34. [M] Let B D f1; cost; cos2 t; : : : ; cos6 tg and C D f1; cost; cos 2t; : : : ; cos 6tg. Assume the following trigonometric identities (see Exercise 37 in Section 4.1). cos 2t D 1 C 2 cos2 t cos 3t D 3 cost C 4 cos3 t cos 4t D 1 8 cos2 t C 8 cos4 t cos 5t D 5 cost 20 cos3 t C 16 cos5 t cos 6t D 1 C 18 cos2 t 48 cos4 t C 32 cos6 t Let H be the subspace of functions spanned by the functions in B. Then B is a basis for H, by Exercise 38 in Section 4.3. a. Write the B-coordinate vectors of the vectors in C, and use them to show that C is a linearly independent set in H. b. Explain why C is a

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb

$15.40 per mile

step-by-step explanation:

you have to round up to 4 because 6 is over 5 so you have to round the 3 up to 4

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.