Express 1+√2/√2 in the form p+q√2
1 answer:
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Answer:
The length of the rectangle is 6 feet
Step-by-step explanation:
Given as :
The length of rectangle is 1 feet less than twice the width
So, let The width of rectangle = w feet
The length of rectangle = ( 2 w - 1 ) feet
The area of the rectangle = 21 feet²
Now,
∵ The area of the rectangle = length × width
Or, 21 feet² = ( 2 w - 1 ) feet × w feet
or, 21 = 2 w² - w
or, 2 w² - w - 21 = 0
or, 2 w² + 6 w - 7 w - 21 = 0
or , 2 w ( w + 3 ) - 7 ( w + 3 ) = 0
or, ( w + 3 ) ( 2 w - 7 ) = 0
So, w = - 3 feet , feet
here we consider only positive value of w i.e feet
∴ The length of rectangle = ( 2 w - 1 ) feet
or, The length of rectangle = 2 × - 1
Or, The length of rectangle = 7 - 1 = 6 feet
Hence The length of the rectangle is 6 feet , Answer
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula
1)
2) In order to find salary in 5 years we need to plug n=5, we get
= 50000(1.21550625)
<h3>=$60775.3125.</h3>3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.
Plugging n=10, a = 50000 and r= 1.05.
= 628894.62678.
<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>