Your credit card has a balance of $3300 and an annual interest rate of 14%. You decided to pay off the balance over two years. I
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
Answer:
y(t) = 3u₂(t) [ ] - 4u₅(t) [
]
Step-by-step explanation:
To find - y″+ 5y′ + 6y = 3δ(t − 2) − 4δ(t −5); y(0) = y′(0) = 0
Formula used -
L{δ(t − c)} =
L{f''(t) = s²F(s) - sf(0) - f'(0)
L{f'(t) = sF(s) - f(0)
Solution -
By Applying Laplace transform, we get
L{y″+ 5y′ + 6y} = L{3δ(t − 2) − 4δ(t −5)}
⇒L{y''} + 5L{y'} + 6L{y} = 3L{δ(t − 2)} − 4L{δ(t −5)}
⇒s²Y(s) - sy(0) - y'(0) + 5[sY(s) - y(0)] + 6Y(s) = 3 - 4
⇒s²Y(s) - 0 - 0 + 5[sY(s) - 0] + 6Y(s) = 3 - 4
⇒s²Y(s) + 5sY(s) + 6Y(s) = 3 - 4
⇒[s² + 5s + 6] Y(s) = 3 - 4
⇒[s² + 3s + 2s + 6] Y(s) = 3 - 4
⇒[s(s + 3) + 2(s + 3)] Y(s) = 3 - 4
⇒[(s + 2)(s + 3)] Y(s) = 3 - 4
⇒Y(s) =
Now,
Let
By Comparing, we get
A + B = 0 and 3A + 2B = 1
⇒A = -B
and
3(-B) + 2B = 1
⇒-B = 1
⇒B = -1
So,
A = 1
∴ we get
So,
Y(s) =
⇒Y(s) =
By applying inverse Laplace , we get
y(t) = 3u₂(t) [ ] - 4u₅(t) [
]
⇒y(t) = 3u₂(t) [ ] - 4u₅(t) [
]
It is the required solution.