What is the true solution to 3 ln 2+ln 8=2ln(4x)
2 answers:
Answer:
x = 2
Step-by-step explanation:
Using the rules of logarithms
• log ⇔ nlog x
• log x + log y ⇔ log(xy)
• log x = log y ⇒ x = y
Given
3 ln2 + ln8 = 2ln(4x)
ln2³ + ln8 = ln(4x)²
ln8 + ln8 = ln16x²
ln(8 × 8) = ln16x²
ln64 = ln16x², hence
16x² = 64 ( divide both sides by 16 )
x² = 4 ( take the square root of both sides )
x = = 2
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Answer:
The equation of the parabola that models the path of the long jumper through the air is ×
Step-by-step explanation:
Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:
×
×
Where:
x - Horizontal distance from the start line, measured in meters.
y - Height of the long jumper, measured in meters.
a,b,c - Polynomial constants, measured in , dimensionless and meters, respectively.
If we know thatand
this system of linear equations is presented below:
The coefficients of the polynomial are, respectively:
The equation of the parabola that models the path of the long jumper through the air is
But we need y measured in centimeters, then, we use the following conversion:
Then, we get that:
Where x and y are measured in meters and centimeters, respectively.
The equation of the parabola that models the path of the long jumper through the air is