rectangle expands and contracts with time t (in seconds). Its area is given by A= 4 + sin t square meters. At t = 3.14 (pi), the following is observed. (1) the width of the rectangle expands at the rate of 0.1 meters per second. (2) The width of the rectangle is 1 meter long How fast is the height of the rectangle changing at t = 3.14 (pi)?

Q: Calculate a light-year in [a] km and [b] Mile

A: We are given with the following information : Speed of light=3*108 m/s=3*105 km/ s=1.86*105 mile/s…

Q: A sphere of radius r has surface area A = 4πr2 and volumeV = (4/3)πr3. If the radius of sphere 2 is…

A: a)The ratio of the areas, A2/A1

Q: Calculate the value of the error with one decimal place for: z = x・y where X = 25 +/- 8% Y and = 35…

A:

Q: As a result of a medical treatment, the number of a certain type of bacteria decreases according to…

A: Here we have P(t) = 500e−0.495t (a) Hence at t=0 we get P(0)= 500e-0.495×0=500e0=500×1=500 (b)At…

Q: Use the "Common Metric Prefix "Chart on your Math Review homework to convert 1 um to meters.

A: We know that1μ=10-6                    11cm=10-2m                 2

Q: Using the equation Ek = mv2/2 , write an equation to solve for (a) m and (b) v.

A: Given data:  Kinetic energy equation Ek = mv2/2 Required: Equation to solve for mass and velocity

Q: For the graph of vx versus t shown, estimate the following: i) What is the slope of the tangent line…

A: The above problem can be solved in two different ways. The first method using the two-point formula…

Q: Perform the following unit conversions: a) 65 miles per hour to meters per second (hint: 1 mile =…

A:

Q: In astronomy, a unit of distance is used called the Astronomical Unit. It is the average distance…

A: The given values with suitable variables are listed below. Here, c denotes the light speed and d…

Q: Suppose your hair grows at the rate 1/31 in. per day. Find the rate at which it grows in nanometers…

A: Given data:  Hair growth rate = 1/31 in. per day Required: Hair growth rate in nm/s

Q: Paleontologists use the function W(x) = 4√/2x to estimate the walking speed of a dinosaur, W(x), in…

A: We are given the walking speed of dinosaur. This speed is a function of length of leg of dinosaur.…

Q: The function f(t)=7600(1.85)^((t)/(7)) represents the change in a quantity over t days. What does…

A:

Q: (a) L² (3x². 2 (3x² - 2x - 1) 8 (x - 3)dx (b) *(cos x) 8(x − n)dx 5 (c)( (cos x)8(x - 2π)dx

A: I have use the concept property of dirac delta function

Q: The average distance between Earth and the Sun is 1.5 ✕ 1011 m. (a) Calculate the average speed of…

A: According to Newtons's law of gravitation There is always gravitational force between two bodies.…

Q: Morty measures a Meeseeks box (an object that is roughly a cube) with an old rusty ruler. Because of…

A: Given that, Width (W)=20.2 cm=0.202 m Height (H)=19 cm=0.19 mDepth(D)=20.31 cm=0.2031 mMass(M)=7.401…

Q: Express this product in units of km3 in standard scientific notation and with the appropriate number…

A: given that (4.2 km) × (4.0 m) × (13.24 × 10−3 mm)

Q: calipers,

A:

Q: A rectangle has a length of (2.3 ± 0.1) m and a width of (1.4 ± 0.2) m. Calculate the area and the…

A:

Q: The density of the Earth can be expressed by the equation density = C{1.22 -(r/R)}, where R is the…

A: The mass can be represented as, M=∫0RρdV=∫0RC1.22-rR4πr2drM=4πC∫0R1.22r2-r3RdrM=4πC1.22r33-1Rr440R

Q: The Bay of Fundy in Nova Scotia, Canada is reported to have the largest tides in the world with high…

A:

Q: 3. A physicist needs to estimate the density of a cube (all sides of the cube have equal length).…

A: The density is given byD=M/L3the data given, the massμM=1σM=0.02the mean value of length and…

Q: A car takes time t=(2.5±0.1) s to travel a distance Ax=(0.922±0.001) m. What is the relative…

A:

Q: The period T of a simple pendulum is the amount of time required for it to undergo one complete…

A: The  expression for the time period of a simple pendulum is given,  T=2πLpgq

Q: Each of the following equations was given by a student during an examination 1/2 mv^2=1/2…

A: 1) The equation is given as, Here, v0 and v denotes the initial and the final velocity, g denotes…

Q: Assume your hair grows at a rate of 1/44th of an inch per day. How fast is that in nm/s (nanometers…

A: Relation between units of length: 1 inch =2.54×107 nm units of time: 1 day=24×3600 s Grow rate of…

Q: The figure shows a man sitting in a bosun's chair that dangles from a massless rope, which runs over…

A:

Q: Problem 1: Suppose A = (-3.03 m)i + (4.35 m)j, B = (2.71 m)i + (-4.29 m)j + (2.99 m)k, and D (-2.48…

A:

Q: You purchased 5.2kg of apples from a store. You noticed that they used the smallest division of 4.2…

A: 1) % relative error = ∆m×100/m  = ( 4.2 × 10^-3 × 100 ) /5.2  = 0.081 % 2) area (A) = L × W =…

Units and Dimensions

These are generally defined as the terms which precede or describes the dimensions further. These are also further divided into two parts namely fundamental units and the derived units.