The fuel for a chainsaw is a mix of oil and gasoline.The label says to mix 6 ounces of oil and 16 ounces of gasoline. How much o
2 answers:
You might be interested in
First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.
We have
130 = 2 • 5 • 13
231 = 3 • 7 • 11
so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.
To verify the claim, we try to solve the system of congruences
Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:
130 = 7 • 17 + 11
17 = 1 • 11 + 6
11 = 1 • 6 + 5
6 = 1 • 5 + 1
⇒ 1 = 23 • 17 - 3 • 130
Then
23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)
so that x = 23.
Repeat for 231 and 17:
231 = 13 • 17 + 10
17 = 1 • 10 + 7
10 = 1 • 7 + 3
7 = 2 • 3 + 1
⇒ 1 = 68 • 17 - 5 • 231
Then
68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)
so that y = 68.
Diagram of two triangles
The two triangles are similar because they are both right triangles, meaning that one angle is 90° and the other two are acute (less than 90°).
The diagram on the left is missing its hypotenuse - the variable <em>c</em><em>.</em><em> </em>The hypotenuse is opposite of the right angle. The diagram on the right side is missing one of its legs.
Note: The hypotenuse is the <em>longest</em><em> </em>side of a right triangle.
Word Problen
The legs are 21 blocks and 20 blocks because they are by the right angle. Use the Pythagorean theorem to find the diagonal path's length, which is the hypotenuse.
Standard form of Pythagorean theorem.
Equation with the legs substituted and the missing hypotenuse value - <em> </em><em>c</em><em>.</em>
Square the legs and add.
Take the square root and simplify. The square root of 841 is 29 and -29, but distance is positive.
Thus the diagonal distance is 29 blocks.
Check by substituting.