Answer:
1) when tomato patch is 6.5 feet the area is 191.75 sq.ft
2) when tomato patch is 7 feet the area is 217 sq.ft
3) when area is 338 sq.ft the tomato patch is 9.0778 feet
4) when area is 147.25 sq.ft the tomato patch is 5.543799 feet
Step-by-step explanation:
The given equation is :
3x^2 + 10x
Length of Tomato (in feet) x, 6.5 , x , 7
Patch Area of Vegetable Garden (in square feet) 338, x , 147.25, x
So we can find the missing terms with the help of the equation 3x^2 + 10x
Putting the values of x from the length of the tomato patch
1) 3x^2 + 10x= 3(6.5)²+ 10 (6.5)=126.75+ 65= 191.75 square feet
2) 3x^2 + 10x= 3(7)² +10 (7)= 147+70= 217 square feet
So the area of her vegetable garden for a variety of lengths of the tomato patch= 6.5 feet is 191.75 square feet
and for 7 feet is 217 square feet
Similarly we can find the length of the tomato patch from the area by again using the given equation 3x^2 + 10x
So when area = 338 square feet
The equation becomes
3x^2 + 10x= 338
Rearranging it : 3x^2 + 10x-338 =0
This is a quadratic equation and can be solved with the help of the formula.
Here a= 3, b= 10 and c= -338
x = -b±√b²- 4ac/2a
Putting the values of a,b,c we get
x= -10±√100+ 4056/6
x= -10± 64.467/6
x= 54.467/6 or -74.467/6 we ignore the negative value because the garden cannot have the negative area.
x= 9.0778 feet
Similarly repeating the same process would give
So when area = 147.25 square feet
The equation becomes
3x^2 + 10x= 147.25
Rearranging it : 3x^2 + 10x-147.25 =0
This is a quadratic equation and can be solved with the help of the formula.
Here a= 3, b= 10 and c= - 147.25
x = -b±√b²- 4ac/2a
Putting the values of a,b,c we get
x= -10±√100+ 1767/6
x= -10± 43.208/6
x= 33.208/6 or -53.208/6 we ignore the negative value because the garden cannot have the negative area.
x= 5.543799 feet
