If the area of the rectangle is given by the polynomial 2x^2-7x-15, what is the dimension of the reactangle in terms of x?​

Answer:

The upper limit for the height of the prism is

Step-by-step explanation:

Let

x------> represent the height of the prism

It is known that

the area of the base of the prism must not exceed

thus

-------> inequality A

------> equation B

-----> equation C

Insert equation B into equation C

------> equation D

Substituting equations B and D into inequality A

-------> using a graphing tool to solve the inequality

The resultant solution for x lies in the interval---------->

consult the attached figure

but bear in mind that

The width of the base must be meters shorter than the height of the prism

thus

the solution for x is confined to the interval ------>

The maximum height of the prism equals

Answer:

Step-by-step explanation:

We are provided with the information that

Function f is decreasing as it moves from quadrant 2 to quadrant 1, tending towards y=0

It intersects the y-axis at the point (0,6) and goes through (1,2).

Function g(x) also approaches y=0 in quadrant 2, but increases in quadrant 1.

It passes through (-1,2) and crosses the y-axis at (0,6).

Reflection across y-axis:

The transformation rule is identified as

Applying this rule, we derive

Then, by substituting

for x=-1

for x=0

Consequently, holds true.

Got it!
There are 2π radians in a complete circle.

Now, let's calculate the circumference.
5/2π = 60/circumference.
Next, solve for the circumference.
By multiplying both sides by 2π, we have: 5 * circumference = 120π.
Now divide both sides by 5, and we find: circumference = 24π.

Using the formula c = 2πr,
we set 24π = 2πr.
Dividing both sides by 2π gives us r = 12. Thus, the radius measures 12cm.

Since this parabola intersects the center, its formula is:

y = ax². Given that it opens downward, the coefficient a must be negative.

Thus, the equation can be expressed as:

y = - ax², with the axis of symmetry located at x = 0.

The height measures 84 ft when the parabola's opening is 42 ft wide.
This indicates that for the height y, the corresponding x-values are +21 and -21 (due to symmetry).
To find a, let's substitute y and x with their respective values:

y = - ax²

84 = - a(21)²

84 = - a(441), leading to a = - 84/441 ↔ a = - 4/21.

Therefore, the final equation is: y = -4/21 x².

8.25 inches after multiplying the 3/4 by 2, and adding that to the previous 3/4, gives you the final height of the plant.