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
Answer:
3.85 gallons
Step-by-step explanation:
11/4 gallons /5 x 7
= 2.75 gallons /5 x 7
= 0.55 gallon x 7
= 3.85 gallons
Answer:
a. AB=12.8km
b.BP=15.3km
c. CB=17.2km
d. angle θ=41.46°
e. PC =10.13 km
Step-by-step explanation:
Hi it is 57 is a becase use a protractor
Sum the first 1000 natural numbers:
Since 1000/5 = 200, there are 200 multiples of 5 in the range 1-1000. Sum them up:
Then the sum we want is
