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3 years ago

The product of 3 and a number increased by 10 is 28

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

3 0

Are those all your options? the answer would be 3x+10= 28 but you dont have it as a multiple choice.

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Find the area of a regular octagon with

vodka [1.7K]

Answer:

Step-by-step explanation:

Area=2(1+ $\sqrt{2}$ )8²

=309.0(round to nearest tenth)

5 0

3 years ago

-2x+2>3x-8 50 points

Blababa [14]

Given:

The inequality is

$-2x+2>3x-8$

To find:

The solution of the given inequality.

Solution:

We have,

$-2x+2>3x-8$

Isolate the variables terms on the left side.

$-2x-3x>-2-8$

$-5x>-10$

Divide both sides by -5 and change the inequality sign as we divide the equality by a negative value.

$\dfrac{-5x}{-5}$

$x$

Therefore, the correct option is D.

5 0

3 years ago

Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

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

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in c)

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution m=α±βi where α=0 and β=2

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where A and B are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

7 0

3 years ago

Find the number of miles in 100 km

Lilit [14]

Answer:

Well, 100 km equals approximately 63 miles.

Step-by-step explanation:

One mile is approximately 1.6 km, so you just divide 100 km by 1.6 and you should get the miles, being 62.5 miles, or 63.

7 0

4 years ago

Melllissa owns 4 sets of jewelry. Each set contains 2 earrings, 1 neckles, 1 bracelet, 1 ring. How many pieces of jewelry does M

Deffense [45]

Answer:

The answer is to the problem is 18.

8 0

3 years ago