Find 4 consecutive even integers whose sum is 156?
2 answers:
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Let A, B and C be the amount machines A, B and C, respectively, produce each hour alone.
With all three machines together produce 520 drinks each hour, we know that the addition of the amount that each produces each hour is equal to 520, that is.
Now, similarly, machines A and B produce together 320 drinks each hour, so the sum of the amounts A and B produce each hour is equal to 320, so:
If machine C produce 30 more drinks than B each hour, than the amount of B plus 30 will be the amount of C:
So, we got the system of equations:
To solve, notice that A + B is known, because of the second equation, so we can substitute A + B by 320 in the first equation:
Now, we can substitute C into the third equation and solve for B:
And, finally, we can substitute B into the second equation and solve for A:
Answers:
First box:
Second box:
Third box:
Fourth box:
Answer: the height of the pole is 16.1 m.
Step-by-step explanation:
The scenario is illustrated in the attached photo.
x represents the height of the pole.
y represents the distance from the foot of one stabilizing wire to the foot of the pole.
30 - y represents the distance from the foot of the other stabilizing wire to the foot of the pole.
In solving the triangles, we would apply the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side.
Considering triangle ACD,
Tan 60 = x/y
x = ytan60 = y × 1.732
x = 1.732y- - - - - - - - -1
Considering triangle BCD,
Tan 38 = x/(30 - y)
x = (30 - y)tan38 = 0.781(30 - y)
x = 23.43 - 0.781y- - - - - - - - -2
Substituting equation 1 into equation 2, it becomes
1.732y = 23.43 - 0.781y
1.732y + 0.781y = 23.43
2.513y = 23.43
y = 23.43/2.513
y = 9.3
x = 1.732y = 1.732 × 9.3
x = 16.1 m
