Step-by-step explanation:
g(5)=3(5)-11
=15-11
=4
f(g(5))=2(4)²+4(4)+10
=2(16)+16+10
=32+26
=58
The length of a curve <em>C</em> parameterized by a vector function <em>r</em><em>(t)</em> = <em>x(t)</em> i + <em>y(t)</em> j over an interval <em>a</em> ≤ <em>t</em> ≤ <em>b</em> is

In this case, we have
<em>x(t)</em> = exp(<em>t</em> ) + exp(-<em>t</em> ) ==> d<em>x</em>/d<em>t</em> = exp(<em>t</em> ) - exp(-<em>t</em> )
<em>y(t)</em> = 5 - 2<em>t</em> ==> d<em>y</em>/d<em>t</em> = -2
and [<em>a</em>, <em>b</em>] = [0, 2]. The length of the curve is then





Answer:

Step-by-step explanation:
The line passes through the origin has an equation y = mx
m - slope
The formula of a slope of a line passes through the origin
and a point (x, y):

We have the point (6, 8). Substitute:

Finally:

Answer:16.50
Step-by-step explanation: hope it helps
1. Distribute
1/125 x 5n - 1/125
2. Simplify 1/125 x 5n to n/25
n/25 - 1/125