In 12 1/2 minutes, Dulce read 50 pages. a. on an average, how many pages did she read per min.?

A scientist cools some water at a constant rate. The graph and table show

Afina-wow [57]

A function assigns the values. The function for this model can be written as y=-4x+50.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

As it can be seen from the graph that the function is linear, therefore, we can write,

y = mx + c

Given two points of the graph, therefore, we can write for the first point,

30 = m(5) + c

30 = 5m + c

c = 30 - 5m

Also, for the second point,

y = mx + c

26 = 6m + c

Substitute the value of c,

26 - 6m = 30 - 5m

-6m + 5m = 30 - 26

-m = 4

m = -4

Now, substitute the value of m in any one of the equation formed above,

c = 30 - 5m

c = 30 - 5(-4)

c = 50

Hence, the function for this model can be written as y=-4x+50.

Learn more about Function:

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7 0

2 years ago

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

Prove the following trigonometric identities

alexandr1967 [171]

Answer:

Greetings !

check the attachment above☝️ but i haven't done the second question wait a moment. thx

4 0

1 year ago

What Is -0.75-(-2/50)+0.4(-3/4)? Explain and answer the question please

lilavasa [31]

The answer is -1.01
I first changed the signs of the ones i could. So <span>-0.75+(2/50)+0.4(-3/4)
Then i multiplied the 0.4*-3/4 which equals -0.3
So you are left with </span><span>-0.75+(2/50)-0.3
2/50 is equal to 0.04 so now it is </span> -0.75+0.04-0.3 and the rest is simple math. Which equals -1.01

3 0

3 years ago

Jesse is playing a game with a number cube with faces numbered 1 through 6. What is the probability of rolling a number that is

lana [24]

Answer:

The probability of rolling a number that is even and a multiple of 3 is $\frac{1}{6}$