In A ABC, right-angled at B,

Q: Among all pairs of numbers whose sum is 24, find a pair whose product is as large as possible. What ...

A: Let one number be = xAnother number be = yGiven that, their sum is 24.x+y = 24y = 24-x              ...

Q: Write a function in slope-intercept form whose graph satisfies the given conditions : Passing throug...

A: To write a function in slope-intercept form whose graph satisfies the given conditions: Passing thro...

Q: Multiply: (2x + 4y)2

A: Our Aim is to multiply (2x+4y)2.

Q: solve the initial value equation

A: Given that:                           1+2exydx+2exy1-xydy=0    .........................(1)      &am...

Q: 2a

A: We have to find the limit: limz→1-iz2-2z+2z2-z+iz Putting the limiting value, limz→1-iz2-2z+2z2-z+iz...

Q: Assume f is continuous on an interval containing zero anddifferentiable for all x not equal to  0. I...

A: Consider the Darboux Theorem: Let I be an open interval, f:I→ℝ, a real- valued differential function...

Q: Hello, I am uncertain about how to go about solving this question. The question is as follows, "The ...

A: Given

Q: Write equations in point-slope form, slope-intercept form, and general form for the line passing thr...

A: Given: A line passes through the point -2,5 The line is perpendicular to the line y=-14x+13 Let m ...

Q: Begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function g(x)...

A: Function: At first we need to find the graph of the function f(x)=2x

Q: Find the limit  x appraoaches infinity (e )- x2

A: Given: limx→∞e-x2 limx→∞1ex2

Q: Find the derivative of  f(x) = (x^2-5) (x+7)

A: We have to find the derivative of  f(x) = (x2 - 5) (x + 7) We know that if f(x) = uv ,  then  f'(x) ...

Q: Arc length of a parabola Find the length of the curve y = ax2 from x = 0 to x = 10, where a >0 is...

A: Arc length of a curve is defined as the distance between two points along the section of the curve. ...

Q: Simplify (variables represent nonzero real numbers). (2-1x-2y-1)-2(2x-4y3)-2(16x-3y3)0 / (2x-3y-5)2 ...

A: To simplify: 2x-1x-2y-1-22x-4y3-216x-3y302x-3y-52. Properties of exponents are: 1. a0=1 2. a-n=1an 3...

Q: Calculus Question

A: Let p=y-z, q=z-x and r=x-y Now determine the partial derivatives. ∂p∂x=0, ∂p∂y=1 Similarly ∂q∂y=0,∂q...

Q: 5b

A: The given function is fz=1z2-3z+2 

Q: On what intervals are the following functions continuous? k(x) = sin x/x

A: The given function is kx=sin xx. Note that the above is not defined at x=0.  

Q: Set w(r, y) = cos(xy) where x = t² and y = el-8t, then dw is dt Select one: a. -2ysin(xy)t^1+8xsin(x...

A: to find the value dw/dt                   dwdt=dwdx.dxdt+dwdy.dydt                     (1)

Q: a)Solve the ecuation y''+3y'=12x-5 symbolic b)Solve the initial value problem y''+3y'=12x-5 where y ...

A: The given function differential equation is  y" +3y' =12x - 5 y(0) = 1,     y'(0) = 0

Q: Find all the second-order partial derivatives of the functions g(x, y) = cos x2 - sin 3y

A: Find all the second-order partial derivatives of the functions g(x, y) = cos x2 - sin 3y

Q: Find the limits

A: Consider the given function, limx→∞x2+25-x2-1 rationalize the function, limx→∞x2+25-x2-1=limx→∞x2+25...

Q: Find a power series representation for the function g(x)= (1)/ (1-x)2 and determine its radius of co...

A: Given:gx=11-x2

Q: A rectangular box was designed to be built for a length of 30 cm and breadth of 20 cm. What is the a...

A: The length of the box l = 30 cm The width of the box b = 20 cm  

Q: Identify the conic, analyze the equation (center, radius, vertices, foci, eccentricity, directrix, a...

A:

Q: Perform the indicated operation or operations. (3x + 4y)2 - (3x - 4y)2

A: We have to perform the indicated operations for the given expression: 3x+4y2-3x-4y2 We know the iden...

Q: Show that the functions are inverse functions of each other.                                  f(x) =...

A: Given: f(x)=2x3−1g(x)=x+123

Q: Determine if the following system is consistent: x1 – 2x2 + x3 = 0 2x2 – 8x3 = 8 5x1 - 5x3 = 10

A: A system of linear equation is given as, x1-2x2+x3=02x2-8x3=85x1-5x3=10 To determine the given syste...

Q: In Exercises 1-8, find the general antiderivative of f and check youranswer by differentiating. f(x)...

A:

Q: Use a right triangle to write the expression cos (sin-1 1/x) as an algebraic expression. Assume that...

A: Consider the following expression: θ=sin-11xsinθ=1x Consider the following trigonometric ratio: sinθ...

Q: Determine all values of p for which the improper integral converges.

A: SOLUTION:-    Determine all values of p for which the improper integral converges.   I=∫011xpdx

Q: Find the derivative of the function. y = x sec k x

A: The function is given as , y=x seckx. To find the derivative for the given function. Solution: The f...

Q: 6. (a) Find the Laplace transformation of the following function by using defi- nition of Laplace tr...

A:

Q: Find the indefinite integral.

A:

Q: A telephone company offers the following plans.Plan A $30 per month buys 120 minutes. Additional tim...

A: Given: The piecewise function for plan A is given by: Ct=30if 0≤t≤12030+0.30t-120if t>120 To dete...

Q: Find the general solution of the given equation y" + 2y' + 4y = 0

A: let ddx=D so, the given equation becomes D2+2D+4=0

Q: Use DeMoivre’s Theorem to find the indicated power of the complex number (1 - i√3)2. Write answers i...

A: Known theorem: cosθ+isinθn=cosnθ+isinnθ.    

Q: Determine the convergence or divergence of the series

A: We have the given series as ∑n=1∞lnn+1n Thus, limn→∞lnn+1n=limn→∞lnnn+1n=ln1+0=ln1=0 From the series...

Q: Use the graph of f to find the interval(s) on which f is increasing, Where applicable, use interval ...

A: A function is said to be increasing if the output of the function increases with value increases wit...

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.