Let x=staplers and y=hole punches.
We have:
x+y=11
7x+12y=112
7x+7y=77
5y=35
y=7
x+7=11
x=4
Therefore, he bought 4 staplers and 7 hole punches.
Answer:
1,620,000 meters
Step-by-step explanation:
Speed- 450 meter----- 1 second
1 minute = 60 seconds
60 minutes (1 hour) = 3600 seconds
Distance in 1 hour
1 ------ 450
3600---- X
X= 3600 x 450
x= 1,620,000 meters
Step-by-step explanation:
a, 3
b,
draw lines through the corresponding corners of each shape These lines will cross at the centre of enlargement O
Answer:
66.992%
Step-by-step explanation:
![Sales, S(t)=7-6\sqrt[3]{t}](https://tex.z-dn.net/?f=Sales%2C%20S%28t%29%3D7-6%5Csqrt%5B3%5D%7Bt%7D)
Since we want to maximize revenue for the government
Government's Revenue= Sales X Tax Rate
![R(t)=t \cdot S(t)\\R(t)=t(7-6\sqrt[3]{t})\\=7t-6t^{1+1/3}\\R(t)=7t-6t^{4/3}](https://tex.z-dn.net/?f=R%28t%29%3Dt%20%5Ccdot%20S%28t%29%5C%5CR%28t%29%3Dt%287-6%5Csqrt%5B3%5D%7Bt%7D%29%5C%5C%3D7t-6t%5E%7B1%2B1%2F3%7D%5C%5CR%28t%29%3D7t-6t%5E%7B4%2F3%7D)
To maximize revenue, we differentiate R(t) and equate it to zero to solve for its critical points. Then we test that this critical point is a relative maximum for R(t) using the second derivative test.
Now:
![R'(t)=7-6*\frac{4}{3} t^{4/3-1}\\=7-8t^{1/3}](https://tex.z-dn.net/?f=R%27%28t%29%3D7-6%2A%5Cfrac%7B4%7D%7B3%7D%20t%5E%7B4%2F3-1%7D%5C%5C%3D7-8t%5E%7B1%2F3%7D)
Setting the derivative equal to zero
![7-8t^{1/3}=0\\7=8t^{1/3}\\t^{1/3}=\dfrac{7}{8} \\t=(\frac{7}{8})^3\\t=0.66992](https://tex.z-dn.net/?f=7-8t%5E%7B1%2F3%7D%3D0%5C%5C7%3D8t%5E%7B1%2F3%7D%5C%5Ct%5E%7B1%2F3%7D%3D%5Cdfrac%7B7%7D%7B8%7D%20%5C%5Ct%3D%28%5Cfrac%7B7%7D%7B8%7D%29%5E3%5C%5Ct%3D0.66992)
Next, we determine that t=0.6692 is a relative maximum for R(t) using the second derivative test.
![R''(t)=-8*\frac{1}{3} t^{1/3-1}\\R''(t)=-\frac{8}{3} t^{-2/3}](https://tex.z-dn.net/?f=R%27%27%28t%29%3D-8%2A%5Cfrac%7B1%7D%7B3%7D%20t%5E%7B1%2F3-1%7D%5C%5CR%27%27%28t%29%3D-%5Cfrac%7B8%7D%7B3%7D%20t%5E%7B-2%2F3%7D)
R''(0.6692)=-3.48 (which is negative)
Therefore, t=0.66992 is a relative maximum for R(t).
The tax rate, t that maximizes revenue for the government is:
=0.66992 X 100
t=66.992% (correct to 3 decimal places)