Having trouble with a few calculus homework problems?

Question

1. Annual sales of sparkling water in the U.S. in the period 1993-2003 could be approximated by
s(t)= -1.3t^2+4t+160 million gallons

(3
where t is the time (in days) since the egg was laid (an egg will typically hatch at around t=28). Use the model to estimate the following (give the units of measurement for each answer and round all answers to two significant digits):
a. The daily oxygen consumption 20 days after the egg was laid
b. The rate at which the oxygen consumption is changing 20 days after the egg was laid
c. The rate at which the oxygen consumption is accelerating 20 days after the egg was laid.

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Grades
2. A production formula for a student's performance on a difficult English examination is given by
g= 4hx-0.2h^2-10x^2
where g is the grade the student can expect to obtain, h is the number of hours of study for the examination and x is the number of hours of student's grade point average. The instructor finds that students GPA's have remained constant at 3.0 over the years and that students currently spend an average of 15 hours studying for the examination. However, scores on the examination are dropping at a rate of 10 points per year. At what rate is the average study time decreasing?

Thanks, I appreciate the help

Answer 1

I can help you with Problem 2....

g= 4hx-0.2h^2-10x^2

We're looking for the change in the study hours for the exam, which is dh/dt.

x = hours in GPA = 3***
h = hours of exam study = 15***

(***Note: Both x and h have remained constant over the years....the importance of this fact will become very clear in the next few steps)

dg/dt = -10 points/year

dg/dt = (dg/dh)*(dh/dt)

dg/dh = 4x - 0.4h - 20x * (dx/dh)

Since GPA's and study time have remained constant....

dx/dh = 0

This simplifies the expression for dg/dh to:

dg/dh = 4x - 0.4h

For x = 3 & h = 15,

dg/dh = 4*3 - 0.4*15 = 6 points/study hours

dh/dt = (dg/dt) *(dh/dg)

= (-10 points/year) * (study hours/6 points)

= - 5/3 study hours/year

Answer 2

1. You have given the sales and asking for oxygen consumption after eggs were laid. I am sorry i am a little confused.

Answer 3

Volume of a cone = V = ?D²h/12 h = 3D/eight ==> D = 8h/three D² = 64h²/nine V = ?64h³/108 = ?16h³/27 dV/dt = (16?h²/nine)dh/dt dV/dt = 10 m³/min : given 10 = (16?h²/nine)dh/dt dh/dt = ninety/(16?h²) = forty five/(8?h²) at h = two, dh/dt = forty five/(32?) ? zero.4476 m/min