Recent content by Bushy

I found it. a+b=6000 and 30a+28000 = 24y+35200 gives the solution.

Oz Jeans has factories in Mydney and Selbourne. At the Mydney factory, fixed costs are \$28 000 per month and the cost of producing each pair of jeans is \$30. At the Selbourne factory, fixed costs are \$35 200 per month and the cost of producing each pair of jeans is $24. During the next...

[FONT=Times New Roman][FONT="Times New Roman"]A rower travels upstream at 6 km[FONT="Arial"]/[FONT="Times New Roman"]hand back to the starting place at 10 km[FONT="Arial"]/[FONT="Times New Roman"]h.The total [FONT=Times New Roman][FONT="Times New Roman"]journeytakes 48 minutes. How far upstream...

Given 3^x=4^y =12^z show that $$z=\frac{xy}{x+y}$$ I've take logs on both sides and find myself going in circles, any hints?

I found it $$a = \frac{1}{2}(5+3\sqrt{5})$$

Well the question comes with a diagram. The linear equation goes through that minimum. What have I tried? I have made the cubic equal to the linear equation but that gives me a value for x in terms of a

For $$ f(x) = (x-1)^2(x-a) $$ Find the exact value of $$a$$ such that the local min lies on the point with equation $$y=-4x $$

For $$P=P_0\times e^{G(t)}$$ and $$G'(t) = a+bt$$ Show $$G(0)=0$$ I get $$G(t) = \int a+bt ~dt = at+\frac{1}{2} b t^2+C$$ therefore $$G(0)=C $$

I think it does

I think this checks out... $$\int \frac{e^{2x}+e^x-1}{e^x+1}~dx$$ $$\int e^x ~dx- \int \frac{1}{e^x+1}~dx$$ $$e^x-\ln(e^x+1)+C$$

For a cubic function $$y=f(x)$$ three points A, B and C lie on a straight line with respective coordinates (-p,f(p)),(0,f(0)) and (p,f(p)) where p is a non zero constant. a. Show that $$\frac{f(-p)+f(p)}{2} =f(0)$$ I tried $$\frac{f(-p)+f(p)}{2} =\frac{0}{2} = 0 = f(0)$$ That doesn't seem...

call these inequality

I have $$\displaystyle c\times \int_2^5 x+1 ~dx = 1$$ $$\displaystyle c\times \left[ \frac{x^2}{2}+x\right]_2^5 = 1$$ $$\displaystyle c\times \left(\left[ \frac{5^2}{2}+5\right]-\left[ \frac{2^2}{2}+2\right]\right) = 1$$ $$\displaystyle c\times \left(\left[ 12.5+5\right]-\left[...

just use x instead of theta

How about $$ r\left(\theta\right) = \int r'(\theta) d\theta = \int 6+\sec ^2 \left({\theta}\right)d\theta = 6\theta +\tan(\theta) +C $$