Answer:
p = (2k + 1)i + j
q = 25i + (k + 4)j
p . q = 11
Find the dot product of p and q
(2k + 1)(25) + (k + 4) = 11
50k + 25 + k + 4 = 11
51k = -18
k = - 18/51 = –6/17.✅
b) p.q = |p||q|cos∅
p= (2k + 1)i + j = [2(-6/17) + 1)i + j ]= 5/17i + j
|p| = √ (5/17)² + 1²
|p| = √314/ 17 ( The square root doesn't cover the 17) = 1.0424
q = 25i + (k + 4)j = 25i + ( -6/17 + 4)j
q = 25i + 62/17 j
|q| = √ 25² + (62/17)²
= 25.2646
Now applying them to the formula above
We already have p.q = 11 from the question.
11 = (1.0424)(25.2646)Cos∅
11 = 26.3358Cos∅
Cos∅ = 11/26.3358
Cos∅ = 0.4177
∅ = 65.31°.
This should be it.
Hope it helps
Since this triangle is an isosceles triangle, two of its angles are going to be equal. We know that all the angles in a triangle are equal to 180o.
Step 1: 180 - 98 = 82
Step 2: divide the sum of the two angles (82) to give me the measurement of one of the angles
82/2 = 41
Formula is 2(wl+hl+hw)
and dimensions are doubled so 5 is 10, 4 is 8, and 3 is 6.
2[(8x6)+(6x10)+(6x8)]
=376 cm^3
Answer:
80 men
Step-by-step explanation:
4 : 5 10 : 9
40 : 50 : 45
40 x 2 = 80
It looks like a scalene triangle but i’m not so sure