Whenever you have a complicated problem like this, it is best to break it down into Sines and Cosines- so csc(t)(sin(t)+cos(t)) since csc(t) = 1/sin(t), we have (sin(t)+cos(t))*1/(sin(t) Distributing out, we get sin(t)/sin(t) + cos(t)/sin(t) This...
Whenever you have a complicated problem like this, it is best to break it down into Sines and Cosines- so csc(t)(sin(t)+cos(t)) since csc(t) = 1/sin(t), we have (sin(t)+cos(t))*1/(sin(t) Distributing out, we get sin(t)/sin(t) + cos(t)/sin(t) This...
When you factor things, you are probably used to seeing something like X2 + BX + C = (X+ )(X+ ), where the two numbers that go in the blanks add up to B and multiply to C. In this case, we can think of the equation as 3X2 + 0X +...
Remember the general form for a parabola which opens to the right: X-h = 1/4p*(Y-k)2 where the vertex is at (h,k) and the distance from the vertex to the focus is p. Thus, h = -5, k = 1, and p = 2-(-5) = 7. Plugging in: X+5 = 1/(4*7) * (Y-1)2 This can...
With any question in this form, we always first completely isolate the 'log' part of the function, and then solve from there. To get the log8(2x+7) alone, we solve for it just as we would solve for any other variable. 3log8(2x+7)+8=10 ...
If the wheels turn 10,000 times, the car will travel 10,000 times the circumference of the wheel. This is because it does not slip- you can see how this affects the movement just by rolling around anything round. The circumference of a circle is pi*diameter, which in this case is pi*28"...
This is a separable equation- meaning the 'y' terms and 'x' terms can be separated. First, we bring the 2xy term to the right side of the equation: y' =x-2xy, which simplifies to y' = x(1-2y). dividing by 1-2y, we get y'/(1-2y) = x which we then rewrite as dy/(1-2y) = xdx....
Since you are given a point, the easiest way to check if it's a solution is to just plug in the point. For both equations, when you plug in x= -1, you should get y=5. First equation: y= -1x+4 = -1*-1+4 = 1+4 =5. Since y=5, this point is on the first line. Second equation:...
The sum of 3 consecutive even integers is at least 80 and at most Call the first number X. The second will be X+2 (the next even number). The third is (X+2)+2=X+4. So the sum is X+X+2+X+4= 3X+6 So we now have 80 ≤ 3x+6 ≤ 90 80 -6≤ 3X+6-6≤...
If you typed the first one correctly, it does not simplify. The rules we have for logs: log(x*y)= log(x) + log(y). log(x/y)=log(x) - log(y). log(x^y)= y*log(x). log base b of x = log(x)/log(b) The first one, as you can see, cannot simplify. We cannot use the rule with exponents,...