A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.18 meter per second. How fast is the end of the plank sliding along the ground when it is 1.5 meters from the wall of the building? (Round your answer to two decimal places.)

1.) Find the sum V in cartesian and polar coordinates of V1=1000 m/s, V2=1800 m/s 2.) Find the difference of V in polar and cartesian coordinates for V3= 800 m/s and V4= 1400 m/s. The angles are angle1= 35 deg, angle2= 60 deg, angle3= 130 deg, angle4= 340 deg.

Find the area of the region enclosed by the graphs of
x=(1/2)(y^2)-3 and y=x-1

5. The rate of excretion of a biochemical compound is given by ? ′ (?) = 0.01? −0.01? , where t is the time in minutes. Find an expression for f(t), the total amount of chemical excreted, if 0 units are excreted at t = 0. a. Find a function for the position of an object if its velocity is given by ?(?) = ? 2 + ? + 16 and whose initial position is 10 meters. b. Find the position of the object at t = 3 seconds.

How have you contributed to classroom participation, either in class pre-pandemic or electronically post-pandemic?

Sketch and find the area of the region bounded by the curves ?=?+? and ?=?²−?.

Suppose the average yearly salary of an individual whose final degree is a master's is $3333 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $117 thousand. Find the average yearly salary of an individual with each of these final degrees.

The volume of a right circular cylinder with base radius ? and height ℎ is given by: ? = ??^2ℎ. If the base radius is decreasing at a rate of 3 inches per minute and the height is increasing at a rate of 2 inches per minute, at what rate is the volume of the cylinder changing when the radius is 8 inches and the height is 3 inches. Will the volume be increasing or decreasing at this instant? Be sure to answer both questions and be sure to include units in your answer.

A trough is filled with a liquid of density 820 kg/m³. The ends of the trough are equilateral triangles with sides 6 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough. (Use 9.8 m/s² for the acceleration due to gravity.)

The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y = 0.5 x ^2 and below the line y = 280 . (Here, distances are measured in meters.) The water level is 34 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000 kg/ m^ 3 , and the acceleration of gravity is 9.8 m/ sec ^2 .)

Answer in Newtons and make sure that it is not in scientific notation. Check answer as last 5 have been wrong answers. Need detailed steps also

COURSE TITLE:Business Research Methods and Statistical Analysis

TOPIC:Literature Review

Q1/Consider the topic of study is STUDY ON IMPACT OF PERFORMANCE APPRAISAL FEEDBACK ON JOB SATISFACTION AND ITS IMPACT ON ORGANISATION COMMITMENT and prepare the chapter two below points. It must fulfill all the headings of the chapter two

Chapter 2 – Review of Related Literature and Studies

2.1 Related Literature

2.2 Related studies

2.3 Syntheses

Note: Page range between 8 to 15 pages

Find the Maclaurin series of f(x) = [sin(x²)]/x and find its radius of convergence.

1. Find the balance after 5 years in a savings account that pays 2.5% APR compounded monthly if deposits are made to the account each month in the amount of $100.

2. A friend has an IRA with an APR of 6.25%. She stared the IRA at age 25 and deposits $50 per month.
          a) How much will her IRA contain when she retires at age 65?
          b) How much money did she contribute to the account?
          c) Use the answers from parts a) and b) to determine the amount of interest earned.

3. What if your friend from question #2 doubled her deposit and saved $100 per month? Do you think her money would double? Let's find out! Redo question #4, all the parts, with a monthly deposit of $100 per month. Were you surprised by the results?

4. At age 35 you start saving for retirement. Your investment plan pays 6% APR compounded monthly and you want to have $2,000,000 when you retire at age 65.
        a) How much do you need to save each month?
        b) Suppose you had started saving when you were 30 years old. How much would you need to save each month?
        c) Suppose you had started saving when you were 25 years old. How much would you need to save each month?
        d) Were you surprised by the answers in parts a - c? Discuss the effect of time on the growth of money.

Use calculus to find three positive numbers that sum to 150 with the greatest possible product.