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3 years ago

What is the answer for the three questions please help

Mathematics

1 answer:

ycow [4]3 years ago

7 0

The driver can drive around the track 54 times for $12. Thus for one dollar, he can drive around the track 54/12 times, or 4.5 times. If for each dollar he drives around 4.5 times, for 8 dollars, he can drive around 8*4.5 or 36 times.

If there are 207 students in 9 classes, in 1 class, there are 207/9 students, or 23 students per class. Since there are 23 students per class and there are classes, there are a total of 23*6 or 138 students in total.

Liam practices 24 times in 4 days. Thus he practices 24/4 or 6 times per day. His brother practices 12 times in 3 days. Thus he practices 12/3 or 4 times a day. Thus their rates are not equivalent.

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Red Riding Hood is making a food basket out of 8 different fruits and 9 different vegetables. If there is only room for 6 items,

Bogdan [553]

Answer:

169,344

Step-by-step explanation:

Data provided in the question

Different fruits = 8

Different vegetables = 9

There is only room for 6 items

Based on the above information, the number of ways for an equal number of fruits & veggies is

For the number of combinations of fruit is

$= 8\times7\times6$

For the number of combinations of vegetables is

$= 9\times8\times7$

So, the total combinations are

$= 9\times8\times8\times7\times7\times6$

= 169,344

6 0

3 years ago

A bus covers a distance of 2.45 km in 2 min. What is the speed of bus?

Vladimir [108]

Answer:

The speed of the bus is 74.242 kilometers per hour.

Step-by-step explanation:

Let suppose that bus runs at constant speed and that speed is measured in kilometers per hour. Then, the speed of the bus ( $v$ ), in kiometers per hour, is determined by following kinematic expression:

$v = \frac{s}{t}$ (1)

Where:

$s$ - Travelled distance, in kilometers.

$t$ - Time, in hours.

If we know that $s = 2.45\,km$ and $t = 0.033\,h$ , then the speed of the bus is:

$v = \frac{s}{t}$

$v = 74.242\,\frac{km}{h}$

The speed of the bus is 74.242 kilometers per hour.

7 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.

8 0

2 years ago

A tree casts a shadow 27 m long. At the same time, the shadow cast by a 66-cm tall statue is 56 cm long. Find the height of the

Nata [24]

$\frac{height _{1} }{shadow_{1}} = \frac{height _{2} }{shadow_{2}}$

$\frac{height _{1} }{27m} = \frac{66cm}{56cm}$

$\frac{height _{1} }{2700cm} = \frac{66cm}{56cm}$

$2700*66=56*h _{1}$

$178200=56h _{1}$

$3182.1cm=h _{1}$

$\frac{3182.1cm}{1000cm} = 3.2m$

$height:3.2m$

6 0

3 years ago

Read 2 more answers

Suzie made a mistake in the following problem. The mistake was made in Line ___. Only input the number of the first incorrect li

zalisa [80]

Answer:

Mistake in Line 2

Step-by-step explanation:

Line 1

7(6) ÷ 5 + 42

Line 2

7(6) ÷ 5 + 16

Line 3

42 ÷ 5 + 16

Line 4

42 ÷ 21

Line 5

To simplify any expression we use order of operation

Line 1 is 7(6) ÷ 5 + 42

Order of operation is PEMDAS

First we start with parenthesis

so we multiply 7(6) in line 2

7*6- 42

So Line 2 is 42 ÷ 5 + 42

Hence there is a mistake in Line 2

3 0

3 years ago