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garyyunga2002
26.07.2020 •
Mathematics
Can someone please explain how to get the answer i've looked it up several times and i'm still stuck. I'm in algebra 2 with trig and doing my summer math packet: "The length of a rectangle is two feet less than four times the width. Find the length and width if the area is 38.2 square feet. let w= width of the rectangle" Btw websites say w is 19.1 but my answer key says its 3.35. Thanks!
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Ответ:
Step-by-step explanation:
Let L be the length of this rectangle
The length of a rectangle is 2 feet less than four times the width
● L+2 = 4w
The area of this rectangle is 38.2 ft^2
● L*w = 38.2
The system of equations is
L+2 = 4w => L-4w =2
L*w = 38.2 => L= 38.2/w
Replace L by 38.2/w in L-4w =2
● L-4w = 2
● (38.2/w)-4w = 2
●(38,2-4w^2)/w = 2
● 38.2-4w^2 = 2w
● 38.2-4w^2-2w = 0
● -4w^2-2w+38.2 =0
Multiply by -1 to reduce the - signs
● 4w^2+2w-38.2 =0
This is a quadratic equation so we will use the discriminant
□□□□□□□□□□□□□□□□□
The discriminant is b^2-4ac
● b= 2 (2w)
● a= 4 (4w^2)
● c= -38.2 (the constant term)
b^2-4ac =2^2-4*4*(-38.2) = 615.2 > 0
The discriminant is positive so we have two solutions w and w' :
●●●●●●●●●●●●●●●●●●●●●●●●
w= (-2-24.8)/8 = -3.35
24.8 is the root square of 615.2(the discriminant)
●w is negative
● a distance is always positive so this value isn't a solution
w'= (-2+24.8)/8 =2.85 > 0
So this value is a solution for our equation
■■■■■■■■■■■■■■■■■■■■■■■■■■
w= 2.85 feet
Ответ:
w=3.35
Step-by-step explanation:
The length of a rectangle is two feet less than four times the width:
length=4W-2
A=L*W
A=(4W-2)(W)
38.2=4W^2-2W
4W^2-2W-38.2=0 complete the square to find the solution add term(b/2)²
4W²-2W+1/4=38.2+1/4
4(W²-W/2+1/16)=38.45
4(w-1/4)^2=38.45
(w-1/4)²=38.45/4=9.6125
w-1/4=+ or -√9.6125 ( since it is width it has to be positive
w=√9.6125+1/4 = 3.35
Ответ:
is it that goood or not cuz i rlly need a show