There is no error, Jacob did everything right :)
Answer: (a), (b), (c), and (d)
Step-by-step explanation:
Check the options
![(a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x](https://tex.z-dn.net/?f=%28a%29%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D%5Csin%20%5E2x%2B%5Ccos%20%5E2x%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B%5Csin%202x)
![(c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x](https://tex.z-dn.net/?f=%28c%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x%7D%7B%5Csin%20x%5Ccos%20x%7D%3D%5Cdfrac%7B3%5Csin%20x-4%5Csin%20%5E3x%7D%7B%5Csin%20x%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%203%5Csec%20x-4%5Csin%20%5E2x%5Csec%20x%5C%5C%5CRightarrow%203%5Csec%20x-4%5B1-%5Ccos%20%5E2x%5D%5Csec%20x%5C%5C%5CRightarrow%20%203%5Csec%20x-4%5Csec%20x%2B4%5Ccos%20x%5C%5C%5CRightarrow%204%5Ccos%20x-%5Csec%20x)
![(d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x](https://tex.z-dn.net/?f=%28d%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x-%5Csin%20x%7D%7B%5Ccos%203x%2B%5Ccos%20x%7D%3D%5Cdfrac%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%20%5Csin%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%5Ccos%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B2%5Ccos%202x%5Csin%20x%7D%7B2%5Ccos%202x%5Ccos%20x%7D%3D%5Cdfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%20%5Ctan%20x)
Thus, all the identities are correct.
Eg. the first loan is x, the second loan will be (9,000 - x)
First, we need to make an equation based on the problem
first interest + second interest = 492
5% of x + 6% of (9,000 - x) = 492
<em>This is the equation</em>
Second, solve the equation and find out the value of x (first loan)
0.05x + 0.06(9.000 - x) = 492
0.05x + 540 - 0.06x = 492
-0.01x + 540 = 492
-0.01x = 492 - 540
-0.01x = -48
x = -48/-0.01
x = 4,800
Third, find the second loan
9,000 - x
= 9,000 - 4,800
= 4,200
SUMMARY
The first loan that has interest of 5% is $4,800
The second loan that has interest of 6% is $4,200
To answer that we just need to multiply the 2 numbers, and consider that 25% = 0.25
so we have:
25% of 395
= (25%)(395)
<span>= (0.25)(395)
</span>= 98.75
Answer:
The rule could be an = 6*2^(n-1)
Step-by-step explanation:
If it is a geometric sequence
Fifth term a5 = a1 r^4 where a1 is the first term
a1 r^4 = 96
r^4 = 96/a1
2^4 = 16 and 96/16 = 6 so a1 could be 6
Check: 6*2^(5-1) = 6*2^4 = 96.
