A boat approaches a 50-ft-high lighthouse whose base is at sea level. Let d be the distance between the boat and the base of the lighthouse. Let L be the distance between the boat and the top of the lighthouse. Let u be the angle of elevation between the boat and the top of the lighthouse. a. Express d as a function of u. b. Express L as a function of u

Q: Find a pair of functions f and g and an interval [a, b] such that fg a

A:

Q: Determine the poles and residues of the following function: cot z

A:

Q: Is the given function a sum, product, quotient, or composition of basic functions? h (x) = (sin æ)?…

A:

Q: Find the other five functions of the acute angle A

A:

Q: Write the function below in the form y = f(u) and u = g(x), then find as a function of x. dx %3D y =…

A: we have to find derivative

Q: f(x,y)=arcsin( x² +y² –1)+Jx² +y² -1 %3D

A: Definition set of the function is the interval in which the function is defined We know that Domain…

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: ------------------------------------------------------------------  r = rv,θRight hand estimate∂r∂v…

Q: Find y as a function of a if x?y" + 15xy + 49y = 0, |3D y(1) = -5, y'(1) = 4. y =

A: Given differential equation is  x2y''+15xy'+49y=0 given y(1)=-5,y'(1)=4

Q: Using Figure 1, complete the following function. V u Figure 1 sing = %3D u/r v/r ^yn O r/v v/u r/u O…

A: Given problem:-

Q: Consider the sketch of a sinusoidal function provided. Then answer the following questions with…

A: Given: From the figure, it can be seen that the amplitude is 2. And the period is 2π.

Q: Differentiate the function.

A:

Q: Using Figure 1, complete the following function. u Figure 1 sece = v/r v/u u/r O r/u r/v u/v

A:

Q: az dz and dy 2. Suppose z is a function of r and y and tan(r +y) = e*. Determine

A: Suppose z is a function of x and y.Given that: tan(x+y)=ez2 ...(1)

Q: h@ = 3 Cosh" (csc) CSC

A: Given hyperbolic function is hx=3cosh-1csc1x.

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: Find the partial derivatives.

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: Given : v = 85 ft/s and angle is 45°

Q: -10 750m

A: Given data is:

Q: Determine the amplitude, period and displacement for the given function, and sketch the graph of the…

A: Solutions

Q: 221 writc a formnla for the function y =f cx) whose is shown fig: 2.

A:

Q: If the legs of a right triangle are 7 and 7 in respectively, then the other two angles are а. 45°…

A: GIVEN: Q1) right triangle, sides 7b and 7 Q2) tan 490° Q3) sec 150°

Q: 30 ft (a) Express the angle of elevation 0 of the sun as a function of the length s of the shadow.

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A:

Q: The .................function takes as input a real number t that corresponds to a point P=(x,y) on…

A: Given statement: The .................function takes as input a real number t that corresponds to a…

Q: Let C be the contour (blue) given in the figure below and let fiz) be any function with Then .…

A:

Q: Determine the position function, s(t),

A:

Q: Write the following function in terms of its cofunction. Assume that all angles in which an unknown…

A: Cofunctions: secπ2-α = cosecα     ,  cosecπ2-α =secαcotπ2-α  = tanα          ,   tanπ2-α     = cotα…

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A:

Q: Which representations show y as a function of x? II. 111. 12 12 -12 14 14 16 -14 18 A I and II only…

A: We will find which representation shows y as a function of x as following.

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: The baseball leaves Nolan's hand at the same height at which it is caught by Ryan. To Find: Estimate…

Q: The figure defines a function f from A={r, s, t, u} into B={a, b, c, d} in the obvious way. Which of…

A:

Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: TO FIND: Partial derivative

Q: Determine whether the following equation defines y as a function of x. x? +y? = 144 Does the…

A:

Q: The velocity of Engr. Garcia in meters/sec when he jumped out of the plane given is given by the…

A:

Q: Find the functions (a) f ° g  , (b)  g ° f , (c)  f ° f  , and(d) g °g  and their domains.   f(x)  =…

A: Consider the given function as fx=1-3x, gx=cosx

Q: An observer views a rocket take off from a distance of 2 miles from the launch pad, and tracks the…

A: To find the following terms

Q: Which of the following functions is an even function? 2 II O f(x) = 5 csc(4x + 平) 3 2 II O f (x) = 5…

A:

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: 80 85 90 95 35 188 212 238 266 40 197 222 249 278 45 200 226 253 281 50 197 222 249 278

Q: Describe the domain and range of the function f(x,y) sin(y/x).

A: Note- Multiple questions are asked, I am answering the first question is chronological order. Please…

Q: Consider the function f : A → B.

A: Given the function f : A→ B. The relation  f^ from ℙ(A) to ℙ(B) is defined by…

Q: (b) Write the following function in the form of y = f(u) and u = g(x), then find as a function of x…

A:

Q: Let U be a function of two variables then Uxy=Uxx

A: Uxy, Uyx These are called mixed partial derivatives of function U. As long as the function U and its…

Q: The volume of a rectangular prism with a square base is fixed at 500 cm3 a) Determine the surface…

A: Volume is the measure of the amount of space occupied by a closed surface. A rectangular prism is a…

Q: a. Find the other functions of the triangle ABC, given that: 1. Sec A = 2 2. Cot A = 5/2

A: Solution is done in step 2

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: the amplitude, period, and horizontal shift of the function. y = = sin((x + 1))

A: This question can be solved using the concept of general equation of sine function.

Q: guy wire is attached to the top of a 90-ft pole and stretched to a point that is d feet from the…

A: Given: By right angle triangle property, tan β=90d⇒ β=tan-190d.

Q: Find y as a function of a if a?y" + 13ry' + 36y = a, %3D y(1) = -2, y'(1) = -1. y =

A:

Q: onsider the following position function. Find ​(a) the velocity and the speed of the object and ​(b)…

A: Given that: rt=4,t5,e-t, for t≥0 To calculate: vt, vt, and at

Q: The period of the function f(x)= 3sin (x - ") is (а) 2. (b) 3 (c) 27 (d)

A: We have to find the period of the function f(x) = 3 sinx-π4.

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.