The height of a pebble in a bicycle wheel is described by the function h(t) where h(t) represents the height of the point in centimetres and t represents the time in seconds. a) What is the diameter of the bicycle wheel? Show your work. b) The pebble falls out of the bike wheel after 3 minutes of riding. At what height did the pebble fall out of the wheel? = 34 cos 4. 6(t + 1.7) + 34

Q: sin x cos? x dx

A:

Q: Make a trigonometric substitution to evaluate / x V25 – x² dx

A: Formulae used: 1-sin2x=cosx ddxsinx=cosx ddxsin2x=2sinxcosx

Q: Based on Degree two function: V x (V f) = ? О 1

A: Answer: None of these.

Q: The definite integral (tan2(x) + sec2(x)]dx when evaluated is equal to AV3+Bx, where A and B are…

A:

Q: A man programs his sprinkler system to have a period of minutes. He notices that the highest point…

A: Given problem can be modeled as: the general equation is given by h(t)=a .Sin(kt)   where a=…

Q: A mass weighing 16 pounds is attached to a spring whose spring constant is 9 Ib/ft. Find the…

A: Let m be the mass attached to a spring with spring constant k then  the equation of motion is…

Q: The displacement of a mass suspended by a spring is modeled by the function h(t) = 7 sin(10zt) %3D…

A:

Q: From the posted lecture notes/video, one estimate for .1 I = sin(x*)dr is Round your answer to two…

A: The complete solutions are given below

Q: For y=−5cos(x)+4, its amplitude is ________?   its midline is y ________?

A: For y=−5cos(x)+4, Rewrite the given equation is sine function is, y=-5sinπ2-x+4y=5sinx-π2+4 ......1…

Q: On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft building on…

A: Given:On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft…

Q: As television cable is pulled from a large spoolto be strung from the telephone poles along a…

A: Given: The truck pulling the cable moves at a steady  6 ft/sec. We have to find the rate the spool…

Q: Find the equation of a sine wave in the form y = a sin(x + c) +d that is obtained by shifting the…

A:

Q: In the given question, verify the identity:- sinh(x + y) = sinh x cosh y + cosh x sinh y

A: Consider the provided identity, sinhx+y=sinhx coshy+coshx sinhy Verify the provided identity.…

Q: A Ferris wheel with diameter 20 feet rotates counterclockwise and makes 2 revolutions per minute. At…

A: Given: Diameter of Ferris wheel = 20 feet Wheel makes 2 revolutions per minute.  Height of car on…

Q: The height of an arch above the ground is given by y = 10 sin sin x , for 0 < x < T. What is the…

A:

Q: Find the value of the trig function indicated. 3) tan 0 7 23

A:

Q: A person's blood pressure (in millimeters of mercury) while resting is given by the function R(t) =…

A: person's blood pressure (in millimeters of mercury) while resting is given by the function R(t) = 25…

Q: sin ede 1- cos e 8.

A: The integral of sinθ is given by -cosθ and the integral of cosθ is given by sinθ. The basic formula…

Q: The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 +40…

A:

Q: A beacon on a lighthouse 1 mile from shore revolves at the rate of 10TT radians per minute. Assuming…

A: Consider the following: The circumference of the circle being swept by the light at the distance 2…

Q: Find the exact value of the function: arctan 1 0 품 -표 ㅅ

A: Value of tan(π/4) is 1

Q: The height of an arch above the ground is given by the function y = 6 cos x for -55x55. What is the…

A:

Q: A typical human heart pumps 70 milliliters(mL) of blood with each heartbeat. Assuming a heart rate…

A: The Fundamental Theorem of Calculus (FTC) states that ∫abf'(x)dx=Fb-F(a), where F(x) is the…

Q: Use the trapezoidal rule with n = 2 to approximate the value of sin(x²)dx. Round your answer to four…

A:

Q: 4. sinx 1-sin² x dx

A: We have to find the value of the given integral ∫sinx1-sin2xdx

Q: An object attached to a spring oscillates around a position and is represented by the function y = 2…

A: Note : As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: The displacement of a mass suspended by a spring is modeled by the function h(t) = 14 sin(15rt)…

A:

Q: Determine a formula for a sinusoidal function which models the height of a point on the…

A: The general form of the sinusoidal cosine function is y=AcosBt+C+D. Where A is the amplitude, B is…

Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

A:

Q: Sketch, on separate graphs, each of the functions : (i)sinh(x). (ii)cosh(x). (iii)tanh(x).

A: Hyperbolic functions: These functions are defined as the algebraic expressions of the exponential…

Q: The graph of f (1) = sin (z) is transformed to a new function, g(1), by stretching it vertically by…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 8km from the lift off point.…

A: A hot air balloon rising vertically is tracked by an observer located 8km from the lift off point.…

Q: Find the extrema of the function on the given interval, and say where they occur. sinx+cosx, 0 less…

A: Given f(x)= sinx+cosx ------(1) let's differenitate (1)f'(x) = cosx -sinx

Q: Q2: Using Trapezoidal rule evaluate sin(x) dx by dividing the range into 6 equal parts (Hint; use…

A:

Q: The graph of a sinusoidal function has a maximum point at (0, 7) and then intersects its midline at…

A: Solution: Let the sinusoidal function be fx=A·coscx     ......(1) (NOTE: in our case sinusoidal…

Q: Between two telephone poles that are 40 feet apart, there is a wire suspended in the shape of a…

A: we have to find slope of the curve and where the wire meets tha left pole

Q: A boat at anchor is bobbing up and down in the vertical distance, y, in feet, between the sea floor…

A:

Q: Find the frequency (in Hz) of a wave whose period is 0.58 s. (Round your answer using the rules for…

A: Given :— Time Period of wave = 0.58 sec. Wave Frequency = ? Using Formula :— Time Period =…

Q: 5. A group studies tides and records the function y = 1.5 sin ( (x – 8)) + 4.25 with time in x…

A: y=1.5sinπ 3x-8+4.25 first, we need to find the period the coefficient of x is π3 so take b=π3 the…

Q: 3. If a body of weight W pounds is dragged along a horizontal floor at constant velocity by means of…

A: Consider the given function F=kwksinθ+cosθ

Q: Given a function f(x)=cosx. For h=0.01, at the point x0 = 0.8, a) (picture1) Find the approximate…

A:

Q: A kite flies horizontally at an altitude of 20 m while unwinding the rope. Then, the angle that his…

A: Solution for a: Given dxdt=1 m/s. Here, cot θ=x20…1 And, sin θ=2050θ=sin-12050θ=0.411516846 radians

Q: f (x) = cos(3æ) – sin(x), xo = 0

A:

Q: As a wave passes by an offshore piling, the height of the water is modeled by the function h(t) = 8…

A: The height function is modeled by h(t)=8cosπ10t. Where t is time. We have to answer the following...

Q: How fast is the distance between the range finder and the balloon increasing (in meters per minute),…

A:

Q: Consider a triangle where two sides have fixed lengths 14 cm and 16 cm. Suppose the two sides are…

A:

Q: Solve the following equation for x. arcsin(x) + 2 arctan(x) = T Enter your answer rounded to three…

A:

Q: From the graph we can determine the range of each sinusoidal function: a) For f(x)=2 sin x, R =, b)…

A:

Q: Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per…

A: Given:-Traffic flow function,F(t)=82+4sint2where,F(t) is measured in car per minutet is measured in…

Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

A:

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.