Consider the following drawing. Let a(x) = x² - x + 2, b(x) = 6x + 6, c(x) = x2 – 10x + 5, and d(x) = 5x + 1. Laundry |Closet Lin. Bath Closet - Kitchen Living Area Bedroom Dining Area a(x) ft b(x) ft Length (a) What is the difference in the length and width of the one-bedroom apartment shown above? (Simplify your answer completely.) (b) Find the perimeter of the apartment. (Simplify your answer completely.) ft y (x)ɔ Width

Q: What will be the axis of symmetry, the line about which a figure or curve is upon itself, between…

A: Given :   y=4x-2

Q: For y=5x^−2+8x^−3−7x−4, find dydx.

A:

Q: Suppose that for a company manufacturing bluetooth and wireless headsets, the cost and revenue…

A: Given:   C(x) = 32,000+60x and R(x) = 130x-0.001x^2

Q: + The Range of y [2x + 1] is Z. %3D TO FO

A: We can use the concept of function In order to solve the given problem.

Q: 15. Find the point on the line y 3x that is closest to the point (50,0).

A:

Q: The area of the largest rectangle that can be drawn with one side along the x-axis and two vertices…

A: The diagram below shows the rectangle as mentioned in the problem, The rectangle is symmetric about…

Q: 3. If y = 4v2 r x – 1, find the length of the graph of f 3 from point a = 0 to x = 1.

A:

Q: 4.3 Verify that for f(x, y) = 4x°y$ - 9x*y³. дх ду ду дх df

A: Explanation of the answer is as follows

Q: 2 Consider the hypocycloid with equation y 3 +x3 =73 2 2

A:

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=9−27xf(x)=9-27x, and the line…

A:

Q: If y2 is negative, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: If y2  is negative, then y1+y2  will lie _______ y1  by a distance equal to ____.

Q: Sx + 1, if { x20} L-2x + 2, if { x < 0} 6)Graph f(x) =

A:

Q: Suppose that f(æ, y) = e-3x² – 4y? + y Then the maximum is

A:

Q: The equation of the line tangnet to the graph of 24e^x at x=2?

A: Find the derivative of the given function.

Q: Find the length of the chord intercepted by the circle x2+y2-x+3y-22=0 on the line y=x-3

A:

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

A:

Q: Suppose that |(3x4-x2) dx=Ax+Bx³+C, for constants A, B, C. What is the value of C if the curve…

A:

Q: - For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3-y = 1?

A:

Q: Find the area of a triangle bounded by the y axis, the line f(x)=4−(6/7x) and the line…

A: Formula Used: Area of triangle is :                                   Where,  b is base of triangle…

Q: , and mz = X+ 20 A (3x) 20 -2 =180 x+20)° What is the value of x? What is the image of the point…

A:

Q: Find y, of+ 3+2y 14x2 + 42x + 6 d'y dx a.) y, = 7x2-4 b.) y, = 7x2 + x-5 c.) yp 7x2-x- 3 d.) y, =…

A:

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Suppose that P is twice as far from (0, 0) as P is from (6, 0 Find such a point on the x-axis.

A: Let A0,0 and B6,0. It is given that P is twice as far from A0,0 as from B6,0. We know that if point…

Q: Find the points on x=3-y^2 that are closest to the given point (1,0)

A:

Q: Find the value/s of x for which y=3x^4-4x^3+1 is maximum?

A: y=3x4-4x3+1 Differentiating with respect to x, we get dydx=34x3-43x2+0=12x3-12x2 Now to find…

Q: csec²x +secx -2=0 3cotx-3=0

A: Given: 3 cotx -3=0

Q: 9. Find the characteristics of the equation pq = xy %3D

A: Given that pq=xy The given equation can be written as px=yq=a(say) Therefore,  px=a ⇒p=axdzdx=axyq=a…

Q: This is a trapazoid Find x. 3x+2 15 2x-2 X=

A:

Q: Find the point on the x-axis that is equidistant from the points (0,−1) and (5,−3)

A: To find the coordinates of the point satisfying the given conditions

Q: y = v1- x+ x2 ||

A:

Q: If / f(x) dx = 4 and g(x). dx = -4, what is the value of %3D where D is the rectangle: -1 < x < 1,…

A:

Q: 3. y = x³ – 3(x² + w²) 4. y = x7 + V7x - 1 TT + 1

A: Differentiation wrt x

Q: The region in the first quadrant bounded by the x-axis and f (x) = 3x – x² is

A: The graph of region bounded by curves y=3x-x^2 and x-axis is

Q: Suppose the graphs of f(X)=x^2 and g(x)=2x^2 are drawn on a coordinate grid where the unit of…

A: Given, graphs  f(x)=x2g(x)=2x2 The graphs of the functions are as follows:

Q: Find the maximum value of 5x2 - 4xy+ 8y subject to x+y? = 1..

A:

Q: What is the fxx, fyy, and fxy of f=(2x^4)+(y^2)-(x^2)-(2y)?

A:

Q: A market analyst working for a small appliance manufacturer finds that if the firm produces and…

A: we are given with profit equation  Lets graph the given equation  the x intercepts are (-45.224,0)…

Q: 3. Find the area of the quadrilateral enclosed by the lines x y = 0, 2x – 5y = –15 and 5x – 2y = 15.…

A: Let's find.

Q: 3 a AB: 4x + 5y = 13; midpoint (2, 1)

A: The equation of the line is 4x+5y=13. The midpoint of the line is 2, 1.

Q: csec?x +secX -2=0

A: Given equation sec2x+secx−2=0

Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: , Affine, or Nonlinear??? x1 + x2 2x3 + 3x2 Y1 ransformation y2 Y3 x1 + x2 + T+x3

A:

Q: For what values of c is there a straight line that intersects the curve y = x' + cx' + 12x² – 5x + 2…

A: Given the equation of a curve , y=x4+cx3+12x2-5x+2. To find the value of c such that there is a…

Q: -2 The domain of f(x,y) = is %3D x² + y?

A: f(x,y)=-2x2+y2

Q: Find the value of the fx(2 − x) dx - 0

A: Solution :- 1250·∫02x2-x49dx Substitute u = x-2dudx=1du = dx-1250∫u49(u+2)du

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A: Given equation - R =-4p2+4000p          ...........(1)Part (a) - Revenue = R = 0p = price = ?From…

Q: If x) is shown below 3 Then y(t) x(3t – 3) – 1 has the shape

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Suppose the manufacturer of staple machines has found that, when the unit price is $x the revenue y…

A: If a×b=0, using the zero-factor property, it can be written that a=0 or b=0. If -p&gt;0, then…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.