) The depth in feet of water at a dock changes with the rise and fall of the tides. The depth is modeled by the function D(t) = 5 sin(t –) + 8, where t is the number of hours after midnight. Find the rate at which the depth is changing at 6am.

Q: Find the equation of the tangent line to the curve y = 5x cos T at the point (T, – 57). The equation…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the derivative of the trigonometric function. g(t) = 5 cos2t

A: g(t) = 5 cos2t We need to find the derivative of the trigonometric function:

Q: on the graph of f(x) = 4 sin (7 pi(x)), points P and Q are at consecutive lowest and highest points…

A:

Q: An equation for the tangent line to the curve In(sec x + y?) = tan(x)+e2" – 1 at the point (x, y) =…

A: Given curveIn (sec x +y2) = tan x +e2x-1We have to find the equation of tangent line at the point…

Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)= —4 sinx…

A: We have to find

Q: 258. [T] The daily temperature in degrees Fahrenheit of Phoenix in the summer can be modeled by the…

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: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: We have given parametric equation x=4sint, y=2cost  We have to find the tangent line of the given…

Q: 3. (a) What is the derivative of sin(g(z))7 (b) What is the derivative of sin(2r + T)?

A: We have to find

Q: Find the equation of the tangent line to the curve y = 5 sec(x) – 10 cos(x) at the point (T/3,5).…

A:

Q: A particle moves along a linear path and its displacement, relative to the start, is modeled by the…

A: In 2pi/3 seconds. displacement of the particle will be

Q: A 4 m long ladder is resting against a vertical wall when it suddenly starts to slide down the wall.…

A: This question can be solved using the concept of rate of change of quantities.

Q: ind the slope of the line that is tangent the curve sin(2x)+sin y=e*y – 1 at (0,0). our answer…

A:

Q: A Ferris wheel has a radius of 70 m, and the bottom of the wheel passes 6 m above the ground. If the…

A: t (minutes) h(t) 0 6 2.5 76 5 146 7.5 76 10 0

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: 3. Find the derivative of the function, and do your best to simplify the result. [P372]| arcsin 3r…

A:

Q: A Ferris wheel of diameter 18.5 m rotates at a rate of 0.2 rad/s. If passengers board the lowest car…

A:

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: Find the equation of the tangent line to the curve y = 4 sin x + 2 cos a at the point (0, 1/2). The…

A:

Q: The current, I, in amperes, flowing through an ac (alternating current) circuit at time t, in…

A:

Q: 6. In the triangle shown, if 0 increases at a constant rate of 3 radians per minute, at what rate is…

A: Given:             θ increases at a constant rate of 3 radians per minute               i.e.,…

Q: The temperature of coffee in a large urn fluctuates as coffee is dispensed and more coffee is added.…

A: The given function is: ft=140+10 sint To find the average rate of change in 0,π

Q: A ladder of length 8 meters leaning against a wall starts to slide. If its upper end slides down the…

A:

Q: Find a function that models the simple harmonic motion having amplitude 10 cm and period of 3…

A:

Q: The number of tons of paper waiting to be recycled at a 24 h recycling plant can be modelled by the…

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 an equation for the line tangent to the curve atthe point defined by the given value of t.…

A:

Q: The amount of daylight in a town can be modelled by the sinusoidal function d(t)= 4.37 cos 0.017t +…

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

Q: A mass suspended from a spring oscillates in simple harmonic motion. The mass completes 9 cycles…

A: The equation of simple harmonic motion will be defined as, y=asinωt  where a is the amplitude of the…

Q: For a person exercising, the velocity v (in liters per second) of airflow during a respiratory cycle…

A:

Q: 1. The Average Rate of Change ("ARC") to. Given that f(x) = -2x² +4, what is the ARC: 1) From 0 to 2…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question. Please…

Q: Find the derivative of the trigonometric function.

A: To Find: The derivative of ht=2cot2π t+2

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A:

Q: The horizontal displacement of a swinging pendulum is given by f(t) = 1.5 cos(t)e-0.05t, where f(t)…

A: Given function is : ft=1.5 cost e-0.05t , f(t) is the horizontal displacement

Q: Find the derivative of the trigonometric function. h(t) = 2 cot2( t + 2)

A: h(t)=2cot2(t+2)Here we use the concept of chain rule. Formulas ddxxn=n xn-1ddxcot x=-csc2x

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

A:

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: (i) One month later, the tower is holding 21.5 million kilograms of water, when it experiences a…

A: Firstly, we need to find the spring constant. It's given that the restoring force is 1.45 million…

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: find an equation for the line tangent to the curve atthe point defined by the given value of t.…

A: Given, To get the equation of the tangent line, finding slope is the first step. Here both x and y…

Q: The rate at which rainwater flows into a drainpipe is modeled by the function R, where R(t) = 20 sin…

A:

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

A:

Q: The function f(z) = e-y sin x is harmonic function

A:

Q: 51. The horizontal range R of a projectile launched from ground level at an angle e and initial…

A:

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Given,         x=t-sint , y=1-3cost , t=π3

Q: Find the equation of the tangent line to the curve y = 4 sec(x) – 8 cos(x) at the poin (T/3, 4).…

A:

Q: find an equation for the line tangent to the curve atthe point defined by the given value of t.…

A: We need to find an equation for the tangent line to the curve at a given point of t. Also, we need…

Q: 1. Suppose that a bunny is running at a rate of 3 ft per second when r = 4. How fast is the angle 0…

A:

Q: The height of a buoy on a lake is changing during a storm. The height's rate of change can be…

A: Given: The height's rate  of change modeled by r(t)=0.5 cos(0.2t)

Q: A. Find an equation for the tangent line to the curve x = -1 + sec? t, y = tan t %3D d2y at t =…

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.