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:
B. -1/4
Step-by-step explanation:
Yes is the answer click it
Answer:
x = ±3 sqrt(2)
Step-by-step explanation:
x^2 + x^2=6^2
Combine like terms
2x^2 = 6^2
Divide each side by 2
x^2 = * 6^2/2
Take the square root of each side
sqrt(x^2) =± sqrt( 6^2/2)
Remember that sqrt(a/b) = ±sqrt(a ) /sqrt(b)
x = ±sqrt(6^2)/sqrt(2)
x = ±6 /sqrt(2)
We do not leave square roots in the denominator, so we multiply the top and bottom by sqrt(2)
x = ±6 /sqrt(2) * sqrt(2)/ sqrt(2)
x = ±6 *sqrt(2) /( sqrt(2)*sqrt(2))
x = ±6 sqrt(2) /(2)
x = ±3 sqrt(2)
Answer:
c < - 6
Step-by-step explanation:
Given
3(2c - 8) - 10c > 0 ← distribute and simplify left side
6c - 24 - 10c > 0
- 4c - 24 > 0 ( add 24 to both sides )
- 4c > 24
Divide both sides by - 4, reversing the inequality symbol as a consequence of dividing by a negative quantity.
c < - 6
