?

So, I'm a pretty thin person but over the wintertime, I do get a little soft around my thighs, tummy, (in place of my normal toned). I do lighter workouts in winter and increase them during the Spring to tone my body before Summer. 

However, recently my chest has been hurting and I went to the doctor and they told me I have costochondritis (inflammation of the ribs) and I should only stick to yoga and stay away from strenuous exercise. 

My issue is how am I supposed to get toned now? Are there any light workout regimens that won't affect my ribs that I can do? I don't even know how to do Yoga, can it tone my belly? Again I don't have much fat whatsoever, I'm 5'1 ~100 lbs woman but I eat like a freight train (call me Shaggy from Scooby Doo) and I don't want to be soft and squishy for summer if you get my gist? My weight actually usually increases after a few months of strenuous exercise. 

Any help is appreciated. 

So about a week ago, it was very hot where I live and I had pulled a muscle in my thigh from a workout so I decided to ice it, but my dumbass was super hot and clearly not in the right headspace because I applied an ice pack directly to my thigh and sat there. I have a very high pain tolerance due to neuropathy issues and altho I felt a little pinprick of pain a few mins in I didn't really care because I was feeling a lot better. I took it off after like an hour and went about my day and then a couple hours later I was changing into my sleep shorts and I noticed a huge *** red spot on my entire thigh and i went "oh **** ice burn". I gradually warmed my skin up and it feels fine (no blistering or cracked skin) but its VERY discoloured. 

The initial burn was an angry red and now its changed colours so many times and it is now a dark purple. The skin of the burn feels like my regular skin but its just dark purple. It stands out horribly and its ******* summer I feel super self conscious in dresses and shorts.... is this going to fade eventually and how long will it take? What can I do to make it fade faster?

It doesn't really hurt, I'll feel an occasional tingle here and there and sometimes in the shower and its quite itchy but other than that completely ignorable except for its appearance! 

1. Consider the circle given by the equation:

(x − 1)^2 + (y − 2)^2 = 4.

(a) Determine the point(s) on the circle where the tangent line is horizontal.

(b) Determine the point(s) on the circle where the tangent line is vertical.

2. Two radar stations located at points A and B, where point B is 6 km east of point A, are tracking a ship (north east of A). Suppose that the distance between the ship and A is increasing at the rate of 28 km/h when the ship is 5 km from A. At this same instant, the ship is also 5 km from B, and the distance between them is increasing at 4 km/h. How fast is the ship moving at that instant?

Please explain how you got the answers so I may use this to study!

Question 1:

Consider a predator-prey model where the prey population density is given by x, and the net growth rate of the prey population, denoted by P(x), is given by (birth rate minus rate of loss to predation)

:P(x) = rx − K(x/a + x) , where r, a, K > 0

(a) What values of x result in the smallest net growth rate? Under what condition(s) does such a minimal net growth rate exist?

(b) Suppose the number of prey is determined to be in the range 0 ≤ x ≤ N, find the absolute maximum net growth rate.

Question 2:

A cylindrical tree trunk is to be cut into a rectangular wooden beam. What is the most economical way to cut the beam so as to waste the least amount of material?

Please explain your reasoning as I wish to understand, my prof went over this weeks lesson rather poorly and I am currently studying for an exam for another class tomorrow. Thank you in advance.

Question 1:

Consider a predator-prey model where the prey population density is given by x, and the net growth rate of the prey population, denoted by P(x), is given by (birth rate minus rate of loss to predation)

:P(x) = rx − K(x/a + x) , where r, a, K > 0

(a) What values of x result in the smallest net growth rate? Under what condition(s) does such a minimal net growth rate exist?

(b) Suppose the number of prey is determined to be in the range 0 ≤ x ≤ N, find the absolute maximum net growth rate.

Question 2:

A cylindrical tree trunk is to be cut into a rectangular wooden beam. What is the most economical way to cut the beam so as to waste the least amount of material?

Please explain your reasoning as I wish to understand, my prof went over this weeks lesson rather poorly and I am currently studying for an exam for another class tomorrow. Thank you in advance.

1. Consider the polynomial

p(x) = K(x^2 − 16)(x − a)

where a and K are constants. Suppose that p(0) = 12, and p(x) has an inflection point at x = 1/3.

(a) Find the values of constants a and K.

(b) Find and classify all critical points of the polynomial p(x).

(c) Which critical point is a maximum?

2. Given the function f(x) = (x^3)/(1-x^2)

(a) Does f(x) have any asymptotes? Justify your answer.

(b) Determine all intervals where f(x) is increasing and where it is decreasing.

Locate and classify all critical points and local extrema of f(x).

a) You jump off a bridge with a (massless) bungee cord (a stretchable spring) tied around your ankle. You fall for 15 m before the bungee cord begins to stretch. Your mass is 60 kg and we assume the cord obeys Hooke’s law, F = –kx, with k = 55 N/m. If we neglect air resistance, use conservation of energy to calculate the distance d below the bridge your foot will be before coming to a stop. (3 marks)

b) What is the magnitude of the acceleration the cord exerts on you when it is fully extended? Give answer in terms of multiples of g = 9.8 m/s2 (i.e. this is how many g’s it is exerting and we can tolerate about 4-5 g’s before passing out). (1 mark)

c) If the river is 60 m below the bridge, what spring constant, k, do you need for the bungee cord so that you get your body fully dunked in the river (i.e. your foot is at the level of the river, 60 m below the bridge)? (2 marks)

d)What is the magnitude of the acceleration the cord exerts on you when it is fully extended for the spring constant found in (c)? Again, give answer in terms of multiples of g = 9.8 m/s2. Which is the softer ride? the bungee cord used in (a) or c)? (1 mark)

I m pretty sure I ve got a) figured out but b,c,and d stump me. Explanations are appreciated.

A ball is hung by a string from the inside roof of a van. The van is moving with a

constant velocity, v, around a curve (radius R = 150 m) on an unbanked road.

(a) What angle does the ball make with respect to the vertical?

(b) Derive an expression for the maximum velocity before the car starts slipping

sideways on the road?

(c) What angle would you need to tilt the road (banked curve) to maintain the van’s

motion in a circle, if the tires were without a frictional force?

Please explain as to how you derive the answers and what approaches you used.

A box of mass, m is on top of a box of mass M. There is friction between the surfaces of the two boxes,

but no friction between the large box and the table. A force F is applied to the large box as shown.

a) You apply a force, F, so that the two boxes move together (i.e. the top box doesn’t slip). Draw a

free body diagram of the forces acting on each box (i.e. you should have two FBDs, one for each

box). (2 marks)

b) For the situation in (a), solve Newton’s equations for the acceleration of the system? (4 marks)

c) Now you want to apply a large enough force to just keep the top box from slipping. Solve for

the maximum force you can apply, Fmax, before the top box just begins to slip? (4 marks)

(The picture in the question is just a box on the ground with a small box on top with an arrow coming out of big box and going to the right titled F for force)

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Calculus help needed!?

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I am taking my first calculus course and I honestly have no idea what I am doing. I took a few approaches to the problems but I'm doing something wrong. Explanations would be highly appreciated so I could see how you did the problems.

Question 1:

Consider the function : f(x)=

(3x^3 + |x|)/x

(a) Write f(x) as a piecewise function.

(b) Sketch the graph of f(x).

(c) Is the function f(x) defined at x = 0? Justify.

(d) Find the slope of the tangent line to the curve at the point x = 3

Question 2:

If an arrow is shot upward on the moon with a velocity of 58 m/s, its height in meters after t

seconds is given by

h(t) = 58 t − 0.83 t

(a) Give an expression for the average velocity of the arrow on the time interval [1, 1 + a],

and simplify the resulting expression.

(b) Find the average velocity on the given time intervals:

(i) [1, 1.1]

(i) [1, 1.01]

(i) [1, 1.001]

(c) Use the definition of the derivative to find the instantaneous velocity after one second

Thank you to anyone who helps.

In a certain biathlon competition the athlete must hit a target using a blowgun after taking a physics exam for 3 hours. A blowgun is a tube in which a dart is sent out by blowing on one end. The target is a 1.0 cm diameter circle at 5.00 m height on a wall 10.0 m from the end of the tube, as in the diagram below. The inexperienced athlete lines up the tube of the blowgun pointing directly at the target, such as along the dotted line shown in the

diagram. They blow a dart with an initial speed of 35.0 m/s. Assuming no air resistance:

a) Where does the dart hit the wall? Show a plot of the projectile y(x) graph indicating the important parameters. (5 pts)

b) Given the same speed as in (a), what must the initial angle of the dart be in order to hit the centre of the target? (4 pts)

c) If there was air resistance, what effects would you expect to have on your answers

above? (1)

(Note: A rifle which shoots bullets at much higher speeds will have calibrated the angle of the aiming sites along the rifle barrel to partially compensate for the effects of gravity and air.)

The prof has said knowing this trig identity may be helpful : 1/cos^2x= 1+tan^2x

But I don't even know how to approach the problem! An explanation would be helpful.

Problem 2 (6 marks). You are running to catch a bus which has just started to

move away from the stop. You are on a flat, straight road and you and the bus both

start from zero velocity at time t = 0 s. Given the data below:

Object Acceleration Max speed Stamina

Human 0 – 30 km/h in 5 s 30 km/h Can go at top speed for 10 s.

Bus 0 – 50 km/h in 15 s 50 km/h Can go at top speed for a long

time

a) How far can you run before you get exhausted?

b) How far has the bus moved in the meantime?

c) Based on your answers in the first 2 parts, what is the maximum distance you

can be behind the bus to catch up with it? (Whether the driver sees you and

stops the bus to let you on is another question.)

Now my scalp is itchy and has this irritated feeling..I used coconut oil on my hair and left it in for three hours so I shampooed my hair three times to get it out but I guess I didn't need that much shampoo. Got an itchy, burning, irritated feeling around the nape of my neck, back of head. What should I do? My hair is also very dry despite the coconut oil mask.