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RUDIKE [14]
3 years ago
5

What is the value of x in the equation 34x+2=54x−6 ?

Mathematics
1 answer:
elixir [45]3 years ago
4 0

Answer:

The value of x in the equation is: x=\frac{2}{5}

Step-by-step explanation:

Given the equation

34x+2=54x-6

Subtract 2 from both sides

34x+2-2=54x-6-2

34x=54x-8

Subtract 54x from both sides

34x-54x=54x-8-54x

-20x=-8

Divide by both sides by -20

\frac{-20x}{-20}=\frac{-8}{-20}

x=\frac{2}{5}

Therefore, the value of x in the equation is: x=\frac{2}{5}

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Lamaj is rides his bike over a piece of gum and continues riding his bike at a constant rate time = 1.25 seconds the game is at
Hitman42 [59]

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. At time = 1.25 seconds, the gum is at a maximum height above the ground and 1 second later the gum is on the ground again.

a. If the diameter of the wheel is 68 cm, write an equation that models the height of the gum in centimeters above the ground at any time, t, in seconds.

b. What is the height of the gum when Lamaj gets to the end of the block at t = 15.6 seconds?

c. When are the first and second times the gum reaches a height of 12 cm?

Answer:

Step-by-step explanation:

a)

We are being told that:

Lamaj rides his bike over a piece of gum and continues riding his bike at a constant rate. This keeps the wheel of his bike in Simple Harmonic Motion and the Trigonometric equation  that models the height of the gum in centimeters above the ground at any time, t, in seconds.  can be written as:

\mathbf {y = 34cos (\pi (t-1.25))+34}

where;

y =  is the height of the gum at a given time (t) seconds

34 = amplitude of the motion

the amplitude of the motion was obtained by finding the middle between the highest and lowest point on the cosine graph.

\mathbf{ \pi} = the period of the graph

1.25 = maximum vertical height stretched by 1.25 m  to the horizontal

b) From the equation derived above;

if we replace t with 1.56 seconds ; we can determine the height of the gum when Lamaj gets to the end of the block .

So;

\mathbf {y = 34cos (\pi (15.6-1.25))+34}

\mathbf {y = 34cos (\pi (14.35))+34}

\mathbf {y = 34cos (45.08)+34}

\mathbf{y = 58.01}

Thus, the  gum is at 58.01 cm from the ground at  t = 15.6 seconds.

c)

When are the first and second times the gum reaches a height of 12 cm

This indicates the position of y; so y = 12 cm

From the same equation from (a); we have :

\mathbf {y = 34 cos(\pi (t-1.25))+34}

\mathbf{12 = 34 cos ( \pi(t-1.25))+34}

\dfrac {12-34}{34} = cos (\pi(t-1.25))

\dfrac {-22}{34} = cos(\pi(t-1.25))

2.27 = (\pi (t-1.25)

t = 2.72 seconds

Similarly, replacing cosine in the above equation with sine; we have:

\mathbf {y = 34 sin (\pi (t-1.25))+34}

\mathbf{12 = 34 sin ( \pi(t-1.25))+34}

\dfrac {12-34}{34} = sin (\pi(t-1.25))

\dfrac {-22}{34} = sin (\pi(t-1.25))

-0.703 = (\pi(t-1.25))

t = 2.527 seconds

Hence, the gum will reach 12 cm first at 2.527 sec and second time at 2.72 sec.

7 0
3 years ago
I NEED HELP WITH THIS ASAP PLEASE!
sdas [7]
(x+1)(x+2)
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5 0
2 years ago
During two years, the population of birds of an island became 7 times more than before. If the first year increase in the popula
9966 [12]

The percent increase of the second year was 85.71%

Step-by-step explanation:

The exponential growth formula is y=a(1+r)^x

where;

y=population after x years

a=original population

r=growth rate as a decimal

x=number of time interval that have passed

Let starting population be p

The first year increase in the population was 40% this means;

r=0.4 , x=1 and a=p thus the equation will be

y=p(1+0.4)^1 ⇒⇒y=1.4 p

In the second year the population of birds of an island became 7 times more than before which is 7p

7p= 7*1.4p= 9.8p

Increase will be;

9.8p-1.4p=8.4

% increase will be;

8.4/9.8 *100 =85.71%

Learn More

Percent increase: brainly.com/question/13882170

Keywords : population, birds, island,increase

#LearnwithBrainly

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3 years ago
Please help me with this! I do need it soon though, before tomorrow. I will give brainliest! also, is the graph i made correct?
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I like to use Desmos Graphing Calculator. The attachment is what I get when I plug the inequalities in.

6 0
2 years ago
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Antonio ate 9/10 of a pizza on Monday. On Tuesday, he ate 3/10 of a pizza. How much pizza did Antonio eat on Monday and Tuesday?
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He ate 1 1/5  (1.2) of pizza

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