Find the cosine of the angle between the planes 4x−1y+2z=−4 and the plane 1x+1y−4z=3.

Try this solution:

1. Given: α:4x-y+2z=-4 and β:x+y-4z=3.

if vector n₁⊥α and n₂⊥β, then required cosine is:

where n₁*n₂=4*1+(-1)*1+2*(-4) and |n₁|*|n₂|=√(4²+1²+2²)*√(1²+1²+4²).

2. Using the formula of cosine:

≈0.2572

1 1/5

step-by-step explanation:

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.