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2 years ago

BRAINLY FOR WHO EVER ANSWERS FIRST PLS GIVE THE RIGHT ANSWER

Mathematics

1 answer:

sineoko [7]2 years ago

8 0

Answer:

See attached

Step-by-step explanation:

Table F shows the proportional relationship: y = 2x

Plotted points and a line connecting them is attached

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Calculate cos(480°) and sin(480°).

hram777 [196]

Answer:

$\cos(480^\circ)=-\dfrac{1}{2}$

$\sin(480^\circ)=\dfrac{\sqrt{3}}{2}$

Step-by-step explanation:

Calculate the value of trigonometry function.

$\cos(480^\circ)$ and $\sin(480^\circ)$

Split the angle between 0 to 90° using trigonometry formula.

$\Rightarrow \cos(360^\circ+120^\circ)$

$\Rightarrow \cos(120^\circ)$ $\because \cos(360+\theta)=\cos\theta$

$\Rightarrow \cos(180^\circ-60^\circ)$ $\because 120=180-60$

$\Rightarrow -\cos(60^\circ)$ $\because \cos(180-\theta)=-\cos\theta$

$\Rightarrow -\dfrac{1}{2}$

Therefore, cos(480°) = -0.5

$\Rightarrow \sin(360^\circ+120^\circ)$

$\Rightarrow \sin(120^\circ)$ $\because \sin(360+\theta)=\sin\theta$

$\Rightarrow \sin(180^\circ-60^\circ)$ $\because 120=180-60$

$\Rightarrow \sin(60^\circ)$ $\because \sin(180-\theta)=\sin\theta$

$\Rightarrow \dfrac{\sqrt{3}}{2}$

Therefore, sin(480°) = 0.866

7 0

3 years ago

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

7 0

2 years ago

What number has factors that add up to thirty

NNADVOKAT [17]

29 = 1 * 29
1 + 29 = 30
thus answer is 29

5 0

3 years ago

The relationship between x and y is proportional. When x is 3, y is 51. What is x when y is 204? Enter your answer in the box.

JulsSmile [24]

Answer:

Step-by-step explanation:

Use the relation between 3 is to 51

eventually... you will

5 0

3 years ago

12 Two plumbers received a job. At first, one of the plumbers worked alone for 1 hour, and then they worked together for the nex

Degger [83]

The answer should be 12

4 0

2 years ago