Answer:
![2 \leqslant y \leqslant \infty](https://tex.z-dn.net/?f=2%20%5Cleqslant%20y%20%5Cleqslant%20%20%5Cinfty%20)
Step-by-step explanation:
y is equal to 2 and goes up to infinity
Set up a proportion.
62 over 9 = x over 1
62/9=6.8
9/9=1
6.8 over 1
rounded would be seven
so 6.8 hotdogs per minute
Answer: 6 recipes
Step-by-step explanation: Just divide the 6 cups of buttermilk by 7/8 because each recipe need 7/8 cup of butter milk. You will get a number like this 6.857142857142857 (there are probably more decimals that come after it.) But, all the numbers after the 6 are useless because more recipes can't be made with those because you need at least 7/8 cups for one recipe. So, this will make 6 recipes. Hope this helps!
If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate
.
We have
![\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20x%5E4%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%28x%2Bh%29%5E4%20-%20x%5E4%7Dh)
Expand the numerator using the binomial theorem, then simplify and compute the limit.
![\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20x%5E4%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%28x%5E4%2B4hx%5E3%20%2B%206h%5E2x%5E2%20%2B%204h%5E3x%20%2B%20h%5E4%29%20-%20x%5E4%7Dh%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B4hx%5E3%20%2B%206h%5E2x%5E2%20%2B%204h%5E3x%20%2B%20h%5E4%7Dh%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%284x%5E3%20%2B%206hx%5E2%20%2B%204h%5E2x%20%2B%20h%5E3%29%20%3D%20%5Cboxed%7B4x%5E3%7D)
In general, the derivative of a power function
is
. (This is the aptly-named "power rule" for differentiation.)
Answer:
Force= Mass×Accelaraion
F=m×a
But as The unit of accelaration is given miles per hour and the SI is meters per second sqaure we have to convert 10mph to m/s²
Thus, we have 10mph = 4.47 meters per second square. (i converted using scientific calculator)
So now we have,
2000N= m×4.47m/s²
= 2000/4.47m/s²=m
= 447.42
Thus the mass of the object is 447.42 (i am not sure of units)