The hyperbolic cosine function (cosh) is defined as
cosh (x) = (e^x + e^-x) / 2
The tangent line's slope at any given point on a function is determined by the derivative of that function at that specific point.
d/dx [cosh(x)] = d/dx[(e^x + e^-x) / 2] = (e^x - e^-x) / 2 = sinh(x)
Assuming the slope equals 2, we have
sinh(x) = 2
thus,
x = sinh^-1 (2) = 1.444
Consequently, the curve of y = cosh(x) has a slope of 2 at the coordinate x = 1.44
To work with the repeating decimals, note that since there are two digits repeating, you will be using a 1 followed by two zeros, which is 100. This factor will be important for subsequent calculations.
Let’s denote the repeating decimal as x.
Thus, you can write
x = 0.212121...
Now, if you multiply this equation by 100, you can write it on top of the previous equation.
This results in:
100x = 21.212121...
x = 0.212121...
Next, set up a subtraction by taking the second equation from the first:
100x = 21.212121...
x = 0.212121...
- ----------------------------
99x = 21
Solving for x involves dividing both sides by 3:
33x = 7
Then, divide both sides by 33:
x = 7/33
Thus, we conclude that the repeating decimal 0.212121... equates to the fraction 7/33.
Answer: the fraction is 7/33
The total volume is stated as 1080 cubic feet.
The height is specified to be 9 feet.
The length exceeds the width by 2 feet, meaning Length = x+2
If the stall measures 10 feet in width, then the corresponding length would be 10 +2 = 12 feet.
Calculating the volume yields 10 x 12 x 9 = 1080 cubic feet.
Therefore, it is feasible for the width to measure 10 feet.
Answer:
8 servings
Step-by-step explanation:
At a ratio of 15:1, for each serving that uses 75 grams of rice, it will need 75/15 = 5 grams of spice. With David having 40 grams of spice, he can prepare ...
40 g/(5 g/serving) = 8 servings
