Answer:
Step-by-step explanation:
if solving for y
solve for y by simplifying both sides of equation, then isolating the variable.
y=-3w+10+W
if solving for W
W=3w-10+y
if solving for w
w=W/3 - y/3 + 10/3
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
x=16
Explanation
the ratio is 2:3
it means for every 2 cars, there are 3 trucks
Now, it the total of trucks is 24,the proportion must be the same, so
Step 1
Let
x represents the number of cars for 24 trucks
Step 2
solve for x
Hence, the answer is 16
Answer:
Step-by-step explanation:
There are two case I used, since we are not give diagram, so I assumed that U can be the right angle and also assume that W can be the right angle so, I used both assumption to solve, check attachment
1. Using Trigonometry
Assuming that U is the right angle
Tan θ = opp / adj
Tan 60 = UW / UV
Tan 60 = UW / 18
UW = 18 × Tan60
UW = 18 × √3
UW = 18√3
UW = 31.18 unit
Also, assume that W is right angle
Using trigonometry
Sinθ = opp / hyp
Sin60 = UW / UV
Sin60 = UW / 18
UW = 18 × sin60
UW = 18 × √3/2
UW = 9√3
UW = 15.59 unit