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:
24
Step-by-step explanation:
2:6
1:3
24:72
Answer:
Step-by-step explanation:
(x,y)→(-x,-y) (180° about the origin)
1.p(-3,2) ,in the second quadrant
P(-2,-3) is in 4th quadrant.
in the clockwise it is rotation of 270° about the origin.
2.
Q(-4,-5) is in 4th quadrant.
Q(4,5) is in 1st quadrant.
so it is 180° rotation in the clockwise direction.
3.
R(1,7) is in 1st quadrant.
R(7,-1) is in 4th quadrant.
Hence it is 90° rotation about the origin in clockwise direction.
<span>210 miles equals 1 and 1/2 inches (3 1/2"s or 0.5"). 1 and 1/2" is equal to two 3/4" (3/4 + 3/4 = 1 and 1/2). 1.5" is equal to 210 miles, and 1.5" is equal to 2 * .75", you can divide 210 miles by two, which gives you 105 miles.</span>
Answer:
#16 = (0, -10)
#17 = (-18, -3)
Step-by-step explanation:
U wouldn't use the distance formula, you would need to use the Midpoint Formula, which is, M = (x1 + x2 / 2, y1 + y2 / 2). For #16, you plug in (4, -5) for M and 8 for x1 and 0 for y1, so the equation should look like this : (4, -5) = (8 + x2 / 2, 0 + y2 / 2). Then separate the equation to make it easier: 4 = 8 + x2 / 2 and the second equation : -5 = 0 + y2 / 2. So let's do the 1st equation, the first step would be to multiply the 2 to both sides. So the equation should look like this, 8 = 8 + x. Then subtract the 8 from both sides and you get 0 as your x. Now moving on to the 2nd equation, you multiply the 2 to both sides, and you get, -10 = 0 + y, as your equation, but since 0 won't affect it, -10 should be your y. Then just use these steps to solve #17, and your answer should be (-18, -3).