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3 years ago

Your local varsity basketball team off ers bus

Mathematics

1 answer:

Korvikt [17]3 years ago

6 0

Answer:

6 buses are used and the last bus has 48 people on it

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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

Lan pays a semiannual premium of $600

disa [49]

Answer:

$225

Step-by-step explanation:

Automobile = 600

Health insurance = 150 x 12 = 1800

Life insurance = 300

1800 + 300+600 = 2700

2700/12 = $225

4 0

3 years ago

How many units long is a segment whose endpoints are (-4,1) and (1,13)?

Ann [662]

Answer:

Step-by-step explanation:

(1−−4)2+(13−1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√(1++0)2+(13−1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√(5)2+(12)2‾‾‾‾‾‾‾‾‾‾‾√25+144‾‾‾‾‾‾‾‾‾√169‾‾‾‾√≈13

Sorry if the explanation is a bit confusing but, I used the distance formula to do this.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

7 0

3 years ago

Read 2 more answers

What is the reason for Statement 2 of the two-column proof?

torisob [31]

We have been given that PQ bisects $\angle RPS$ . In the second statement of the given two-column proof, the statement is $\angle RPQ\cong\angle QPS$ .

This implies that the two angles formed by bisection of angle $\angle RPS$ by the line PQ are equal. We know that the reason for this is simple. It is the definition of bisection of an angle that the two smaller angles formed will be equal to each other.

Therefore, the reason for statement 2 of the given two column proof is c) Definition of bisect

5 0

3 years ago

Read 2 more answers

What is the value of (u-t)(u^2-t^2)?

Umnica [9.8K]

Answer:

Step-by-step explanation:

u-t = 2

u+t= 5

(u-t) (u²-t²)

(u-t) (u-t) (u+t) (a²-b²= (a+b) (a-b))

put the values

(2)(2)(5)

=20

5 0

3 years ago