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3 years ago

The acceleration function a(t) (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.

Mathematics

1 answer:

klemol [59]3 years ago

7 0

Answer:

A: $v(t)=-t^2+4t-5$

Step-by-step explanation:

Acceleration is second derivative of position, velocity is first derivative. Therefore, the velocity is the integral of acceleration.

$v(t)=\int\ {2t+4} \, dt$

Integrate:

$-t^2+4t+C$

V(0)=-5:

$-0^2+4(0)+C=-5\\C=-5$

Therefore, v(t):

$v(t)=-t^2+4t-5$

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What is the coefficient of x in 4x/5 a)1/5 b.5 c.4/5 d.4 e.-0.8

almond37 [142]

Answer:

$\frac{4}{5}$

Co efficient means the number or value beside preventing the variable from standing alone

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3 years ago

Read 2 more answers

Plz help and explain

Westkost [7]

Answer: B

<u>Step-by-step explanation:</u>

In order to get the best representative sample, you should choose the widest range of students, which is from a random sample of all students.

(A) Choosing from only the 6th graders, eliminates the choices the other grade-level students would choose.

(C) Choosing only from students who participate in after-school activities, eliminates the choices the other students would choose.

(D) Chhosing only from students not participating in the fundraiser is silly since you want to know what the students participating in the fundraiser would choose.

The only possible option is B - students from all grades, regardless of whether or not they participate in after-school activities.

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3 years ago

Construction This section of a concrete skateboard ramp has the shape of a triangular prism. Find the volume

irina [24]

Answer:

volume = 73.3ft³

value = $194.4

Step-by-step explanation:

volume of prism = (½bh)l

=(½×4×4)×9.2

=73.6ft³

value of concrete

1ft³ : $4.00

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X : $294.4

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2 years ago

Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p

kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

$\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)$

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>

In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In second quadrant(π/2 < θ < π), only sin and cosec are positive.
In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

$y= 3\cos(2(x + \pi/2)) - 2$

The options are:

$y= 3\sin(2(x + \pi/4)) - 2$
$y= -3\sin(2(x + \pi/4)) - 2$
$y= 3\cos(2(x + \pi/4)) - 2$
$y= -3\cos(2(x + \pi/2)) - 2$

Checking all the options one by one:

Option 1: $y= 3\sin(2(x + \pi/4)) - 2$

$y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2$

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

Option 2: $y= -3\sin(2(x + \pi/4)) - 2$

This option if would be true, then from option 1 and this option, we'd get:
$-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0$