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2 years ago

F(x)=-12x^3-14x^2+6x

Mathematics

1 answer:

Ne4ueva [31]2 years ago

4 0

There has to be x equals of f is something or u can’t solve

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Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t ==> dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

5 0

2 years ago

HELP ME ASAP I NEED HELP PLEASE SOMEONE

scZoUnD [109]

Answer:

welll there no like answers to give here so i dont know might want to check what you post before you post it

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

An object is moving at a speed of 2 feet every 8.5 minutes. Express this speed in meters per hour

jekas [21]

Answer:

4.30m/hr

Step-by-step explanation:

2 feet/8.5 mins is 0.235294118 feet per minute, which is 4.3030553875397 metres per hour, which to 2 s.f. is 4.30

8 0

3 years ago

A, B & C lie on a straight line.

vekshin1

Answer:

x = 27°

Step-by-step explanation:

m<D

m<CBE = 63° (Given)

m<CBE = m<ABD (vertical angles)

m<ABD = 63° (substitution)

x = 180 - (m<ABD + m<D) (Sum of triangle)

x = 180 - (90 + 63)

x = 27°

3 0

3 years ago

What is the unit rate of 8 miles and 92 minutes?

Alinara [238K]

11.5 minutes per mile

5 0

3 years ago