Answer:
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Step-by-step explanation:
Let a, b, c represent the three numbers. The problem statement gives rise to three equations:
- a +b +c = 26
- 2a -b = c -2
- -3a +b = c
Adding the first two equations gives
... (a +b +c) +(2a -b) = (26) +(c -2)
... 3a +c = 24 +c . . . . . simplify
... 3a = 24 . . . . . . . . . . subtract c
... a = 8 . . . . . . . . . . . . divide by 3
Adding the second and third equations gives ...
... (2a -b) +(-3a +b) = (c -2) +(c)
... -a = 2c -2 . . . . simplify
... -6 = 2c . . . . . . add 2, substitute for a
... -3 = c . . . . . . . . divide by 2
Using the third equation we can find b.
... -3·8 +b = -3 . . . . substitute for a and c
... b = 21 . . . . . . . . .add 24
The numbers are 8, 21, -3.
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The method above is sort of "ad hoc", taking advantage of the numbers in this particular set of equations. You can use more formal methods of Gaussian elimination or Cramer's Rule to solve these by just following a procedure. Or, your graphing calculator can do it for you.
Here’s how you would work it out
The only way 3 digits can have product 24 is
1 x 3 x 8 = 241 x 4 x 6 = 242 x 2 x 6 = 242 x 3 x 4 = 24
So the digits comprises of 1,3,8 or 1,4,6, or 2,2,6, or 2,3,4
To be divisible by 3 the sum of the digits must be divisible by 3.
1+ 3+ 8=12, 1+ 4+ 6= 11, 2 +2 + 6=10, 2 +3 + 4=9Of those sums of digits, only 12 and 9 are divisible by 3.
So we have ruled out all but integers whose digits consist of1,3,8, and 2,3,4.
Meanwhile they must be odd they either must end in 1 or 3.
The only ones which can end in 1 are 381 and 831.
The others must end in 3.
They must be greater than 152 which is 225. So the
First digit cannot be 1. So the only way its digits can contain of1,3,8 and close in 3 is to be 813.
The rest must contain of the digits 2,3,4, and the only way they can end in 3 is to be 243 or 423.
So there are precisely five such three-digit integers: 381, 831, 813, 243, and 423.
m∠R = 27.03°
Solution:
Given In ΔQRP, p = 28 km, q = 17 km, r = 15 km
To find the measure of angle R:
Law of cosine formula for ΔQRP:
Substitute the given values in the above formula.
Switch the given equation.
Subtract 1073 from both side of the equation.
Divide by –952 on both sides.
Hence m∠R = 27.03°.
