The slope of the line is +2
this means that Jan runs 2 laps every 1 minute
75 > 62
the way I was taught it is that the < and > are alligators and the alligator mouth always opens for the bigger number, because he is hungry
a) plug in x =2700 into the given equation and solve for y
b) plug in y = 43 into the given equation and solve for x
c) plug in y = 0 into the given equation and solve for x
hope this helps.
Answer:
A. It does not matter. The volumes of X and Y are equivalent.
Step-by-step explanation:
Volume of the pyramid = Base area × Height
For rectangular pyramid X:
Given Height of pyramid = 10cm
Base area = Length × Breadth
Base Area = 6cm×5cm = 30cm²
Volume = 10×30
Volume of the pyramid = 300cm²
For pyramid Y:
Given Height = 10cm
Base area = 1/2 base×height
Base area ,= 1/2 × 7.5×8
Base area = 30cm²
Volume of the triangular pyramid = 10×30 = 300cm³
We can see that the volume of X and Y is the same, therefore the type of chocolate Jeremy chose doesn't matter.
Answer:
![f^{-1}(x)=3\frac{ln(\frac{t}{80})}{ln(2)}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D3%5Cfrac%7Bln%28%5Cfrac%7Bt%7D%7B80%7D%29%7D%7Bln%282%29%7D)
It will take 20.9 hours to reach 10000
Step-by-step explanation:
![f(t)=80(2)^{\frac{t}{3}}](https://tex.z-dn.net/?f=f%28t%29%3D80%282%29%5E%7B%5Cfrac%7Bt%7D%7B3%7D%7D)
To find inverse of the function , replace f(x) with y
![y=80(2)^{\frac{t}{3}}](https://tex.z-dn.net/?f=y%3D80%282%29%5E%7B%5Cfrac%7Bt%7D%7B3%7D%7D)
swap the variables
![t=80(2)^{\frac{y}{3}}](https://tex.z-dn.net/?f=t%3D80%282%29%5E%7B%5Cfrac%7By%7D%7B3%7D%7D)
solve the equation for y
![t=80(2)^{\frac{y}{3}}\\\\\frac{t}{80} =(2)^{\frac{y}{3}}](https://tex.z-dn.net/?f=t%3D80%282%29%5E%7B%5Cfrac%7By%7D%7B3%7D%7D%5C%5C%5C%5C%5Cfrac%7Bt%7D%7B80%7D%20%3D%282%29%5E%7B%5Cfrac%7By%7D%7B3%7D%7D)
take ln on both sides
![ln(\frac{t}{80} )= \frac{y}{3} ln(2)\\\\\frac{ln(\frac{t}{80} }{ln(2)} =\frac{y}{3}\\3\frac{ln(\frac{t}{80} }{ln(2)} =y](https://tex.z-dn.net/?f=ln%28%5Cfrac%7Bt%7D%7B80%7D%20%29%3D%20%5Cfrac%7By%7D%7B3%7D%20ln%282%29%5C%5C%5C%5C%5Cfrac%7Bln%28%5Cfrac%7Bt%7D%7B80%7D%20%7D%7Bln%282%29%7D%20%3D%5Cfrac%7By%7D%7B3%7D%5C%5C3%5Cfrac%7Bln%28%5Cfrac%7Bt%7D%7B80%7D%20%7D%7Bln%282%29%7D%20%3Dy)
the inverse function is
![f^{-1}(x)=3\frac{ln(\frac{t}{80})}{ln(2)}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D3%5Cfrac%7Bln%28%5Cfrac%7Bt%7D%7B80%7D%29%7D%7Bln%282%29%7D)
for part b plug in 10000 for t in f^-1(x)
![f^{-1}(10000)=3\frac{ln(\frac{t}{80} }{ln(2)} \\f^{-1}(10000)=3\frac{ln(\frac{10000}{80} }{ln(2)} \\=20.89](https://tex.z-dn.net/?f=f%5E%7B-1%7D%2810000%29%3D3%5Cfrac%7Bln%28%5Cfrac%7Bt%7D%7B80%7D%20%7D%7Bln%282%29%7D%20%5C%5Cf%5E%7B-1%7D%2810000%29%3D3%5Cfrac%7Bln%28%5Cfrac%7B10000%7D%7B80%7D%20%7D%7Bln%282%29%7D%20%5C%5C%3D20.89)
It will take 20.9 hours to reach 10000