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3 years ago

Question Progress Simplify x²–9/x² – 3x

Mathematics

1 answer:

Bond [772]3 years ago

5 0

Step-by-step explanation:

Given

$= \frac{ {x}^{2} - 9 }{ {x}^{2} - 3x} \\ = \frac{(x + 3)(x - 3)}{x(x - 3)} \\ = \frac{(x + 3)}{x}$

Hope it will help :)❤

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Colin invests £980 into his bank account. He receiv 0.3% per year simple interest. How

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Answer: 1,000.77

Step-by-step explanation:

After 1 year: 980 + 0.3% = 982.94

After 2 years: 982.94 + 0.3% = 985.89

After 3 years: 985.89 + 0.3% = 988.85

After 4 years: 988.85 + 0.3% = 991.82

After 5 years: 991.82 + 0.3% = 994.80

After 6 years: 994.80 + 0.3% = 997.78

After 7 years: 997.78 + 0.3% = 1,000.77

Brainliest?

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2 years ago

rock is thrown upward with a velocity of 27 meters per second from the top of a 23 meter high cliff and it misses the cliff on t

ahrayia [7]

the rock will be at 11 meters from the ground level after 5.92 seconds

Step-by-step explanation:

The motion of the rock is a free-fall motion, since the rock is acted upon the force of gravity only. Therefore, it is a uniformly accelerated motion, so its position at time t is given by the equation:

$y=h+ut+\frac{1}{2}at^2$

where

h = 23 m is the initial height

u = 27 m/s is the initial velocity, upward

$a=g=-9.8 m/s^2$ is the acceleration of gravity, downward

t is the time

We want to find the time t at which the position of the rock is

y = 11 m

Substituting and re-arranging the equation, we find

$11=23+27t-4.9t^2\\4.9t^2-27t-12=0$

This is a second-order equation, which has solutions:

$t=\frac{27\pm \sqrt{(-27)^2-4(4.9)(-12)}}{2(4.9)}=\frac{27\pm \sqrt{964.2}}{9.8}$

$t_1 = -0.41 s$

$t_2=5.92 s$

The first solution is negative so we neglect it: therefore, the rock will be at 11 meters from the ground level after 5.92 seconds.

Learn more about free fall:

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3 years ago

A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four re

ddd [48]

Answer:

62.8 km per min

Step-by-step explanation:

Let the diagram of this situation is shown below,

In which $\theta$ is the angle made by light to the straight line joining the lighthouse and P,

∵ Light makes 4 revolutions per minute.

Also, 1 revolution = $2\pi$ radians

So, the change in angle with respect to t ( time ),

$\frac{d\theta}{dt}=8\pi\text{ radians per min}$

Let x be the distance of beam from P,

$\implies \tan \theta = \frac{x}{2}$

Differentiating with respect to x,

$\sec^2 \theta \frac{d\theta}{dt}=\frac{1}{2}\frac{dx}{dt}$

$(1+\tan^2 \theta) (8\pi) = \frac{1}{2}\frac{dx}{dt}$

$(1+\frac{x^2}{2^2})(8\pi) = \frac{1}{2}\frac{dx}{dt}$

If x = 1 km,

$(1+\frac{1}{4})8\pi =\frac{1}{2}\frac{dx}{dt}$

$\frac{5}{4}8\pi = \frac{1}{2}\frac{dx}{dt}$

$\implies \frac{dx}{dt}=\frac{80\pi}{4}= 20\pi\approx 62.8\text{ km per min}$

Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min

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4 years ago

Please help<br> Which one is correct?

zlopas [31]

Answer:

The first one

Step-by-step explanation:

3/5 and 9/25

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3 years ago

Solve the inequality. Graph the solution.

xenn [34]

Answer:

n-75

Step-by-step explanation:

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3 years ago