Math Answers

Solve sqrt1-2r=-2+sqrt4r+9

Q. Prove that α′(s) and α′′(s) are orthogonal.

Theorem
Let α(s) be parametrized by arc length. Then |α′(s)| =1. (Prove it)

what does that symbol stand for ф

All sections of an Introduction to Criminology course at a large university were given the same final exam. Test scores were distributed normally with a mean of 68 and a standard deviation of 6.
a) What percentage of students scored between 60 and 69 (a grade of C) and what percentage scored between 70 and 79 (a grade of B)?
b) In words, briefly summarize your findings.

Consider the given vector equation.
r(t) = 4eti + 5e−tj
(a) Find r'(t).
r'(t) =


(b) Sketch the plane curve together with the position vector
r(t)
and the tangent vector
r'(t)
for the given value of
t =0

Q.Find the length of the astroid x=acos3t, y=asin3t, [0, 2π].

Q.Find the length of the Asteroid x=acos3t, y=asin3t.

A batch of 10 products comes randomly from three factories A, B and C. This batch is checked to detect the defective products. The defective rates of three factories A, B and C are 5%, 10% and 15% respectively
a. Determine the probability that there are exactly two defective products
b. Given that this batch has two defectives, what is the probability that it comes from factory B
c. If there are two batches come from the same factory and first one has exactly two defective items, what is the probability that the second one has two defectives?

Test the hypothesis that the average dissolution time is 20 seconds, using the random sample of dissolution times below.
Dissolution time (secs): 23 19 26 22 18 27

(b) Two different instruments were used to make a number of replicate measurements. The results were:
Instrument A: 12.06 12.14 12.03 12.09 12.05
Instrument B: 14.62 14.97 14.60 14.51 14.01 14.11
Do these results indicate that either instrument is more precise?