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4 years ago

In 2008 the population of 10 to 14-year-olds in the United States was 24 84163 right this number in expanded form

Mathematics

1 answer:

Ket [755]4 years ago

6 0

(2,000,000) + (400,000) + (80,000) + (4,000) + (100) + (60) + (3) = 2,484,163

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3xy'+y=12x find general solution

Eduardwww [97]

The equation is linear, as you can write

$3xy'+y=12x\implies y'+\dfrac1{3x}y=4$

An integrating factor would be

$\mu(x)=\exp\left(\displaystyle\int\frac{\mathrm dx}{3x}\right)=x^{1/3}$

Multiplying both sides of the ODE by this yields

$x^{1/3}y'+\dfrac1{3x^{2/3}}y=4x^{1/3}$

where the LHS is a derivative:

$\dfrac{\mathrm d}{\mathrm dx}\left[x^{1/3}y\right]=4x^{1/3}$

Integrating both sides, we get

$x^{1/3}y=4\displaystyle\int x^{1/3}\,\mathrm dx$
$x^{1/3}y=3x^{4/3}+C$
$y=3x^{3/3}+Cx^{-1/3}=3x+\dfrac C{x^{1/3}}$

5 0

3 years ago

Find the value of z in the triangle shown below.

suter [353]

Answer:

x = 69.4 degrees

Step-by-step explanation:

∠x = sin(a·sin(B)/b) = 1.21158 rad = 69.419°

5 0

3 years ago

An escalator lifts people to the second floor of a building, 21 ft above the first floor. the escalator rises at a 30 degree ang

Ira Lisetskai [31]

We use the trigonometric function for this case. An escalator is an inclined path. We form a right triangle since we have given the value of the height. The height from the first floor to second floor is called the adjacent while the travelled distance of the people is called the hypothenuse. We use cosine function because we are given in terms of adjacent and hypothenuse. The ratio of cosine function is
cos x = a/h
where x is the angle
Solving for h,
h = a/(cos x) = 21/(cos 30) = 24.25 ft

7 0

3 years ago

The distance d in miles that can be covered by a rabbit in X hours is given in the equation y = 30 x The distance covered by a b

AveGali [126]

Answer:

Rabbit is faster than bear.

Step-by-step explanation:

Speed of rabbit or bear is determined by their rate of change of their distances with time.

The distance covered by rabbit in $x$ hours is given as:

$y=30x$

The above equation is of the form $y=mx$ , where, $m$ is the rate of change of $y$ with $x$ .

Therefore, the rate of change of rabbit's distance with time is 30 mi/h.

Now, from the graph, the slope is given as the rise over run.

Rise is 50 miles and run is 2 miles.

So, rate of change of bear's distance with time is, $m_b=\frac{50}{2}=25\ mi/h$

Now, 30 is greater than 25. So, rabbit is faster than bear.

6 0

3 years ago

Modern car company has come out with a new car model. Market analysts predict that 4,600 cars will be sold in the first month an

Arte-miy333 [17]

The first five terms of the sequence are; 4,600, 4,550, 4,500, 4,450, 4,400 and the total predicted number of sold cars for the first year is 51,900 cars

<h3>Arithmetic sequence</h3>

First month, a = 4,600 cars
Common difference, d = -50 cars

First five terms;

a = 4,600

a + d = 4600 + (-50)

= 4600 - 50

= 4,550

a + 2d

= 4600 + 2(-50)

= 4600 - 100

= 4,500

a + 3d

= 4,600 + 3(-50)

= 4,600 - 150

= 4,450

a + 4d

= 4600 + 4(-50)

= 4,600 - 200

= 4,400

cars predicted for the twelfth month.

a + 11d

= 4600 + 11(-50)

= 4600 + 550

= 4,050

Total predicted number of sold cars for the first year:

Sn = n/2{2a + (n - 1)d }

= 12/2{2×4600 + (12-1)-50}

= 6{9200 + 11(-50)}

= 6(9,200 - 550)

= 6(8,650)

= 51,900 cars

Learn more about arithmetic sequence:

brainly.com/question/6561461

#SPJ1

7 0

2 years ago