The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Hi there!
To solve, we can use right triangle trigonometry.
Recall that:
sin = O/H, cos = A/H, tan = O/A.
For angle G, HF is its OPPOSITE side, and FG is the hypotenuse.
Therefore, we must use sine to evaluate:
sinG = 14 / 17
sin⁻¹ (14/17) = ∠G. Evaluate using a calculator.
∠G ≈ 55.44°
Answer:
24xy+2y−234x2fromy+14x
Step-by-step explanation:
24xy−10y−(18×13)xxfromy+12y+14x
24xy−10y−234xxfromy+12y+14x
24xy−10y−234x2fromy+12y+14x
24xy+(−10y+12y)−234x2fromy+14x
X - number of the adults, y - number of children;
The system is:
10 x + 6 y = 3292
x + y = 350 => y = 350 - x
----------------------
10 x + 6 * ( 350 - x ) = 3292
10 x + 2100 - 6 x = 3292
4 x = 3292 - 2100
4 x = 1192
x = 1192 : 4
x = 298
y = 350 - 298
y = 52
Answer:
There were 598 adults and 52 children at the showing.
Take the deritivive
remember
the deritivive of f(x)/g(x)=(f'(x)g(x)-g'(x)f(x))/(g(x)^2)
so
deritiveive is ln(x)/x is
remember that derivitive of lnx is 1/x
so
(1/x*x-1lnx)/(x^2)=(1-ln(x))/(x^2)
the max occurs where the value is 0
(1-ln(x))/(x^2)=0
times x^2 both sides
1-lnx=0
add lnx both sides
1=lnx
e^1=x
e=x
see if dats a max or min
at e/2, the slope is positive
at 3e/2, the slope is negative
changes from positive to negative at x=e
that means it's a max
max at x=e
I realize I didn't find the max point, so
sub back
ln(x)/x
ln(e)/e
1/e
the value of the max would be 1/e occuring where x=e
4th option is answer (1/e) because that is the value of the maximum (which happens at x=e)
