Question asked:Jacob and Sarah are saving money to go on a trip. They need at least $1975 in order to go. Jacob mows lawns and Sarah walks dogs to raise money. Jacob charges $25 each time he mows a lawn and Sarah charges $15 each time she walks a dog. The number of dog walks that Sarah has scheduled is no more than four times the number of lawns Jacob has scheduled to mow. Sarah will walk at least 50 dogs.Write a set of constraints to model the problem, with x representing the number of lawns mowed and y representing the number of dogs walked.
My answer:
They need at least $1975. Jacob charges $25 each time he mows a lawn and Sarah charges $15 each time she walks a dog.
25x + 15y ≥ 1975
The number of dog walks that Sarah has scheduled is no more than four times the number of lawns Jacob has scheduled to mow.
y ≤ 4x
Sarah will walk at least 50 dogs.
y ≥ 50
OH right! I should have realised that!
S6 = 7,812 = a1 * (5^6 - 1)
----------- were a1 = first term
5 - 1
3906*a1 = 7812
a1 = 7812 / 3906 = 2
Therfore the second term = 2*5 = 10 Answer
Answer:
![\log_{2} [\frac{x^{3}(x + 4)}{3}]](https://tex.z-dn.net/?f=%5Clog_%7B2%7D%20%5B%5Cfrac%7Bx%5E%7B3%7D%28x%20%2B%204%29%7D%7B3%7D%5D)
Step-by-step explanation:
We have to write the following logarithmic expression as a single logarithm.
The given expression is
![3\log_{2} x - [\log_{2} 3 - \log_{2}(x + 4)]](https://tex.z-dn.net/?f=3%5Clog_%7B2%7D%20x%20-%20%5B%5Clog_%7B2%7D%203%20-%20%5Clog_%7B2%7D%28x%20%2B%204%29%5D)
= 
{Since, 
, from the properties of logarithmic function }
= 
{Since, 
, which also a logarithmic property}
= ![\log_{2} [\frac{x^{3}}{\frac{3}{x + 4}}]](https://tex.z-dn.net/?f=%5Clog_%7B2%7D%20%5B%5Cfrac%7Bx%5E%7B3%7D%7D%7B%5Cfrac%7B3%7D%7Bx%20%2B%204%7D%7D%5D)
= (Answer)
