Mathematics, 30.08.2021 17:00 rileyeddins1010

suppose the velocity of a particle traveling along the x-axis is given by v(t)= 3t^2+8t+15 m/s at time t seconds. The particle is initially located 5 meters left of the origin. How far does the particle travel from t=2 seconds to t=3 seconds? After 3 seconds, where is the particle with respect to the origin?

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Answer from: snoodledoodlebop

Step-by-step explanation:

1) How far does the particle travel from t=2 seconds to t=3 seconds?

$\int\limits^3_2 {(3t^2+8t+15)} \, dt =\Bigg [ t^3+4t^2+15t\Bigg]^3_2\\\\=27+36+45-(8+16+30)\\\\=108-54\\\\=54 (m)\\\\$

$\int\limits^3_0 {(3t^2+8t+15)} \, dt =\Bigg [ t^3+4t^2+15t\Bigg]^3_2=108\\\\$

After 3 seconds, where is the particle with respect to the origin?

108-5=103 (m)

Answer from: Quest

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram. we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2. so it's not a square or a rhombus.

we check the dot product of direction vectors of adjacent sides. we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular. we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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suppose the velocity of a particle traveling along the x-axis is given by v(t)= 3t^2+8t+15 m/s at ti...

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