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3 years ago

Is y=-3 a linear equation?

Mathematics

1 answer:

Stels [109]3 years ago

7 0

If degree of variable is one then eq. is linear
so given is linear.

You might be interested in

What is the greatest common denominator

Eva8 [605]

3 is the greatest common denominator

5 0

3 years ago

What’s 5/10 + 1/3 I really need help

kap26 [50]

5/10 + 1/3

15/30 + 10/30 = 25/30 = 5/6

Answer : 5/6 in its simplified form

7 0

2 years ago

In ΔDEF, the measure of ∠F=90°, DF = 24, FE = 7, and ED = 25. What ratio represents the sine of ∠E?

kumpel [21]

Answer:

24/25

Step-by-step explanation:

In this triangle DF and FE are legs (because they form the right angle) , ED is the hypotenuse (it is the largest side, it is opposite to the right angle).

son of E is the ratio of the leg opposite to the angle E (DF) to the hypotenuse

it is 24/25

4 0

2 years ago

Here are two offers for batteries.

trapecia [35]

OFFER A is cheaper.

Step-by-step explanation:

Given,

OFFER A

Pack of 5

£2.75

Pay for 3 packs get 1 free

And

OFFER A

Pack of 5

£2.75

Pay for 3 packs get 1 free

To find which offer is cheaper.

<u>For OFFER A</u>

For 4 Packets he needs to pay £2.75

He needs to buy 40 batteries.

He needs to buy 40÷(4×5) = 2 packets.

Total cost = £2.75 ×2 = £5.5

<u>For OFFER B</u>

For 4 Packets he needs to pay £2.52

He needs to buy 40 batteries.

He needs to buy 10 packets.

After discount he has to pay = £2.52 -(£2.52 × $\frac{1}{3}$ ) = £1.68

Total cost = £1.68×10 = £16.8

Hence,

OFFER A is cheaper.

7 0

2 years ago

x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco

igomit [66]

Answer:

$x=-cos(t)+2sin(t)$

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

$a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

$r_1_,_2=\lambda \pm \mu i$

Let's find the solution for $x''+x=0$ using the previous information:

The characteristic equation is:

$r^{2} +1=0$

So, the roots are given by:

$r_1_,_2=0\pm \sqrt{-1} =\pm i$

Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

And

$x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2$

Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

3 0

3 years ago