Answer:
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
Step-by-step explanation:
Let x represent the number of 30-day periods.
Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used.
Therefore the equation =
$165 -$4 × x
= 165 - 4x.......... Equation 1
He has another gift card for $145 that loses $3.50 for each 30-day period it is not used.
$145 -$3.50 × x
= 145 - 3.50x........... Equation 2
Hence, an equation for the number of 30-day periods until the value of the gift cards will be equal is obtained by equating Equation 1 and Equation 2 together
So, we have
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
We simplify further:
165 - 145 = -3.50 + 4.0x
20 = 0.5x
x = 20/0.5
x = 40
Therefore, number of each 30-day periods until the value of the gift cards will be equal is 40
Answer:
f'(x)![=2(e^4^x)+(x^2+1)(4e^4^x)](https://tex.z-dn.net/?f=%3D2%28e%5E4%5Ex%29%2B%28x%5E2%2B1%29%284e%5E4%5Ex%29)
Step-by-step explanation:
The derivative of the function:
![(x^2+1)e^4^x](https://tex.z-dn.net/?f=%28x%5E2%2B1%29e%5E4%5Ex)
The rule for the product of two functions:
f'(x)![=g'(x)h(x)+g(x)h'(x)](https://tex.z-dn.net/?f=%3Dg%27%28x%29h%28x%29%2Bg%28x%29h%27%28x%29)
Therefore
g(x)![=x^2+1](https://tex.z-dn.net/?f=%3Dx%5E2%2B1)
g'(x)![=2](https://tex.z-dn.net/?f=%3D2)
f(x)![=e^4^x](https://tex.z-dn.net/?f=%3De%5E4%5Ex)
f'(x)![=4e^4^x](https://tex.z-dn.net/?f=%3D4e%5E4%5Ex)
f'(x)![=2(e^4^x)+(x^2+1)(4e^4^x)](https://tex.z-dn.net/?f=%3D2%28e%5E4%5Ex%29%2B%28x%5E2%2B1%29%284e%5E4%5Ex%29)
Seventy- two thousand three hundred twelve
Answer:
482.84 cm
Step-by-step explanation: