Please Solve some Maths questions?

Question

Q1_ Evaluate Sin^2 33 + Sin^2 57.

Q2_ If a & b are Zeros of a polynomial P(x)=2x^2 - 7x + 3. Find the value of a^2 + b^2.

Q3_ Which term of A.P. 21, 18, 15, ....... is -81.

Q4_ Find the length of a tangent drawn from a point 13cm away from the center of a circle of radius 5cm.

Q5_ Find the value of m If equation mx^2 +2x + m = 0 has two equal roots.

Q6_ A card is drawn from a pack of cards. Find the probability that is a red face card.

Q7_ 11 good pens are mixed with 5 bad pens. A pen is taken from the lot. Find the probability that is a good pen.

Q8_All three face cards of spades are removed from a well shuffled pack of 52 cards. A card is drawn from remaining pack. Find the probability of getting: A black face card, A queen.

Q9_ On dividing 3x^3 - 2x^2 + 5x - 5 by a polynomial g(x), the quotient & remainder are x^2 - x +2 & -7 respectively. Find g(x).

Q10_ Show that the points (1, -1) (5, 2) (9, 5) are collinear.

Answer 1

1. Note: cos(33) = sin(90-33) = sin57
Thus sin^2(33) + sin^2(57) = sin^2(33) + cos^2(33) = ?

2. Note also from the property of roots... 7/2 = a+b ... 3/2 = ab
Thus (a^2 + b^2) = (a+b)^2 - 2ab = 49/4 - 3

3. formula for the nth term: u_n = 21 + (n-1)(-3). Equate to -81 and solve for n.

4. you have a right triangle whose hypotenuse is 13 and one leg is 5. You are looking for the other leg.

5. m = 1 or m = -1. Discriminant is zero. b^2 - 4ac=0.

6. There are 6 red faces, from hearts and diamonds... thus it will be 6/52.

7. 11/16.
§
8. black faces... 3 faces of clubs ... its 3/48.
queen: 3 queens... still 3/48

9. Use division algorithm: P = Q*D + R .. P is the polynomial, Q is the quotient, D is the divisor, R is the remainder.
D = g.
D = (P-R)/Q = ([3x^3 - 2x^2 + 5x - 5] - [-7]) / [x^2 - x +2]

10 . Get the slope bet (1,-1) & (5,2). It should be equal to the slope bet (1,-1) & (9,5).

Answer 2

Q2. It is easy to find the roots of the equation. They are 1/2 and 3. These are a nd b. You can compute a^2 + b^2.

Q3. The n=th term t_n is given by t_n = a + (n - 1)*d, where a is the first term (21) and d is the common difference (-3). Solve -81 = 21 + (n - 1)*(-3) and you will have the answer.

Q5. The discriminant is 4 - 4m^2. The roots are equal if and only if the discriminant = 0. Therefore m = +/-1.

Q9. Since the quotient is of second degree, g(x) is linear, say g(x) = ax + b. Compute (ax + b)*(x^2 - x + 2) - 7 and equate corresponding coefficients with those of the given cubic.

Maybe someone else will complete your homework assignment for you.

Answer 3

Simplify 2x + 6 - 3 = 8 - 3x Collect like terms on each side 2x + 3x = 8 - 6 + 3 Combine 5x = 5 Divide x = 1