given as a = 20, b = 15, and c = 25.

We will use Hero's formula to find the area of this triangle.

It is a three-face polygon that consists of three edges and three vertices.

We use Heron's formula to find the area of a triangle with 3 sides:

Herons formula:

Area of a triangle =  \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Where a, b, and c are sides of a triangle.

And s = semi perimeter of a triangle.

s = \(\frac{a+b+c}{2}\)

If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.

Let the given sides be:

a = 20, b = 15 and c = 25.

(20 + 15) > 25

(20 + 25) > 15

(15 + 25) > 20 so the given sides are true.

Now,

Semi perimeter of the triangle:

s = (a+b+c) / 2

s = (20+15+25) / 2

s = 60 / 2

s = 30

Putting s = 30 in the area of the triangle.

we get,

Area of the triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Area of the triangle = \(\sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150\)

Thus, the area of a triangle is 150.

Learn more about the Area of triangles here:

https://brainly.com/question/11952845

#SPJ1