Answer:
6 mph
Step-by-step explanation:
Let x mph be the rate of the boat. Going up the river boat has the rate x-2 mph (the current decreases the rate of the boat) and going down the river boat has the rate x+2 mph (the current increases the rate of the boat). Then it will take
hours to go up the river and
hours to go down the river. Thus,
![\dfrac{12}{x-2}-\dfrac{12}{x+2}=1\dfrac{1}{2},\\ \\\dfrac{12x+24-12x+24}{(x-2)(x+2)}=\dfrac{3}{2},\\ \\96=3(x^2-4),\\ \\x^2-4=32,\\ \\x^2=36,\\ \\x=\pm6\ mph.](https://tex.z-dn.net/?f=%5Cdfrac%7B12%7D%7Bx-2%7D-%5Cdfrac%7B12%7D%7Bx%2B2%7D%3D1%5Cdfrac%7B1%7D%7B2%7D%2C%5C%5C%20%5C%5C%5Cdfrac%7B12x%2B24-12x%2B24%7D%7B%28x-2%29%28x%2B2%29%7D%3D%5Cdfrac%7B3%7D%7B2%7D%2C%5C%5C%20%5C%5C96%3D3%28x%5E2-4%29%2C%5C%5C%20%5C%5Cx%5E2-4%3D32%2C%5C%5C%20%5C%5Cx%5E2%3D36%2C%5C%5C%20%5C%5Cx%3D%5Cpm6%5C%20mph.)
The rate of the boat cannot be negative, hence, x=6 mph.
Answer:
<u>(r³)⁻² = r ³ ˣ ⁻² = r ⁻⁶ = 1/r⁶</u>
Step-by-step explanation:
1. Let's recall the rules about the power of a power and the rule of negative exponents to simplify the expression provided:
The first rule tells us that to raise a power to a power, just multiply the exponents. Here you see that r³ raised to the ⁻² power.
The second rule says that any number different than zero, raised to a negative power equals its reciprocal raised to the opposite positive power.
Thus, x ⁻ⁿ = 1/x ⁿ
2. Now, let's find the equivalent after following these rules:
<u>(r³)⁻² = r ³ ˣ ⁻² = r ⁻⁶ = 1/r⁶</u>
Answer:
(6,0)
Step-by-step explanation:
Answer:
this is the answer but it must be 20 character long
8x+3