Answer:
<4,22>.
Step-by-step explanation:
This question involves the concepts of addition and scalar multiplication of vectors. It is given that the vector u = <-4, 1> and v = <-1, 6>. To find -2u, simply multiply -2 with the elements of u. This will give:
-2u = <-4*-2, 1*-2> = <8, -2>.
Similarly:
4v = <-1*4, 6*4> = <-4, 24>.
Hence,
-2u + 4v = <8, -2> + <-4, 24> = <8-4, -2+24> = <4,22>.
So the correct answer is <4,22>!!!
Answer:19.74 gallons of the gas in the tank is wasted.
Step-by-step explanation:
Since the efficiency of the gas engine is 6%, wastage is #= 100 - 6 = 94%.
Therefore wastage = 94% x 21=94 x21/100=19.74 gallons
Answer:14pi and 43.98 (2dp)
Step-by-step explanation:
circumference =2xpixr
radius = 14 divide by2 =7
2x pi x 7=14pi
14pi =43.98229715
=43.98 (2dp)
Answer:
m<N = 76°
Step-by-step explanation:
Given:
∆JKL and ∆MNL are isosceles ∆ (isosceles ∆ has 2 equal sides).
m<J = 64° (given)
Required:
m<N
SOLUTION:
m<K = m<J (base angles of an isosceles ∆ are equal)
m<K = 64° (Substitution)
m<K + m<J + m<JLK = 180° (sum of ∆)
64° + 64° + m<JLK = 180° (substitution)
128° + m<JLK = 180°
subtract 128 from each side
m<JLK = 180° - 128°
m<JLK = 52°
In isosceles ∆MNL, m<MLN and <M are base angles of the ∆. Therefore, they are of equal measure.
Thus:
m<MLN = m<JKL (vertical angles are congruent)
m<MLN = 52°
m<M = m<MLN (base angles of isosceles ∆MNL)
m<M = 52° (substitution)
m<N + m<M° + m<MLN = 180° (Sum of ∆)
m<N + 52° + 52° = 180° (Substitution)
m<N + 104° = 180°
subtract 104 from each side
m<N = 180° - 104°
m<N = 76°
