A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point. At a certain moment, the angle between the observer's line of sight and the horizontal is 4, and it is changing at a rate of 0.4 rad/min. How fast is the balloon rising at this moment? Let y be the height of the balloon (in km), t be time (in minutes), and 0 the angle between the line-of-sight and the horizontal (in radians). (Use decimal notation. Give your answer to two decimal places.) dy km/min dt

Q: Evaluate the integral 7-2x dx /7+12x-4x²

A:

Q: Find the area of the region enclosed by the parabolas y=x and y=2x-x. Make a sketch and shade in the…

A:

Q: in(2x) – 5 cos(x) = 0 for all solutions 0 < a < 2n .68

A: Please refer to the image below

Q: dx, n = 5 x2 M5 = Need Help? Read It

A: Midpoint rule

Q: or Divergence applies to en +2 Σ n=1 n*+6

A: We have to choose the correct option from the given options according to the given information

Q: -At the minimum point the value of second derivative is choices a. imaginary b. negative c. positive…

A: Solution: At the minimum point the value of the second derivative

Q: 00 Determine el valor de a e R tal que: /" -dx e2x + 1 a ||

A: ∫1u2+a2du = 1atan-1ua+C

Q: Question Given f(x) below, find f' (x). f(x) = 'dt Provide your answer below: S) =D %3D FEEDBACK…

A: Given query is to find the derivative of the expression.

Q: Solve the initial value problem : y +6 y +13 y=0; y (0)=2,y0)=0

A:

Q: [2 -37 -2 0 For matrices A=| 0 2 the matrix 3(A +2B) is equal to? ' 2. 3. and B = 1 -2

A: Topic: Matrix addition and scalar multiplication

Q: Hemegeneus y= JーX

A:

Q: Let f (x) = 1(1 2 2 +4. Evaluate f(-8). f(-8) = Number

A: Given f(x) = -½(½)x + 4 We have to find f(-8)

Q: (x- 2), (y-6)² Problem #4: Find the slope of the line tangent to the conic section =1 at 16 25…

A: This question is related to Straight lines, we will solve it using given information.

Q: Solve fæ² In(æ) dæ using Integration by Parts. Use u In(x) and v = x². Ansuw or:

A: The detailed solution is given below thank you

Q: Evaluate the following integrals Li l2l e(1+x²) dx i.

A:

Q: Find the Taylor expansion of f(x) = (x2 + 7)(7/3) for x near to 1, up to and including the x2 term.

A: Taylor series

Q: 3. a) Describe the translations applied to the graph of y= x² to obtain a graph of the quadratic…

A: Here we have to use the transformation of graphs.

Q: Lim (x- 7).tanx

A: Use limit concept

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Given that      r(t) = (2 sint)i +(t3-cost)j +e2tk , t=0

Q: The difference between two angles, how is the result of the same trigonometric function

A:

Q: Q2/ Find the Laplace transform of the following function: f(t) = t3 + 3t2 – 6t + 4. %3D

A:

Q: TL 12+3i-2 (e) lim 71 00 n3

A:

Q: y 3 to 2.

A:

Q: The derivative of a fraction (that is, the quotient obtained by the division of two functions) is…

A:

Q: Siven the curve X = 2 y – y´ and the line X = 0 ind the area of the region bounded by the curve and…

A:

Q: 00 Determine el valor de a e R tal que: e+1

A:

Q: Find the area of the region that lies outside the circle r = 3 cos and inside the cardioid r = 1+…

A: Given r=3cosθr=1+cosθ

Q: separable 9-X(2lnX+1) Sin y+ ycosy

A:

Q: Solve 4 cos (x) 13 cos(x) – 12 = 0 for all solutions 0 < x < 27 I = 138.6 Give your answers accurate…

A: Let's find.

Q: D) Decreasing on (-00, 0) Determine where the given function is concave up and where it is concave…

A:

Q: The width of a rectangle increases at a rate of 2 cms. The length is five times its width. Find the…

A:

Q: If the partial fraction decomposition of 2s2+13s–17 A s+3 Bs+C s2 –2s+4 (s+3)(s² –2s+4) then, the…

A:

Q: Evaluate each definite integral. y f(x)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use the substitution x = 3 sin t to evaluate the integral f V9 – x² dx. | Note: Use C for an…

A: Given; I=∫9-x2dx   ...1   Use the trigonometric identity; 1). sin2x+cos2x=1 2). cos2x=2cos2x-1 And…

Q: 2. Find the Area bounded by the curve y = 4-x? and the x-axis.

A: Topic = Area

Q: (8")(10") (7")(9") +1' n=1

A:

Q: Find all values of x and y such that Px(x,y)=0 and Py(x,y)=0 simultaneously.   P(x,y)=…

A:

Q: If x = t^2 + 1 and y = t^3, then the second derivative is? (Show your complete solution). a. 3/(4t)…

A: Given that,   x=t2+1 and y=t3

Q: 3"n2 is n! Zn=1 а. 1 b. 0 c. Diverge с. d. Converge d O b

A:

Q: The equation 3y" +12y = 3sin(4t) where y(0) = 0 , y'(0) = 0 when solved using Lapla transform,…

A:

Q: Let f(x, y, z) = xy + z°, x = r + s – 61, y = 3rt, z = s'. Use the Chain Rule to calculate the…

A: Given;  f(x,y,z)=xy+z3, x=r+s-6t, y=3rt, z=s5.

Q: An object moving in a straight line has an acceleration in m/s2 given by a = 18t + 4. Find its…

A:

Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A: We will differntiate, and find the values.

Q: 1 f(z) = 1+ 6z

A:

Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

A:

Q: бу + 4z Зх + Зу = -24 %3D -6 %D 2x 3z = 4 (х, у, 2) -

A:

Q: Find the sum and express the answer in its lowest term. 3 =N 4 10 1) 9 3 2) + 13 6. 4 3) + + 7. 9.…

A:

Q: Evaluate the integral In(x) le2 x[ln4(x)-1] e3

A: The integration of the integral is  ln(x)/[x(ln4x -1)] limit from e2 to e3.

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. dx

A:

Q: Find parametric equations for the line through (- 4,6,1) perpendicular to the plane 7x + 3y + 9z =…

A: Note that, a vector which is perpendicular to the plane ax+by+cz+d=0 is (a, b, c). A parametric…