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3 years ago

Given an integer, how do you find it's opposite?

1 answer:

6 0

Given an integer, how do u find its opposite....

change the sign

example :
2....its opposite is -2
-3...its opposite is 3
5....its opposite is -5
-4...its opposite is 4

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Solve the system: x' = (2 4 -1 6)x

sertanlavr [38]

Answer:

$x=e^{8t}+c$

Step-by-step explanation:

we have given x'=(24-16)x=8x

x' denotes the differenation

$\frac{dx}{dt}=8x$ differentiation is performed with respect to t

by variable separable method we can write

$\frac{dx}{x}=8dt$

on integrating both side

$lnx=8t+c$

$x=e^{8t}+c$ (property of log )

so the solution for x will be $x=e^{8t}+c$

6 0

3 years ago

Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + ... + 24 + 25, find the value of

Anastaziya [24]

Answer:

325

Step-by-step explanation:

You must have heard about Arithmetic Progressions (AP)

Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.

Our very own counting numbers form AP

For example :-

2 = 1 + 1

3 = 2 + 1

4 = 3 + 1

The number in bold (1) is that constant number which is added to a number to form its successive number.

To find the sum of series forming AP, we use the formula :-

$sum = \frac{n}{2} \{ a + a _{n} \}$

here,

n is the number of terms
a is the first number of the series
an is the last number of the series

So we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).

and n is 25

$S = \frac{25}{2}\{ 1 +25\}$

$= \frac{25 \times 26}{2}$

$= 25 \times 13$

$= 325$

So, the value of S comes out to be 325.

8 0

2 years ago

Read 2 more answers

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UNO [17]

Answer:

$\frac{15}{8}$

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Describing Key Features of a Graph of a Polynomial Function:

Diano4ka-milaya [45]

End behavior:

The parent function is: f(x) = x³, which starts (from the left side) at -∞ and ends (on the right side) at +∞.

Zeroes:

f(x) = x³ + 2x² - 8x

0 = x³ + 2x² - 8x

0 = x(x² + 2x - 8)

0 = x(x + 4)(x - 2)

0 = x 0 = x + 4 0 = x - 2

x = 0 x = -4 x = 2

Intervals:

Put the zeroes in order: -4, 0, 2

since f(x) is increasing from the left then the interval from -4 to 0 is positive and the interval from 0 to 2 is negative.

Graph:

see attachment

3 0

3 years ago

Read 2 more answers

Olga worked 37.5 hours last week at the library and earned 12.50 an hour.if she gets a 2.50 per hour raise,how many hours will s

ruslelena [56]

Olga worked 37.5 hours last week and earned $12.50 an hour.

[ h = the number of hours y = total earnings ]

12.50h = y

12.50(37.5) = y

468.75 = y

She earned $468.75 last week

If she gets a $2.50 per hour raise:

12.50 + 2.50 = 15.00

She gets $15 per hour.

How many hours will she have to work to make $468.75?

15h = 468.75 Divide 15 on both sides to get "h" by itself

h = 31.25

She needs to work 31.25 hours

4 0

2 years ago