What is the answer for this problem

A 4-centimeter rod is attached at one end A to a point on a wheel of radius 2 cm. The other end B is free to move back and forth

zloy xaker [14]

Answer:

Step-by-step explanation:

The triangle that was formed has radius 2:

hypotenuse = 2

adjacent = x = 2*cosθ

opposite = y = 2*sinθ

from the first picture on the left, we see that the rod has length of 4.

We then use pythagoras theorem with respect to the triangle formed with the rod, i.e, the opposite leg, and the length of the remaining side (say, L), we have:

2²sin²θ +L² = 4²

On rearranging and making L subject of formula, we have

L = √(16 - 4sin²θ)

or

L = 2√(4 - sin²θ)

Also, the distance of point B is from the center of the circle, and it is:

2cosθ + 2√(4 - sin²θ)

We know that

3.5 revolutions per second means 3.5(2π) per second.

or

7π radians per second

So we try to write the angle formed as:

θ = 7π*t

where t is the time in seconds.

(a)

2cos(7πt) + 2√(4 - sin²(7πt))

at t = 1/21 we substitute for t, and then

2cos(π/3) + 2√(4 - sin²(π/3))

= 1 + √13 or approximately 4.6

(b)

(c)

B = 2cos(7πt) + 2√(4 - sin²(7πt))

dB/dt = - 14πsin(7πt) - { 14π*cos(7πt)sin(7πt)/√(4 - sin²(7πt)) }

4 0

2 years ago

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what

Anvisha [2.4K]

Question:

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.

Type of Crust Number Sold

Thin crust 312

Thick crust 245

Stuffed crust 179

Pan style 304

Based on this information, of the next 4500 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answer:

1060 thick crusts

Step-by-step explanation:

Given

The above table

Required

Expected number of thick crust for the next 4500

For last week data, calculate the proportion of thick crust sold

$\hat p = \frac{Thick\ crust}{Total}$