Answer:
![-\frac{3\sqrt[3]{t} }{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%5Csqrt%5B3%5D%7Bt%7D%20%7D%7B2%7D)
Step-by-step explanation:
1: Write g(t) as y, resulting in 
2: Interchange the variables y and t, resulting in 
3: Multiply both sides by 27, resulting in 
4: Divide both sides by -8, resulting in 
5: Find the cube root of both sides, resulting in ![\sqrt[3]{-\frac{27t}{8} }=y](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-%5Cfrac%7B27t%7D%7B8%7D%20%7D%3Dy)
6: Apply a radical rule, resulting in ![-\sqrt[3]{\frac{27t}{8} } =y](https://tex.z-dn.net/?f=-%5Csqrt%5B3%5D%7B%5Cfrac%7B27t%7D%7B8%7D%20%7D%20%3Dy)
7: Apply another radical rule, resulting in ![-\frac{\sqrt[3]{27t} }{\sqrt[3]{8} } =y](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%5B3%5D%7B27t%7D%20%7D%7B%5Csqrt%5B3%5D%7B8%7D%20%7D%20%3Dy)
8: Simplify the denominator, resulting in ![-\frac{\sqrt[3]{27t} }{2} =y](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%5B3%5D%7B27t%7D%20%7D%7B2%7D%20%3Dy)
9: Apply yet another radical rule, resulting in ![-\frac{\sqrt[3]{27}\sqrt[3]{t} }{2} =y](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%5B3%5D%7B27%7D%5Csqrt%5B3%5D%7Bt%7D%20%20%20%7D%7B2%7D%20%3Dy)
10: Simplify ![\sqrt[3]{27}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D)
, resulting in ![-\frac{3\sqrt[3]{t} }{2} =y](https://tex.z-dn.net/?f=-%5Cfrac%7B3%5Csqrt%5B3%5D%7Bt%7D%20%20%20%7D%7B2%7D%20%3Dy)
Answer:
4.80 mm to 2 d.p
Step-by-step explanation:
w = f(r)
f'(r) = (dw/dr) = (0.0218 mm/mm)
So, for a small difference in rainfall of 220 mm, what is the corresponding small difference in width of leaves in the two forests given.
One definition of a derivative or a rate of change is that it is the ratio of very small differences in the dependent variable to very small differences in the independent variable.
Mathematically,
(dw/dr) = (Δw/Δr) for very small Δw and Δr.
0.0218 = (Δw/220)
Δw = 0.0218 × 220 = 4.796 mm = 4.80 mm to 2 d.p
Hope this Helps!!!
Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250.
According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a).
In this case,
f(x)=x^3-75x+250
(x+a)=(x+10)
Therefore, the remainder f(-a)=f(-10)
=x^3-75x+250
=(-10)^3-(75*-10)+250
=-1000+750+250
=1000-1000
=0.
The remainder is 0. So, (x+10) is a factor of x^3-75x+250.
Answer:
Step-by-step explanation:
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