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Savatey [412]
3 years ago
12

What is the domain of y = cos-1^x?

Mathematics
2 answers:
NISA [10]3 years ago
7 0

Answer:

A) [-1,1]

Step-by-step explanation:

The function of y=cos⁻¹(x) has a domain of [-1,1] and a range of [0,π]. Observe the graph.

kirza4 [7]3 years ago
3 0

Answer:

A

Step-by-step explanation:

correct on edge

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How do I solve for constant rate of change
barxatty [35]

You use the slope formula, (y2-y1/x2-x1)

6 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 <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
PLS HELP QUICK I WILL GIVE BRAINLIEST
Volgvan

Answer:

B

Step-by-step explanation:

The equation for B equals a negative answer

7 0
2 years ago
Read 2 more answers
X x=?1<br> 612<br> 21<br> 6V2<br> Can someone please help
Romashka-Z-Leto [24]

Answer:

612

Step-by-step explanation: Im guessing ran out of time

7 0
2 years ago
If x varies directly as d and d varies directly as e and c=4 when e=12, find c where e=3
Nata [24]
 c = 1 is the answer when e = 3
3 0
3 years ago
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