Integration Question: ∫ [f(x) / (1 + x)^2]dx, where f(x) is a polynomial of degree two in x, such that f(0)=1,f(1)=3,f(-1)=5.?
Answer Since f(x) is a polynomial of degree two in x, Let f(x) = ax^2 + bx +…
-
-
Orbital geometry of sun, earth and moon?
Question 3- body theorem, What is the orbital geometry of the sun earth and moon Answer The First…
-
Where would you feel more pressure 100 ft. above water or 100 ft. below water?
Answer Below. Why? Because at 100ft above water you only feel the air pressure there. While at 100ft…
-
Least common multiple (lcm) and Greatest common divisor (gcd) question: “Prove lcm(m,n) = m*n/gcd(m,n)?”
Answer It’s equivalent to proving m*n = (lcm(m,n) ) * ( gcd(m,n) ) Now, i’ll have to use…
-
Verify this trigonometrical identity?
Question Show that cos^4(x)-sin^4(x)=cos(2x) Answer We use the identities below. (you should know them by heart) sin^2(x) +…
-
Complete the following pattern and what do you think this pattern really is? 6, 24, 60, 120, 210, …?
Answer 6 = 1 x 2 x 3 24 = 2 x 3 x 4 60 = 3…
-
What is the discriminant of the equation x^ 2 + 4x – n^2= 0 ? And how many solutions does it have?
Answer Discriminant for ax^2 + bx + c is b^2 – 4ac. Thus, in our case, Discriminant =…
-
Time question
Question Martina leaves home at 9 am, bicycling at a rate of 24 mi/h. Two hours later, John…
-
Can someone PROVE hero’s (or Heron’s) formula?
Answer We use the formula area = (1/2)bc.sin(A) The formula above can be “proven” easily by definition that…
-
Is the sine and cosine of a 60 degree angle A in a right triangle always the same?
Answer No. Here are the “sames’”. Sin(60 deg) = Cos(30 deg) = 0.866 Sin(30 deg) = Cos(60 deg)…