Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
Answer:
The answer is option C
Step-by-step explanation:
sin C = opposite / hypotenuse
the opposite is 40
the Hypotenuse is 50
so
sin C = 40/50 = 4/5
Hope this helps you
Answer:
1) B. on, 2) D. 19.2, 3) C. 0
Step-by-step explanation:
1) The value of y according to the regression line is:
Hence, the point (8,19.2) is <em>on </em>the least-squares regression line.
2) The value of y according to the regression line is 19.2.
3) The residual is the difference between the value from the regression line and the real value. In this case, the residual value is 0.
Answer:
The answer to your question is y = -2x + 11
Step-by-step explanation:
A (1, 9)
B (3, 5)
- Find the slope
m = - 2
- Find the line equation
y - y1 = m (x - x1)
y - 5 = -2(x - 3)
y - 5 = -2x + 6
y = -2x + 6 + 5
y = -2x + 11
