Answer:
x = 500 yd
y = 250 yd
A(max) = 125000 yd²
Step-by-step explanation:
Let´s call x the side parallel to the stream ( only one side to be fenced )
y the other side of the rectangular area
Then the perimeter of the rectangle is p = 2*x + 2* y ( but only 1 x will be fenced)
p = x + 2*y
1000 = x + 2 * y ⇒ y = (1000 - x )/ 2
And A(r) = x * y
Are as fuction of x
A(x) = x * ( 1000 - x ) / 2
A(x) = 1000*x / 2 - x² / 2
A´(x) = 500 - 2*x/2
A´(x) = 0 500 - x = 0
x = 500 yd
To find out if this value will bring function A to a maximum value we get the second derivative
C´´(x) = -1 C´´(x) < 0 then efectevly we got a maximum at x = 500
The side y = ( 1000 - x ) / 2
y = 500/ 2
y = 250 yd
A(max) = 250 * 500
A(max) = 125000 yd²
Responder:
x = 42,4
Explicación paso a paso:
Podemos encontrar el valor de x ya que no se nos dice qué buscar
La suma de dos ángulos suplementarios es 180 grados, por lo tanto;
2x - 14 + 3x - 18 = 180
2x + 3x - 32 = 180
5 veces = 180 + 32
5 veces = 212
x = 212/5
x = 42,4
Por tanto, el valor de x es 42,4
Answer:
The graph of the function is negative on (3, ∞)
Step-by-step explanation:
The function starts negative at the left side of the graph, crosses the x-axis at x = -5, touches the x-axis at x = 1, again crosses into negative values at x = 3.
The function is positive on the open intervals (-5, 1) and (1, 3). It is negative on the open intervals (-∞, -5) and (3, ∞). The latter description matches the last answer choice:
the graph of the function is negative on (3, ∞).
Answer:
x = 20
Step-by-step explanation:
Angle 2 and Angle 5 are corresponding angles
Corresponding angles are congruent
If angle 2 = 3x - 20 and angle 5 = x + 20
Then 3x - 20 must equal x + 20 ( because corresponding angles are congruent )
Notice that weve just created an equation that we can use to solve for x
We now solve for x using the equation we created
3x - 20 = x + 20
Step 1 add 20 to both sides
3x = x + 40
Step 2 Subtract x from both sides
2x = 40
Step 3 divide both sides by 2
x = 20
Answer:
r², or the radius squared
Step-by-step explanation:
The formula for the area of a circle is
πr²
So the the radius squared is being multiplied by pi.