Answer:
366.6 mm²
Step-by-step explanation:
Step 1: find XY using the Law of sines.
Thus,
m < W = 180 - (70+43) (sum of angles in a triangle)
W = 180 - 113 = 67°
WY = 24 mm
X = 43°
XY = ?
Cross multiply:
Divide both sides by 0.68 to solve for XY
XY ≈ 32.5 mm
Step 2: find the area using the formula, ½*XY*WY*sin(Y).
Area = ½*32.5*24*sin(70)
Area = ½*32.5*24*0.94
= 32.5*12*0.94
Area = 366.6 mm² (nearest tenth)
Answer:
(a) -6
Step-by-step explanation:
P(x) = ax^3 +bx - 3
- P(-1) = -a-b-3 = 0
- therefore a+b=-3
- P(1) = a+b-3
- P(1) = -3 - 3 = -6
- (a)
Answer:
16 hours
Step-by-step explanation:
let t be time, n the number of computers and w the number of workers, then
t = 
← k is the constant of variation
To find k use the condition n = 30, w = 6 and t = 10 , then
10 = 
( multiply both sides by 6 )
60 = 30k ( divide both sides by 30 )
2 = k
t = 
← equation of variation
When w = 5 and n = 40 , then
t = 
= 
= 16 hours
The 7 out of ten adds up to 56 the last 3 add up to 36 which equals 92 divided by ten is 9.2 average
Answer: a) An = An-1 + An-2
b) 55ways
Step-by-step explanation:
a) a nickel is 5 cents and a dime is 10cent so a multiple of 5 cents is the possible way to pay the tolls in both choices.
Let An represents the number of possible ways the driver can pay a toll of 5n cents, so that
An = 5n cents
Case 1: Using a nickel for payment which is 5 cents, the number of ways given as;
An-1 = 5( n-1)
Case 2: using a dime which is two 5 cents, the number of ways is given as;
An-2 = 5(n-2)
Summing up the number of ways, we have
An = An-1 + An-2
From the relation,
If n= 0, Ao= 1
n =1, A1= 1
b) 45 cents paid in multiples of 5cents will give us 9 ways(A9)
From the relation, we have that
Ao = 1
A1 = 1
An =An-1 + An-2
Ao = 1
A1 = 1
A2 = A1+Ao = 1+1= 2
A3 = A2 + A1 = 3
A4 = A3+A2=5
A5=A4+A3=8
A6=A5+A4=13
A7 =A6+A5 = 21
A8= A7+A6= 34
A9= A8+A7= 55
So there are 55ways to pay 45cents.
