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2 years ago

14

Find the most general antiderivative of the function. (Use C for the constant of the antiderivative).

1 answer:

ArbitrLikvidat [17]2 years ago

7 0

Answer:

$x^6 - \frac{7x^5}{5} - 3x^3 + C$

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Given points A(3,7) and B(8, -3) are the end points of AB, calculate the coordinates of M, the midpoint.

tester [92]

Answer:

(5.5,2)

Step-by-step explanation:

see the pic for the steps

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3 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

What percentage of adult men are between 5'-4" and 6'-0"?

inna [77]

Answer: I think the answer is 88.5%

Step-by-step explanation:

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3 years ago

Change one digit from the number 238882 so that it is divisible by 3 not not divisible by 2

Aleksandr-060686 [28]

Answer:

238882 -> 238881

Step-by-step explanation:

To make it not divisable by 2, you have to change the rightmost digit.

Simply divide the number by 3, round it, then multiply it by 3 again.

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2 years ago

A young boy is growing at a rate of 3.5 cm per month. He is currently 90 cm tall. At that rate, in how many months will the boy

Olenka [21]

It will take months for the boy to grow to a height of 132cm. 132-90= 42 cm left to grow. 42÷3.5= 12months, or a year.

7 0

3 years ago