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3 years ago

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a company bought 12 boxed lunches from a delli for $74.50 each boxed lunch costs the same amount which equation represents the p

roportional relationship between y the total cost of the boxed lunches and x the number of boxed lunches

1 answer:

Snowcat [4.5K]3 years ago

4 0

I they each cost 6.21$ caz if u do 6.21 you get 74.53 but if you do 6.20 you get74.40 what ever u prefer

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

6 0

3 years ago

How do I find the vertex and the standard form? Plz explain

xenn [34]

Answer:

Vertex form

y = -4(x + 3)^2 + 10

Standard form;

y = -4x^2-24x - 26

Step-by-step explanation:

Mathematically, we have the vertex form as

y = a(x-h)^2 + k

(h,k) represents the vertex

We have h as -3 and k as 10

y = a(x+3)^2 + 10

To get a, we substitute any of the points

Let us use (-1,-6)

-6 = a(-1+3)^2 + 10

-6-10 = 4a

4a = -16

a = -16/4

a = -4

So we have the equation as;

y = -4(x+3)^2 + 10

For the standard form;

We expand the vertex form;

y = -4(x + 3)(x + 3) + 10

y = -4(x^2 + 6x + 9) + 10

y = -4x^2 - 24x -36 + 10

y = -4x^2 -24x -26

7 0

3 years ago

Which system is equivalent y=-2x^2 y=x-2

german

The wording of your question suggests that there were answer choices. Mind sharing them?

The system <span>y=-2x^2 y=x-2 would be best written as:

</span><span>y=-2x^2
y=x-2 If you subst. x-2 for y in the first equation, you'll get:
x-2 = -2x^2, or 2x^2 + x - 2 = 0.
</span>

7 0

3 years ago

Read 2 more answers

5000 people attend 1 movie each in one week. Regular show ticket is $9.50 and matinee tickets are $7. The total amount spent was

yuradex [85]

Answer:

1400

Step-by-step explanation:

Given: Cost of Regular ticket = $9.50

Cost of Matinee tickets= $7

Total number of people= 5000

Total spending in watching movie= $44000.

Lets assume total number of people attended matinee be "x".

∴ Number of people attended Regualr show= $(5000-x)$

We know, total cost= $Price\ of\ each\ ticket \times number\ of\ people$

Now, forming an equation to show total spending on tickets.

⇒ $\$ 9.50(5000-x)+ \$ 7x= \$ 44000$

Using distributive property of multiplication to multiply 9.50 with 5000 and -x.

⇒ $47500-9.50x+7x= 44000$

⇒ $47500-2.5x= 44000$

Adding both side by 2.5x

⇒ $47500 = 44000 + 2.5x$

subtracting both side by 44000

⇒ $3500= 2.5x$

Dividing both side by 2.5

⇒ $x= \frac{3500}{2.5}$

∴ $x= 1400$

Hence, number of people attended the matinee show are 1400.

7 0

3 years ago

Please help me im stuck

agasfer [191]

Multiply 3 by 2 and you get six I think

8 0

3 years ago