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3 years ago

Use technology to solve for x. 3^x - 4= 6x - 7

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

4 0

Answer:

$x=1,1$

Step-by-step explanation:

$3x^2 - 4= 6x - 7$

For the given equation :

Making the coefficients of x to L.H.S

$3x^2-6x-4+7$ $=0\\$

$3x^2-6x+3=0$

Taking 3 as common from the above equation

$x^2-2x+1=0$

Splitting the equation to make factors

$x^2-x-x+1=0$

Taking common from the equation:

$x(x-1)-1(x-1)\\(x-1)(x-1)=0$

Equating 'x' to zero

$x=1,1$

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A rocket is shot straight up into the air with an initial velocity of 500 ft per second and from a height of 20 feet above the g

iragen [17]

The height of the rocket above the ground after $t$ seconds is given by the equation : $H= -16t^2+Vt+h$ , where $V$ is the initial velocity and $h$ is the initial height.

Given that, $V= 500 ft/second$ and $h= 20 ft$

So, the equation will become: $H= -16t^2 +500t+20$

A) For finding the height of the rocket 3 seconds after the launch, we will plug $t=3$ into the above equation. So....

$H= -16(3)^2+500(3)+20\\ \\ H= -16(9)+1500+20\\ \\ H= -144+1500+20=1376$

So, the height of the rocket 3 seconds after the launch is 1376 feet.

B) When the rocket at a height of 400 feet, then we will plug $H= 400$

$400=-16t^2+500t+20\\ \\ 16t^2-500t-20+400=0\\ \\ 16t^2-500t+380=0\\ \\ 4(4t^2-125t+95)=0\\ \\ 4t^2-125t+95=0$

Using quadratic formula, we will get......

$t= \frac{-(-125)+/-\sqrt{(-125)^2-4(4)(95)}}{2(4)}\\ \\ t= \frac{125+/-\sqrt{14105}}{8}\\ \\ t= 30.4705... \\ and \\ t= 0.7794...$

So, after 0.7794...seconds and 30.4705...seconds the rocket is at a height of 400 feet above the ground.

C) The time duration that the rocket remains in the air means we need to find the time taken by the rocket to reach the ground. When it reaches the ground, then $H=0$ . So.....

$0=-16t^2+500t+20\\ \\ -4(4t^2-125t-5)=0\\ \\ 4t^2-125t-5=0$

Using quadratic formula, we will get.....

$t= \frac{-(-125)+/-\sqrt{(-125)^2-4(4)(-5)}}{2(4)}\\ \\ t= \frac{125+/-\sqrt{15705}}{8}\\ \\ t=31.2899...\\ and\\ t= -0.0399...$

(Negative value is ignored as time can't be in negative)

So, the rocket will remain in the air for 31.2899... seconds.

5 0

4 years ago

Ben is paid £12.40 per hour.

andreev551 [17]

Answer:

£156.24

Step-by-step explanation:

Ben worked for 12 hours.

Total = Normal working hours + overtime working hours

12 hours = 9 hours + 3 hours

Ben is paid £12.40 per hour(normal working hours)

he is paid overtime for the additional hours at a rate of 1.2 times his normal rate of pay.

Amount earned Overtime = 1.2 × £12.40

= £14.88

Total amount earned for 12 hours of work = 9(£12.40) + 3(£14.88)

= £111.60 + £44.64

= £156.24

Total amount earned for 12 hours of work = £156.24

4 0

3 years ago

Please I need help with this question asap.

kiruha [24]

Answer:

The table is:

x y

1 1

2 5

3 9

The graph B shows the relationship y=4x-3

Step-by-step explanation:

We need to fill the table using the rule:

To find y multiply x by 4 and then subtract 3.

Writing rule in mathematical form:

y=4x-3

Now for completing the table we need to put x=1,2 and 3 and find values of y

$For x=1//y=4x-3\\ y=4(1)-3\\ y=4-3\\ y=1\\$

$For \ x=2\\y=4x-3\\ y=4(2)-3\\ y=8-3\\ y=5$

$For \ x=3\\y=4x-3\\ y=4(3)-3\\ y=12-3\\ y=9$

So, the table is:

x y

1 1

2 5

3 9

The graph B shows the relationship y=4x-3

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3 years ago

Please help! Confused and my teacher sucks lol

iren [92.7K]

(4,3) should be the coordinates for point V

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4 years ago

Find the surface area of the cylinder in terms of pi

topjm [15]

Answer:

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Plugging in you will get 168 pi

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3 years ago