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3 years ago

10. Write the ratio as a fraction in simplest form. 12 : 42

Mathematics

2 answers:

Pavel [41]3 years ago

8 0

Answer:

2/7

Step-by-step explanation:

12 : 42 is the same as 12/42

simplify the fraction by dividing the numerator and denominator by 6

you get 2/7

Nookie1986 [14]3 years ago

5 0

Answer:

2/9 and 7/9

Step-by-step explanation:

<h2><u>RATIO INTO FRACTION</u></h2><h3>find the common factor for 12 and 42</h3>

12/6 = 2

42/6 = 7

hence ratio simplified is :

2:7

the fraction is : 2 + 7 for the denominator

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In a trolley ride around an amusement park, a child traveled from one signpost to a second signpost at a constant speed of 125 m

Inessa05 [86]

Answer:

Given speed of trolley = 125 meters per minute

$Speed= 125 meters/minute\\\\Speed =\frac{125}{60}meters/second\\\\Speed=2.083m/s$

Now we know that

Distance= Speed x time

Thus for the first case since the time of travel is less than 450 seconds thus the distance traveled is less than

Distance < 2.083 x 450 =937.5 meters

hence depending on the given information we cannot come to any conclusion weather the distance travelled is less than 800 m or greater than 800 m.

For the second case

since the time of travel is greater than 400 seconds

Thus the distance traveled is

$Distance>2.083\times 400=833.2meters$

which is greater than 800 meters.

4 0

3 years ago

Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is

strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is $121y''+110y'-24y=0$ . We propose that the solution of this equations is of the form $y = Ae^{rt}$ . Then, by replacing the derivatives we get the following

$121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)$

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

$121r^2+110r-24=0$

Recall that the roots of a polynomial of the form $ax^2+bx+c$ are given by the formula

$x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}$

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

$r_1 = -\frac{12}{11}$

$r_2 = \frac{2}{11}$

So, in this case, the general solution is $y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}$

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

$c_1 + c_2 = 1$

$c_1\frac{-12}{11} + c_2\frac{2}{11} = 0$ (or equivalently $c_2 = 6c_1$

By replacing the second equation in the first one, we get $7c_1 = 1$ which implies that $c_1 = \frac{1}{7}, c_2 = \frac{6}{7}$ .

So $y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}$

b) By using y(0) =0 and y'(0)=1 we get the equations

$c_1+c_2 =0$

$c_1\frac{-12}{11} + c_2\frac{2}{11} = 1$ (or equivalently $-12c_1+2c_2 = 11$

By solving this system, the solution is $c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}$

Then $y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}$

The Wronskian of the solutions is calculated as the determinant of the following matrix

$\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2$

By plugging the values of $y_1$ and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

$e^{\int -p(x) dx}$

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

$e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}$

Note that this function is always positive, and thus, never zero. So $y_1, y_2$ is a fundamental set of solutions.

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3 years ago

F (-2)=x+6. evaluate the function

damaskus [11]

X= -8 that uis your answer for that question :)

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3 years ago

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grin007 [14]

Whats the questions???

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3 years ago

I was just wondering this is one of my questions in my math books and i needed help (Its really long i did all the work i just w

slava [35]

Answer:

no not that wuch

Step-by-step explanation:

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3 years ago