Solve the initial value problem for x as a function of t.. (t²-19t+90) dx dt x(t) = (Type an exact answer.) 1 for (t>10), x(11) = 0 ***

Q: If x² + y² - 3xy² = -1, find dy/dx in terms of x and y. Using your answer for dy/dx, fill in the…

A: Given equation:- x2+y3-3xy2=-1

Q: An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by…

A: Profit = Revenue - Cost

Q: Consider the following planes. -5x + y + z = 5 15x - 3y + 5z = 25 (a) Find the angle between the two…

A: Consider the following planes -5x+y+z=515x-3y+5z=25a To find the angle between the two planes.b To…

Q: Suppose that the position of a particle is given by f(t) = 5t³ +7t + 9. s = f(t)

A:

Q: Solve using the elimination method. Also determine whether the following system is consistent or…

A:

Q: Integral e^x/9+e^2x=

A:

Q: Evaluate lim x →∞ -6x²-x+6 -2x³ + x² + 5x +4

A:

Q: Find the Laplace transforms

A:

Q: (x)) = main of f(g(x)). (Enter your answer using interval notation.) (x)) main of g(f(x)). (Enter…

A:

Q: A volume is described as follows: 1. the base is the region bounded by x = -y² +12y +7 and x = y² −…

A: Given that x=-y2+12y+7 and x=y2-24y+151we have to find volume of object

Q: The joint density function for a pair of random variables X and Y is given. [cx(1 + y) f(x, y) if 0…

A:

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A:

Q: Question 3 Find the value of the derivative (if it exists) of f(x) = (x-2) 4/5 at the indicated…

A: The graph of f(x) is given.

Q: 3. Evaluate the limit, if it exists: lim a. 0 b. 7 x² + x + 1 x+2 X²-2 c. 3.5 d. does not ex

A: H=limx→2x2+x+1x2-2

Q: 3x³+1 f) lim x →∞0 4x³-1

A:

Q: If n(A) = 2, n(B) = 5, and n(A U B) = 7, find n(A n B). Need Help? Read It

A:

Q: The gradient of f(x, y) = xy at (x, y) = (2,3) is

A:

Q: Find and classify the critical points of z= (a²-8x) (y² – 4y) Local maximums: Local minimums: Saddle…

A: The given function is;  z=(x2-8x) (y2-4y).

Q: Find the unique solution to the differential equation that satisfies the stated conditio dy In(x) dx…

A: given:differential equation dydx=lnxxy,  y1=6

Q: Find the arc length of the curve y = ln x - ²² on the interval [1,3].

A:

Q: Consider the ellipse 25x² + 64y² = 1600. Consider the point P(16,5). Find an equation for both lines…

A:

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

A: Need to find out the rate of changing of area outside the circle but inside the square changing.

Q: Solve for b. Use all lower case letters. -(a + b) b = S =

A:

Q: Consider the function ƒ(x) = −2x² + 8x – 3. f(x) has a critical point at x = A. Find the value of A:…

A: Application of Derivative

Q: 2. Find polar coordinates a. (3-√3.3) b. (0, -2)

A: We need to find the polar coordinates of the given points :

Q: Suppose a product's revenue function is given by -8q² + 800q, where R(q) is in dollars and q is the…

A: The given revenue is Rq=-8q2+800q, where Rq is in dollars and q is the number of units sold. To find…

Q: Let f(x) = 5x + 4 and g(x) = ax + c where a and c are non-zero constants. Use lower case letters in…

A:

Q: mine the average rate of change of f(x) = x³. - x over the interval 1 ≤x≤ 3.

A: We will find the required.

Q: A 200-foot cable weighing 5 pounds per foot is hanging from a winch 200 feet above ground level.…

A:

Q: Urves with more than two asymptotes and/or oblique asymptotes: k a) Graph y ==+x and y = X k where…

A:

Q: QUESTION 24 Write the expression in expanded form. x2-9 (x+2)2 3 logg O 6 logg(x-3)-6 logg(x + 2) O…

A:

Q: Find two unit vectors u such that Duf(1, 1) Here, f(x, y) = x² +9y². NOTE: you must enter your FIRST…

A: To solve the following problem

Q: Differentiate the function with respe z' = Z A .6 yo + Bey

A:

Q: 2. When a particle is located a distance x meter from the origin, a force of f(x) = 3x² + 4x…

A: When a particle is located at distance x meter from the origin, a force of  fx=3x2+4x newtons acts…

Q: A company operates two plants which manufacture the same item and whose total cost functions are…

A:

Q: The Third Gate You arrive at the third gate and look for the inscription. Your computer translates…

A: For x approaching c from the left, x<c  ⇒  x-c5<0The denominator is a negative  approaching…

Q: Locate all the critical points of the function f(x,y)=8x−x^2−4xy^2.

A:

Q: The data in the table concerns the lactonization of hydroxyvaleric acid at 25°C. They give the…

A:

Q: For what values of p does the following series n=2 (Inn)p-2 n converge or diverge?

A:

Q: 3. Select the sine wave so the parent function is f(x) = sin (x). Start with a and b both set to 1.…

A: We have to draw the graph of sine wave with the changing values of b.

Q: Find the point on the graph of the function f(x)=(sqrt x) that is closest to the point (18,0) .…

A: The solution is shown below-

Q: An object traveling in a straight line travels s(t) kilometers after t hours, where s(t) = t² + 3t.…

A:

Q: Find the sum of the convergent series. (Round your answer to four decimal place Σ (sin(7))" n = 1

A:

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 3x² +…

A:

Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: The given function is;  f(x)=sqrt(4-34x).

Q: 3. Find the centroid (, y) of the region bounded by y = 2 cos(3x) and y = 2 sin(3x) from z = 0 to z…

A: Centroid is given by x¯=1A∫abxf1(x)-f2(x)dx and y¯=1A∫ab12f1(x)2-f2(x)2dx where A=∫abf1(x)-f2(x)dx

Q: 6. y =√1+√8x-1 y 1$)+ (x-1) ¹4 y'= 1 + 7. y = [(x-1)(2x³ +1)]¹0 8. y = (4x²-1)³ (5x³ + 2)*

A: 5

Q: Differentiate the function. g(t) = 4t-1/8 g'(t) =

A:

Q: Suppose that f (x, y) = xy. The directional derivative of f(x, y) in the directional (1,-4) and at…

A: Given: f(x,y)=xy To Find: Directional derivative at point (4,-1) in the direction <1,-4>

Q: The graph of y=f(x) has f(5) = 1, f(x) has f(5) = 1, f'(5) = -1, and f(5) = -1-

A: