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pantera1 [17]
3 years ago
11

What is the first operation that you will perform when you evaluate this expression? 12 + (18 - 2) x 3 ÷ 24

Mathematics
1 answer:
Temka [501]3 years ago
7 0

Answer:

(18-2)

Step-by-step explanation:

Use the formula of PEMDAS to determine which is first.

The p stands for parentheses so you would perform that operation first.

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Write 124 in scientific notation.
Artemon [7]

Answer:

Step-by-step explanation:

Write 124 in scientific notation.

Then, in scientific notation, 124 is written as 1.24 × 102. Actually, converting between "regular" notation and scientific notation is even simpler than I just showed, because all you really need to do is count decimal places.

6 0
3 years ago
Read 2 more answers
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 <em>c)</em>

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

This becomes the solution <em>m=α±βi</em> where <em>α=0</em> and <em>β=2</em>

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 <em>A</em> and <em>B</em> 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
A pole is centre of a circular pond of diameter 14m. Total height of a pole is 20m and its part inside a water is 3.5m. If a man
monitta

Answer:

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4 0
3 years ago
Name an altitude for ABC
valina [46]
Altitude is another word for height so it would be the first answer
8 0
3 years ago
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Graph the linear equation to -2x+7y=-21
mr Goodwill [35]

Answer:

This equation is in standard form, so to make graphing easier you need to put it in y=mx+b form or slope, intercept form.

Step-by-step explanation:

I have attached a photo of what the graph would look like.

However, in the future you should know how to turn this into a slope intercept equation.

-2x+7y=-21

+2x        +2x

7y=2x-21

divide the entire equation by 7

y= 2/7x-3

That is a full equation in slope intercept form.

Hopefully this helps!

8 0
3 years ago
Read 2 more answers
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