Answer:
I(x) = 12x² + 8x + 5
Step-by-step explanation:
* Lets talk about the solution
- P(x) is a quadratic function represented graphically by a parabola
- The general form of the quadratic function is f(x) = ax² + bx + c,
where a is the coefficient of x² and b is the coefficient of x and c is
the y-intercept
- To find I(x) from P(x) change each x in P by 2x
∵ P(x) is dilated to I(x) by change x by 2x
∵ I(x) = P(2x)
∵ P(x) = 3x² + 4x + 5
∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify
∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²
∵ 4(2x) = 8x
∴ I(x) = 3(4x²) + 8x + 5
∵ 3(4x²) = 12x²
∴ I(x) = 12x² + 8x + 5
If you measure the amount of water before and after putting the object in the body of water and finding the difference between the two measurements you can approximate the volume of the irregularly shaped solid
Well if you have a radius remember to divide by 2 . So divide your number by 2. And you should get 5x
=±22
x
=
±
2
x
2
Using the fact that 2=ln2
2
=
e
ln
2
:
=±ln22
x
=
±
e
x
ln
2
2
−ln22=±1
x
e
−
x
ln
2
2
=
±
1
−ln22−ln22=∓ln22
−
x
ln
2
2
e
−
x
ln
2
2
=
∓
ln
2
2
Here we can apply a function known as the Lambert W function. If =
x
e
x
=
a
, then =()
x
=
W
(
a
)
.
−ln22=(∓ln22)
−
x
ln
2
2
=
W
(
∓
ln
2
2
)
=−2(∓ln22)ln2
x
=
−
2
W
(
∓
ln
2
2
)
ln
2
For negative values of
x
, ()
W
(
x
)
has 2 real solutions for −−1<<0
−
e
−
1
<
x
<
0
.
−ln22
−
ln
2
2
satisfies that condition, so we have 3 real solutions overall. One real solution for the positive input, and 2 real solutions for the negative input.
I used python to calculate the values. The dps property is the level of decimal precision, because the mpmath library does arbitrary precision math. For the 3rd output line, the -1 parameter gives us the second real solution for small negative inputs. If you are interested in complex solutions, you can change that second parameter to other integer values. 0 is the default number for that parameter.
Answer:
Multiply each side by 24.
Step-by-step explanation:
To get x by itself, you need to do the opposite of what is with it. So, if it's in a fraction, you must multiply it. So, on the right side the 24's would cancel out. That put's X by itself. Then on the left side you multiply 9/2 by 24. I find it easier to put it as 24/1x9/2 to make it easier. Basically, you just multiply 9 by 24 and then multiply 1 by 2, so the answer to this equation would be x=216/2, and when simplified, X=108.
