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3 years ago

13

An ice cream shop uses 4 pints of ice cream to make 6 sundaes. The same amount of ice cream was used for each sundae. How many p

ints of ice cream are used for each sundae?

1 answer:

lawyer [7]3 years ago

5 0

Answer:

1.5 pints per sundae

Step-by-step explanation:

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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

4 years ago

Does anyone know how to do this by solving with substitution

IRISSAK [1]

Answer:

Step-by-step explanation:

Question 1

System of equations is,

y = -6x -------(1)

y = -4x - 2 ---------(2)

Substitute the value of y from equation (1) to equation (2)

-6x = -4x - 2

-6x + 4x = -2

-2x = -2

x = 1

From equation (1)

y = -6(1)

y = -6

Question (2)

System of equations is,

-y = x --------(1)

3x + 5y = 20 ---------(2)

Substitute the value of x from equation (1) to equation (2)

3(-y) + 5y = 20

-3y + 5y = 20

2y = 20

y = 10

From equation (1)

-y = x

x = -10

Question (3)

System of the equations is,

y = -2x - 7 --------(1)

9x - 10y = 12 ----------(2)

Substitute the value of y from equation (1) to equation (2)

9x - 10(-2x - 7) = 12

9x + 20x + 70 = 12

29x = 12 - 70

29x = -58

x = -2

From equation (1)

y = -2(-2) - 7

y = 4 - 7

y = -3

8 0

3 years ago

What is the slope of the line y= 7x - 8?

weqwewe [10]

$y=mx+b\\\\slope\ is\ m\\\\\\y=7x-8\\\\slope\ i\n\ m=7$

5 0

3 years ago

How many times does a thousand go into 1,000,000,000

Harman [31]

The answer would be 1,000,000 times

7 0

3 years ago

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What is 4/9 - 1/3 = <br> help

brilliants [131]

1/9

Hope this helps! :))

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3 years ago

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