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
A(n)=3+2(n-1)
Hope this helps
Answer:
the cost of the replacement window will be $<u>1501.44</u>.
Step-by-step explanation:
area of an equilateral triangle:
A = (√3)/4 * (17)^2
A = 125.12 in^2
125.12 * 12 = <u>$1501.44</u>
Answer:
D) 49.1 in²
Step-by-step explanation:
area of entire cake = πr² = (3.14)(5²) = 78.5 in²
area of 5 slices = (78.5)(5/8) = 49.1 in²
Answer:
6
Step-by-step explanation:
First- replace the variables
<u>-6² -3</u>
6 + 3
Second- eliminate
<u>-6²</u>
6
Third- exponents (remember, 2 negatives = a positive)
<u>36</u>
6
Lastly- divide
6
