When 27x^2z divided by -3x^2z^6 is correctly simplified, the exponent on the variable z is _____.
1 answer:
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<u>Answer:</u>
<em>Mathew invested</em><em> $600 and $2400</em><em> in each account.</em>
<u>Solution:</u>
From question, the total amount invested by Mathew is $3000. Let p = $3000.
Mathew has invested the total amount $3000 in two accounts. Let us consider the amount invested in first account as ‘P’
So, the amount invested in second account = 3000 – P
Step 1:
Given that Mathew has paid 3% interest in first account .Let us calculate the simple interest earned in first account for one year,
Where
p = amount invested in first account
n = number of years
r = rate of interest
hence, by using above equation we get as,
----- eqn 1
Step 2:
Mathew has paid 8% interest in second account. Let us calculate the simple interest earned in second account,
Step 3:
Mathew has earned 4% interest on total investment of $3000. Let us calculate the total simple interest (I)
Step 4:
Total simple interest = simple interest on first account + simple interest on second account.
Hence we get,
By substituting eqn 1 , 2, 3 in eqn 4
12000=3P + 24000 - 8P
5P = 12000
P = 2400
Thus, the value of the variable ‘P’ is 2400
Hence, the amount invested in first account = p = 2400
The amount invested in second account = 3000 – p = 3000 – 2400 = 600
Hence, Mathew invested $600 and $2400 in each account.
Write tan in terms of sin and cos.
Recall that
Rewrite and expand the given limand as the product
Then using the known limit above, it follows that