Answer:
£1,049
Step-by-step explanation:
The computation of the amount after 5 years is shown below:
Here we have to determined the future value
As we know that
Future value = Present value × (1 + rate of interest)^number of years
= £950 × (1 + 0.02)^5
= £950 × 1.02^5
= £950 × 1.1040808032
= £1,049
<h3>The lateral area for the pyramid with the equilateral base is 144 square units</h3>
<em><u>Solution:</u></em>
The given pyramid has 3 lateral triangular side
The figure is attached below
Base of triangle = 12 unit
<em><u>Find the perpendicular</u></em>
By Pythagoras theorem
![hypotenuse^2 = opposite^2 + adjacent^2](https://tex.z-dn.net/?f=hypotenuse%5E2%20%3D%20opposite%5E2%20%2B%20adjacent%5E2)
Therefore,
![opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8](https://tex.z-dn.net/?f=opposite%5E2%20%3D%2010%5E2%20-%206%5E2%5C%5C%5C%5Copposite%5E2%20%3D%20100%20-%2036%5C%5C%5C%5Copposite%5E2%20%3D%2064%5C%5C%5C%5Copposite%20%3D%208)
<em><u>Find the lateral surface area of 1 triangle</u></em>
![\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base](https://tex.z-dn.net/?f=%5Ctext%7B%20Area%20of%201%20lateral%20triangle%20%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20opposite%20%5Ctimes%20base)
![\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48](https://tex.z-dn.net/?f=%5Ctext%7B%20Area%20of%201%20lateral%20triangle%20%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%208%20%5Ctimes%2012%5C%5C%5C%5C%5Ctext%7B%20Area%20of%201%20lateral%20triangle%20%7D%20%3D%2048)
<em><u>Thus, lateral surface area of 3 triangle is:</u></em>
3 x 48 = 144
Thus lateral area for the pyramid with the equilateral base is 144 square units
Answer:
i beleive its option number 1
Applying exponential properties, the simplified base for the function is given as follows:
![f(x) = 2(3)^{2x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%283%29%5E%7B2x%7D)
<h3>What is the function?</h3>
The function is represented by the following definition:
![f(x) = 2\sqrt[3]{27^{2x}}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%5Csqrt%5B3%5D%7B27%5E%7B2x%7D%7D)
As an exponent, the function is given by:
![f(x) = 2(27)^{\frac{2x}{3}}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%2827%29%5E%7B%5Cfrac%7B2x%7D%7B3%7D%7D)
27 can be simplified as follows:
27 = 3 x 3 x 3 = 3³
Hence:
![f(x) = 2(3^3)^{\frac{2x}{3}}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%283%5E3%29%5E%7B%5Cfrac%7B2x%7D%7B3%7D%7D)
Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:
![f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%283%29%5E%7B%5Cfrac%7B3%20%5Ctimes%202x%7D%7B3%7D%7D%20%3D%202%283%29%5E%7B2x%7D)
Hence the simplified base for the function is given as follows:
![f(x) = 2(3)^{2x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%283%29%5E%7B2x%7D)
More can be learned about exponential properties at brainly.com/question/25263760
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I think it's 400 inches^2 because 23x4x4=268 and 4x4x2=32. Add them together to get 400.