Ask question

Ask question

All categories

3 years ago

12

Emma has 18 yellow flowers and 30 white flowers she wants to split them into vases in equal groups what is the largest number of

groups she can make

1 answer:

Julli [10]3 years ago

3 0

6, it’s because 6x5=30 6x3=18.

You might be interested in

Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

3 years ago

How can you show that two objects are proportional with a table?

vredina [299]

So this is our table:

-----------------
x-values | a b c d e f |
-----------------
y-values | g h i j k l |
-----------------

You can know that the values in the table are proportional if:

$\frac{a}{g}=\frac{b}{h} =\frac{c}{i}=\frac{d}{j}=\frac{e}{k}=\frac{f}{l}$

Hope that helps :)

5 0

3 years ago

Deon is riding his bicycle. He rides for 7 hours at a speed of 22.4 kilometers per hour. For how many kilometers does he ride

salantis [7]

By hypothesis, Deon is riding at a speed of 22.4 kilometers per hour. So each hour, he completes 22.4 km.

If he rides for 7 hours, he completes 22.4 * 7 = 156.8 km

So in 7 hours, he rides 156.8 kilometers.

Hope this helps! :)

6 0

3 years ago

Steven is driving to Texas pulling a 12 ft. boat. If he drives 150 miles in

ziro4ka [17]

Answer: 975

Step-by-step explanation:

Because you multiply 6 times 150 and then you add 75 because that is half of 150 and you only need one more mile

6 0

3 years ago

Anna saves 5/8 of her money. What percent of her money does Anna save?

scoray [572]

the amnwer is 1.6. all you do is 8 dived by 5

6 0

3 years ago

Read 2 more answers