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2 years ago

Simplify: (3x-4)+(-2x+8).

Mathematics

1 answer:

maxonik [38]2 years ago

4 0

Answer:

Step-by-step explanation:

x+4

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There were two candidates in an election and the successful candidates won by 160 votes. If 2,800 votes were cast, how many vote

Phantasy [73]

Answer: The losing candidate got 1240 and the winning candidate got 1560.

Step-by-step explanation:

First divide the number of votes by the number of people: 2800/2= 1400.

add 160 to one candidate and subtract 160 from the other.

6 0

2 years ago

Solve the initial value problem y'=2 cos 2x/(3+2y),y(0)=−1 and determine where the solution attains its maximum value.

zloy xaker [14]

Answer:

$y=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

$x={\pi}{4}$

Step-by-step explanation:

We are given that

$y'=\frac{2cos2x}{3+2y}$

y(0)=-1

$\frac{dy}{dx}=\frac{2cos2x}{3+2y}$

$(3+2y)dy=2cos2x dx$

Taking integration on both sides then we get

$\int (3+2y)dy=2\int cos 2xdx$

$3y+y^2=sin2x+C$

Using formula

$\int x^n=\frac{x^{n+1}}{n+1}+C$

$\int cosx dx=sinx$

Substitute x=0 and y=-1

$-3+1=sin0+C$

$-2=C$

$sin0=0$

Substitute the value of C

$y^2+3y=sin2x-2$

$y^2+3y-sin 2x+2=0$

$y=\frac{-3\pm\sqrt{(3)^2-4(1)(-sin2x+2)}}{2}$

By using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$y=\frac{-3\pm\sqrt{9+4sin2x-8}}{2}=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

Hence, the solution $y=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

When the solution is maximum then y'=0

$\frac{2cos2x}{3+2y}=0$

$2cos2x=0$

$cos2x=0$

$cos2x=cos\frac{\pi}{2}$

$cos\frac{\pi}{2}=0$

$2x=\frac{\pi}{2}$

$x=\frac{\pi}{4}$

3 0

2 years ago

The population of a city in the year 2000 was 4,400. In 2010, the population was 5,060. Find the percent increase in the populat

larisa86 [58]

Answer:

total population in the year 2000=4400

total population in the year 2010=5060

no of people increased=5060-4400

=660

increase percent=660/4400*100%

=3/20*100%

=15%

Step-by-step explanation:

15/100*5060

0.15*5060

759

in 2020 population will be

5060+759

5819

therefore the population will be 5819 in 2020

6 0

2 years ago

Read 2 more answers

Which function has the same range as y = csc

SSSSS [86.1K]

Was this a multiple answer question? If so, if this was one of your choices then that's your answer: Y = sec X

8 0

2 years ago

The speed of a current in the river is 4 mph a boat travels 10 miles downstream in this river in the same time they would travel

Art [367]

It would be 4mph because the current would move the boat in still water.

6 0

2 years ago