The answer is 4x^12-24x^9+36x^6
For a more detailed answer, check the picture below.
Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).
Let <em>x</em> be the inverse. Then <em>x</em> is such that
23<em>x</em> ≡ 1 (mod 1000)
Use the Euclidean algorithm to solve for <em>x</em> :
1000 = 43×23 + 11
23 = 2×11 + 1
→ 1 ≡ 23 - 2×11 (mod 1000)
→ 1 ≡ 23 - 2×(1000 - 43×23) (mod 1000)
→ 1 ≡ 23 - 2×1000 + 86×23 (mod 1000)
→ 1 ≡ 87×23 - 2×1000 ≡ 87×23 (mod 1000)
→ 23⁻¹ ≡ 87 (mod 1000)
Answer:
multiply either sides by 3:
divide either sides by πr² :
Again using the Pythagorean Theorem:
h^2=x^2+y^2, where h is the hypotenuse of a right triangle and x and y are the side lengths. You are given that the hypotenuse is 34 ft and the base side is 16ft. Let h=34, x=16, and y=height, then you have:
34^2=16^2+y^2
y^2=34^2-16^2
y^2=1156-256
y^2=900
y=√900
y=30 ft
So the ladder will reach a spot 30 feet high on the building.
Remember that there is 100 centimeters in a meter, and 1000 meters in a kilometer. If you multiply both values together (so you have a conversion of centimeters to kilometers) you get 100,000. Therefore, 100,000 centimeters makes a kilometer. Divide 320,000 by 100,000 and you get 3.2. Therefore, a centimeter would represent 3.2 kilometers.
