98 PTS! Can someone please help?
2 answers:
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First let's solve the general case for an isosceles triangle of base 2 and height k. If the triangle is drawn so the base is on the x-axis and the apex is on the y-axis, the equation for the line containing the right side is
y = -k(x-1)
Then a rectangle with x-dimension w will have an area that is the product of this width and the height y = -k((w/2)-1).
area = w(-k(w/2 -1)) = (-k/2)w² +kw
The derivative of area with respect to w will be zero where the area is a maximum:
d(area)/dw = 0 = -kw +k
w = 1 . . . . . . add kw and divide by k
Using the formula for area, we find
area = 1(-k(1/2-1)) = k/2
This value is 1/2 the total area of the triangle we started with.
If the side lengths of your triangle are 8, √80, and √80, the height will be given by the Pythagorean theorem as
h = √((√80)² - (1/2·8)²) = √(80-16) = 8
Your triangle's area will be
triangle area = (1/2)(8)(8) = 32
The maximum area of the inscribed rectangle will be half this value,
16 square units
y = -k(x-1)
Then a rectangle with x-dimension w will have an area that is the product of this width and the height y = -k((w/2)-1).
area = w(-k(w/2 -1)) = (-k/2)w² +kw
The derivative of area with respect to w will be zero where the area is a maximum:
d(area)/dw = 0 = -kw +k
w = 1 . . . . . . add kw and divide by k
Using the formula for area, we find
area = 1(-k(1/2-1)) = k/2
This value is 1/2 the total area of the triangle we started with.
If the side lengths of your triangle are 8, √80, and √80, the height will be given by the Pythagorean theorem as
h = √((√80)² - (1/2·8)²) = √(80-16) = 8
Your triangle's area will be
triangle area = (1/2)(8)(8) = 32
The maximum area of the inscribed rectangle will be half this value,
16 square units
Answer : <em>Equation of line is</em> y=Equation of line is y=x+
Step-by-step explanation:
Theory :
Equation of line is given as y = mx + c.
Where, m is slope and c is y intercepted.
Slope of given line : y = x+1 is m=
We know that line : y = x+1 is parallel to equation of target line.
therefore, slope of target line will be .
we write equation of target line as y= x+c
Now, It is given that target line passes through point ( -5,-2)
hence, point ( -5,-2) satisfy the target line's equation.
we get,
y= x+c
-2=
-5+ c
-5= +c
c=
thus, Equation of line is y=Equation of line is y=x+