Write the logarithm in terms of ln 2 and ln 3. ln 6
We know by properties of logarithms that, ln(uv) = ln u + ln v So, in this case let u = 2 and v = 3. Therefore, we can rewrite the ln6 as ln(2*3), which based on our property, can be rewritten as ln 2 + ln 3.
What is the area of a trapezoid with base 1 (b1) = 2 in base 2 (b2) = 7in and height (h) = 10 in?
The formula for area of a trapezoid is A = 1/2h(b1 + b2). We know that: b1 = 2 in b2 = 7 in h = 10 in. We can now substitue bot bases and height into out equation. So, A= (1/2)(10)(2 + 7) A=5(9) A=45 in.
In one semester, Kate and Joe spend a combined 250 hours in the tutoring lab. If Joe spent 40 more hours in the lab than Kate, how many hours did Kate spend in the lab?
Let k = # of hours Kate spent in the tutoring lab Let j = # of hours Joe spent in the tutoring lab. We could now form a system of equations to figure out how many hours Kate spent in the lab. k + j = 250 and j = k + 40 Now, substitute the second equation in for j in the first equation. k + (k + 40) =250 combine like terms 2k + 40 = 250 subtract 40 on both sides 2k = 210 divide each side by 2 k = 105 Kate spent 105 hours in the tutoring lab.