Given with a polynomial 4X² + 36/4X *1/5X, we can combine terms with the same power. First, let us perform multiplication of the 2nd and 3rd terms such as the given become 4X² + 36/20X². Then, we can reduce 36 and 20 by 4 and the result is 4X² + 9/5X². We can now proceed combining the terms since they have same power and result will be same as below:
(20X^4 + 9)/5X²
the ratio that is equal to 10:85 is 20:170 because if you multiply both sides by two you get 20:170
Answer:
Interest rate: 9%
Step-by-step explanation:
Using the simple interest formula: A=P(1+rt)
A=Final amount
P=Principal amount
r=rate
t=time (years)
We just need to put in the information we have from the question and solve for r.
7,620=6000(1+r3)
7,620/6000=1+r3
1.27=1+r3
0.27=r3
r=0.09
r=9%
Answer: 7x^2+21x+14
Step-by-step explanation:
(7x+7)(x+2)
Multiply each term in the first parentheses by each term in the second parentheses (FOIL)
7x×x+7x×2+7x+7×2
↘ ↙
7x×x calculate product
7x^2+7x×2+7x+7×2
↘ ↙
7x×2 calculate product
7x^2+14x+7x+7×2
↘↙
7×2 multiply numbers
7x^2+14x+7x+14
↘ ↙
21x collect like terms
7x^2+21x+14 is your end result.
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
