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3 years ago

Meredith has 8 pens and 9 pencils. Brody has 4 pens and 9 pencils.

Mathematics

2 answers:

nikdorinn [45]3 years ago

6 0

8/9 > 4/9
Meredith has more pens to pencils than Brody

Kipish [7]3 years ago

3 0

Answer:

$\frac{8}{9}>\frac{4}{9}$

Step-by-step explanation:

We have been given that Meredith has 8 pens and 9 pencils. Brody has 4 pens and 9 pencils.

We can see that Meredith and Brody has same number of pencils, but Meredith has more pens than Brody.

We can represent the pen to pencils ratio for Meredith and Brody as:

$\text{Meredith's pens to pencils proportion}=\frac{8}{9}$

$\text{Brody's pens to pencils proportion}=\frac{4}{9}$

We can compare the pens and pencils proportions that Meredith and Brody have as:

$\frac{8}{9}>\frac{4}{9}$

Therefore, $\frac{8}{9}>\frac{4}{9}$ is the correct comparison of their ratios of pens to pencils.

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First-order linear differential equations

kkurt [141]

Answer:

$(1)\ logy\ =\ -sint\ +\ c$

$(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Step-by-step explanation:

1. Given differential equation is

$\dfrac{dy}{dt}+ycost = 0$

$=>\ \dfrac{dy}{dt}\ =\ -ycost$

$=>\ \dfrac{dy}{y}\ =\ -cost dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}$

$=>\ logy\ =\ -sint\ +\ c$

Hence, the solution of given differential equation can be given by

$logy\ =\ -sint\ +\ c.$

2. Given differential equation,

$\dfrac{dy}{dt}\ -\ 2ty\ =\ t$

$=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty$

$=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})$

$=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}$

$=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c$

$=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Hence, the solution of given differential equation is

$log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

8 0

3 years ago

What is the slope of a line that is parallel to the line joining (7,-5) and (-5,7)

brilliants [131]

Answer:

Step-by-step explanation:

If two lines are parallel then they will have the same slope. So all you need to do is find the slope of the line that joins the two given points. You can use the slope formula $\frac{y_2-y_1}{x_2-x_1}$ . You can also graph the two points and use rise over run. $\frac{7-(-5)}{-5-7} =\frac{12}{-12}=-1$