<span>Sixty percent of the days in the desert were hot and dry. Out of the 365 days, how many were hot and dry?
Solution is simple.
There are 365 days and 60% of those are hot and dry. What is 60% of 365?
365 x .60 = 219
</span>
Answer:
7
Step-by-step explanation:
Move the -8 to the other side and use the rule change side change sign:
2x=6+8
2x=14
Move the 2 and convert the multiplication(as its 2×x ) into division:
x= 14÷2
x=7
We have an equation: 27/?= 36/100
Cross multiply:
36*?= 27*100
⇒ ?= 27*100/36= 75
36% of 75 is 27~
Answer:
(a)![L(x)=48x-64](https://tex.z-dn.net/?f=L%28x%29%3D48x-64)
(b)![P_{2}(x)=48x-64+3(x-4)^{2}](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3D48x-64%2B3%28x-4%29%5E%7B2%7D)
(c)Using Linear Approximation,L(4.2)=137.6
Using Quadratic Approximation,![P_{2}(4.2)=137.72](https://tex.z-dn.net/?f=P_%7B2%7D%284.2%29%3D137.72)
Step-by-step explanation:
Given: ![f(x) = 16x^{3/2}, a = 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%2016x%5E%7B3%2F2%7D%2C%20%20a%20%3D%204)
(a)Linear Approximation, ![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)
![f(4) = 16*4^{3/2}=128](https://tex.z-dn.net/?f=f%284%29%20%3D%2016%2A4%5E%7B3%2F2%7D%3D128)
![f'(x) = 24\sqrt{x}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%2024%5Csqrt%7Bx%7D)
![f'(4) = 24\sqrt{4}=24*2=48](https://tex.z-dn.net/?f=f%27%284%29%20%3D%2024%5Csqrt%7B4%7D%3D24%2A2%3D48)
![L(x)=128+48(x-4)](https://tex.z-dn.net/?f=L%28x%29%3D128%2B48%28x-4%29)
![L(x)=128+48x-192\\L(x)=48x-64](https://tex.z-dn.net/?f=L%28x%29%3D128%2B48x-192%5C%5CL%28x%29%3D48x-64)
(b)Quadratic Approximation, ![P_{2}(x)=f(a)+f'(a)(x-a)+\frac{1}{2}f''(a)(x-a)^{2}](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3Df%28a%29%2Bf%27%28a%29%28x-a%29%2B%5Cfrac%7B1%7D%7B2%7Df%27%27%28a%29%28x-a%29%5E%7B2%7D)
![f''(x)=12x^{-1/2}\\f''(4)=12*4^{-1/2}=6](https://tex.z-dn.net/?f=f%27%27%28x%29%3D12x%5E%7B-1%2F2%7D%5C%5Cf%27%27%284%29%3D12%2A4%5E%7B-1%2F2%7D%3D6)
![P_{2}(x)=48x-64+3(x-4)^{2}](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3D48x-64%2B3%28x-4%29%5E%7B2%7D)
(c)To approximate:
L(x)=48x-64
L(4.2)=48(4.2)-64=137.6
Also, Using Quadratic Approximation
![P_{2}(x)=48x-64+3(x-4)^{2}\\P_{2}(4.2)=48(4.2)-64+3(4.2-4)^{2}=137.72](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3D48x-64%2B3%28x-4%29%5E%7B2%7D%5C%5CP_%7B2%7D%284.2%29%3D48%284.2%29-64%2B3%284.2-4%29%5E%7B2%7D%3D137.72)
Answer:
The origin of the coordinate plane is taken at the vertex of the arch in such a way that its vertical axis is along the positive y-axis.
y =3