2r^2+3s^3-r^2+4t^2-r^2
Lets just plug everything in
2(-2)^2+3(-3)^3-(-3)^2+4(5)^2-(-2)^2
Simplify
8+(-81)-9+100-4
108-94
14
Step-by-step explanation:
it means that x has now to be the result variable, and y the input variable.
so,
y = 3x - 5
y + 5 = 3x
x = (y + 5)/3
and as a final touch, to make the inverse a "normal function", we rename x to y and y to x and get
y = (x + 5)/3
as the inverse function
Answer:
The perimeter is 52
Step-by-step explanation:
The area is 36x^2 -60x+25
We set this equal to 0 to find the length and width
A= 36x^2 -60x+25
We notice that this is a perfect square trinomial
(a^2 -2ab-b^2) = (a-b)^2
let a = 6x and b=5
A=(6x-5) (6x-5)
The length and width are the same since is it a square (we know it is a square so they have to be equal)
The perimeter of a square is
P =4s
P =4 (6x-5)
Distribute the 4
= 24x -20
Let x =3
P = 24(3) -20
=72 -20
= 52
The perimeter is 52
The domain would be D. The number of minutes the student studied.
Answer:
Rectangular area
side a = 3 units
side b = 2.60 units
Step-by-step explanation: See annex
We have an equilateral triangle (3 equal sides, three equal inside angles)
side length = 6
∠ ABC = ∠BCA = ∠CAB = 60⁰
tan 60⁰ = sin 60⁰/cos 60⁰ = √3/2 / 1/2
tan 60⁰ = √3
From annex
tan ∠ ABC = √3 = b/x then b = √3 * x
and a = 6 - 2*x ( by symmetry)
Then
A = a*b
A(x) = ( 6 - 2*x ) * √3 *x
A(x) = 6*√3 *x - 2*√3 *x²
Taking derivatives on both sides of the equation we get:
A´(x) = 6*√3 - 4*√3 *x ⇒ A´(x) = 0 ⇒ 6*√3 - 4*√3 *x = 0
x = 6/4 ⇒ x = 1.5
then a = 6 - 2*x ⇒ a = 6 - 3 ⇒ a = 3 (units)
and b = √3*x = 1.5 *√3 = 2.60 units
We get a rectangle (almost a square)
