Answer:
24 cm³
Step-by-step explanation:
V = LWH = 2 × 3 × 4 cm³ = 24 cm³
Answer:
It is correct
Step-by-step explanation:
Gr8 job
Answer:
hope it helps
Step-by-step explanation:
Answer:
![L(x)=1+\dfrac{1}{3}x](https://tex.z-dn.net/?f=L%28x%29%3D1%2B%5Cdfrac%7B1%7D%7B3%7Dx)
![\sqrt[3]{0.95} \approx 0.9833](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B0.95%7D%20%5Capprox%200.9833)
![\sqrt[3]{1.1} \approx 1.0333](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1.1%7D%20%5Capprox%201.0333)
Step-by-step explanation:
Given the function: ![g(x)=\sqrt[3]{1+x}](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%5B3%5D%7B1%2Bx%7D)
We are to determine the linear approximation of the function g(x) at a = 0.
Linear Approximating Polynomial,![L(x)=f(a)+f'(a)(x-a)](https://tex.z-dn.net/?f=L%28x%29%3Df%28a%29%2Bf%27%28a%29%28x-a%29)
a=0
![g(0)=\sqrt[3]{1+0}=1](https://tex.z-dn.net/?f=g%280%29%3D%5Csqrt%5B3%5D%7B1%2B0%7D%3D1)
![g'(x)=\frac{1}{3}(1+x)^{-2/3} \\g'(0)=\frac{1}{3}(1+0)^{-2/3}=\frac{1}{3}](https://tex.z-dn.net/?f=g%27%28x%29%3D%5Cfrac%7B1%7D%7B3%7D%281%2Bx%29%5E%7B-2%2F3%7D%20%5C%5Cg%27%280%29%3D%5Cfrac%7B1%7D%7B3%7D%281%2B0%29%5E%7B-2%2F3%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Therefore:
![L(x)=1+\frac{1}{3}(x-0)\\\\$The linear approximating polynomial of g(x) is:$\\\\L(x)=1+\dfrac{1}{3}x](https://tex.z-dn.net/?f=L%28x%29%3D1%2B%5Cfrac%7B1%7D%7B3%7D%28x-0%29%5C%5C%5C%5C%24The%20linear%20approximating%20polynomial%20of%20g%28x%29%20is%3A%24%5C%5C%5C%5CL%28x%29%3D1%2B%5Cdfrac%7B1%7D%7B3%7Dx)
(b)![\sqrt[3]{0.95}= \sqrt[3]{1-0.05}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B0.95%7D%3D%20%5Csqrt%5B3%5D%7B1-0.05%7D)
When x = - 0.05
![L(-0.05)=1+\dfrac{1}{3}(-0.05)=0.9833](https://tex.z-dn.net/?f=L%28-0.05%29%3D1%2B%5Cdfrac%7B1%7D%7B3%7D%28-0.05%29%3D0.9833)
![\sqrt[3]{0.95} \approx 0.9833](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B0.95%7D%20%5Capprox%200.9833)
(c)
(b)![\sqrt[3]{1.1}= \sqrt[3]{1+0.1}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1.1%7D%3D%20%5Csqrt%5B3%5D%7B1%2B0.1%7D)
When x = 0.1
![L(1.1)=1+\dfrac{1}{3}(0.1)=1.0333](https://tex.z-dn.net/?f=L%281.1%29%3D1%2B%5Cdfrac%7B1%7D%7B3%7D%280.1%29%3D1.0333)
![\sqrt[3]{1.1} \approx 1.0333](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1.1%7D%20%5Capprox%201.0333)
Answer:
b)
Step-by-step explanation:
The line with positive slope is 3x-5y≥15 and the line with negative slope is 2x+3y≤12.
This is because such inequalities represent half planes which are divided by the corresponding lines.
Put (0,0) in both lines to check if the origin lies in the shaded half plane or not.