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2 years ago

The amount $180.00 is what percent greater than $135.00?

Mathematics

1 answer:

sergiy2304 [10]2 years ago

4 0

Answer:

Its Option C

Step-by-step explanation:

The difference is 180 - 135 = $45

So it is 45 * 100 / 135

= 33.33% greater

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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

3 years ago

If the actual length of a boat is 120 inches and the model of the same boat is 6 inches, identify the scale factor of these two

monitta

Answer:

The answer is 1/20

Step-by-step explanation:

7 0

2 years ago

A 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental

OLga [1]

Answer:

The experimental probability of rolling anumber less than 3 is 3/20

Step-by-step explanation:

16+14=30

30/200

=3/20

7 0

2 years ago

If you are driving 20 meters per second, what would be the equivalent of that in miles per hour?

melomori [17]

$\frac{20 meters}{1 second} \frac{60 seconds}{1 minute} \frac{60 minutes}{1 hour}$

the fractions are set up so that each unit cancels out until its only meters/hour

you can multiply all the numerators together to get 72000 and all the denominators to get 1

72000 meters/1 hour

72000 meters in 1 hour

hope this helped

8 0

2 years ago

In a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of th

11111nata11111 [884]

Answer:

Required probability is 0.784 .

Step-by-step explanation:

We are given that in a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students passed both exams.

Let Probability that the students passed the first exam = P(F) = 0.74

Probability that the students passed the second exam = P(S) = 0.72

Probability that the students passed both exams = $P(F \bigcap S)$ = 0.58