Answer:
9th Triangle
Step-by-step explanation:
Given the area of four triangles:![40 cm^2, 90 cm^2, 202.5 cm^2 \:and\: 455.6 cm^2](https://tex.z-dn.net/?f=40%20cm%5E2%2C%2090%20cm%5E2%2C%20202.5%20cm%5E2%20%5C%3Aand%5C%3A%20455.6%20cm%5E2)
If the Scale factor is 1.5.
This is a geometric sequence and the common ratio is 1.5 X 1.5.
Therefore, the area of any n triangle can be determined using the function:
![A(n)=40\cdot1.5^{2(n-1)}](https://tex.z-dn.net/?f=A%28n%29%3D40%5Ccdot1.5%5E%7B2%28n-1%29%7D)
We want to determine which triangle has an area greater than
.
When A(n)=15000
![40\cdot1.5^{2(n-1)}>15000\\1.5^{2(n-1)}>\frac{15000}{40} \\1.5^{2(n-1)}>375\\\text{Change to Logarithm form}\\2(n-1)>Log_{1.5}375\\\text{Applying logarithm change of base to base 10 law}\\2(n-1)>\frac{Log 375}{Log 1.5} \\2n-2>14.62\\2n>14.62+2=16.62\\n>8.31](https://tex.z-dn.net/?f=40%5Ccdot1.5%5E%7B2%28n-1%29%7D%3E15000%5C%5C1.5%5E%7B2%28n-1%29%7D%3E%5Cfrac%7B15000%7D%7B40%7D%20%5C%5C1.5%5E%7B2%28n-1%29%7D%3E375%5C%5C%5Ctext%7BChange%20to%20Logarithm%20form%7D%5C%5C2%28n-1%29%3ELog_%7B1.5%7D375%5C%5C%5Ctext%7BApplying%20logarithm%20change%20of%20base%20to%20base%2010%20law%7D%5C%5C2%28n-1%29%3E%5Cfrac%7BLog%20375%7D%7BLog%201.5%7D%20%5C%5C2n-2%3E14.62%5C%5C2n%3E14.62%2B2%3D16.62%5C%5Cn%3E8.31)
Therefore, the 9th triangle has an area greater than
.
Answer:
I.4
ii.13
Step-by-step explanation:
....ur welcome........
3/2
<em>Step One:</em> 1 3/8, transform the number into a improper fraction:
- To have a mixed number in to a improper fraction, you need to use addition and multiplication. For 1 3/8, We first multiply the denominator (8, also know to be the bottom number of the fraction) to the whole number (1). 8x1= 8
- NOTE: The original denominator (8) will be use for are improper, again playing as the denominator, we only multiply the denominator for the numerator (which is the top number of a fraction).
- After multiplying, we'll add are product with the numerator (3) for the process. 8+3= 12
- Now we have both numerator and denominator for 1 3/8, we can create the improper fraction. 12 as the numerator and 8 as the denominator. 12/8
- We still need to simplify the number. To that, we need the biggest whole number, or rather I call it the lowest number, that can be divide both in 12 and 8.
- 4 can be divide by both number so: 12/4= 3 and 8/4=2
- Now 3 is are simplify numerator and 2 is are simplify denominator.