The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters longer than the other. The area of the parallelogram is 20 square meters. If the shorter diagonal is increased by 10 cm and the longer diagonal is decreased by 15 cm, what must be the approximate increase or decrease of the acute angle (degrees) between the diagonals so that the approximate change in area will not exceed 4 square meters? Use differentials. Change in (=

Q: Topic: Arc Length Find the length of the arc of the function x^2 = 4y from x = -3 to x = 3. a) Graph…

A:

Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

A:

Q: A parabola has an equation of y-32= 0. Compute for the surface area of the solid generated by…

A: Given: y=3x12 At y=0, x=0 The surface area of the surface of revolution formed by revolving the…

Q: x= t2 - 4t y= 2t3 - 6t what is the minimum and the maximum point?

A:

Q: d. lim+ In 1000 X X5

A:

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A:

Q: 3. f(x)=x-x³-x²+1 3

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Setan2 sec² 2xdx Select one: O a. 0.4325 O b. 0.0287 O c. 0.6543 d. 0.0177

A:

Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

A:

Q: The first derivative of the function y = 3x cannot be solved using implicit differentiation. Select…

A:

Q: A parabola has an equation of y - 3x = 0. Compute for the surface area of the solid generated by…

A:

Q: 6. Find the intersection of the line I and the plane . 1:7=(4,-1,4) +t(5,-2,3) 2x+5y+z+2=0

A:

Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x 2. f(x)=x²-3x³ + 3x²…

A:

Q: 1. A man is standing on a horizontal ground 30 ft away from a hot air balloon. After a moment, the…

A:

Q: What is the expansion of the binomial expression (x + y)⁵ ? What are the binomial coefficients?

A: Solution of given question is written in below steps.

Q: 4 0 dx 1+ √x

A:

Q: 5. Determine whether the following statements are True or False? y = f(x) 2 X 0 (a) lim f(x) = 1 (b)…

A: Given graph of y= f(x)

Q: A cubic block of ice whose side is 2 inches long is melting at a rate of 1 in^3 per minute. How fast…

A:

Q: Question 7 Determine the area of the triangle bounded by the coordinate axes and the tangent to x² -…

A: This is a problem related to area calculation by integration. Based on the general formula and…

Q: . Find the equation of the curve whose slope is the inverse of the sum of the square root of five…

A: Topic:- function  and application of integration

Q: 4) (1, 150°) 120° 150° 180° 210⁰ 240 90° 270⁰ 60° 2 3 300⁰ 30° 4 330⁰ Ꭴ

A:

Q: 3√3 dx √3 x² √√x² +9 2

A:

Q: dr Evaluate - x(x²-4) ² Select one: Ⓒa.- +aresec)+c √√√²4 b. (+aresec)+c (+arcsec)+c O.C. - O d.…

A: This is a problem related to integral calculation. Based on the general formula and concepts we will…

Q: 2. Show that the function g defined by VVT y² + √² 2, is not continuous at (0,0). (z,y) = (0,0)…

A:

Q: dy Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dx…

A:

Q: Evaluate the following limits 2x a. limx→>+00 3x²

A:

Q: Find the relative extrema, determine if it is relative minima/maxima, and sketch the graph. 6. f(x)…

A:

Q: 4. Find the member of the curve whose slope at any point is and passes through the point (3, 4)

A: Given slope (m) = 3x/4y Passing through a point (3,4) Therefore member of the curve whose slope…

Q: 3. f(x)= x² + 3

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx,…

A:

Q: Find dy dx If y = 1- t² and x = 4+²

A:

Q: (x-1) dy + (y-2) dx = 0

A: To solve the given differential equation

Q: If zs² + yt²= 1 and 2²s+y³t = ry - 4, find 0x/0s, az/at, Əy/08, Əy/ot, at (x, y, s. t) = (1, -3,2,…

A:

Q: Physical Applications of First-Order Differential Equations A body at a temperature of 50° F is…

A:

Q: A lamina occupies the part of the rectangle 0 ≤ x ≤ 1,0 ≤ y ≤7 and the density at each point is…

A:

Q: 1. Evaluate the given integral Q. Q - CC² LL- (x - y) dx dy y²

A:

Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

A:

Q: The displacement d (in meters) of an object at time t (in seconds) is given by the following…

A: This is a problem related to harmonic motion. Based on the general formula and concepts we will…

Q: Find the derivative of both a and b a. x csc-1(1/x) b.(esin2x)/[In(cos2x)]2

A:

Q: In 1000 5 X limx→ +00 X

A:

Q: The graph of y=f(x) is shown. Draw the graph of y = -f(x). 17 Ex X 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: x³ +7x X-00 √4x³+5 Find the lim

A: A detailed solution is given below.

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

A:

Q: Find the area of the region bounded by the curve y=x^3-3x^2+3 and the x-axis.

A:

Q: Fermat's theorem states that if f has a relative extremum and if f'(x) exists, then f'(c) = 0.…

A:

Q: Andrew is an ecologist investigating a pond. He notices that an algal bloom is growing in the pond.…

A: To find out the rate of area.

Q: 222 = 456=_

A:

Q: 2. F(s): = 1 (S-2)(s-4) (s-8)

A:

Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

A: