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2 years ago

Adriana and Sophie have summer jobs selling newspaper subscriptions door-to-door, but their

Mathematics

1 answer:

IRISSAK [1]2 years ago

8 0

Answer:

The each have to place 2 subscriptions

Step-by-step explanation:

Adriana

E (earnings) = 6 + 2*x where x is the number of subscriptions

Sophie

E (earnings) = 4 + 3x

For them to earn the same amount, their right sides must be equated.

4 + 3x = 6 + 2x Subtract 2x from both sides

4 + 3x - 2x = 6+ 2x - 2x Combine

4 + x = 6 Subtract 4 from both sides

4 - 4 + x = 6 - 4

x = 2

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A company manufactures running shoes and basketball shoes. The total revenue (in thousands of dollars) from x1 units of running

Alborosie

Answer:

$x_1 =2 , x_2=7$

Step-by-step explanation:

Consider the revenue function given by $R(x_1,x_2) = -5x_1^2-8x_2^2 -2x_1x_2+34x_1+116x_2$ . We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).

$\frac{dR}{dx_1} = -10x_1-2x_2+34 =0$

$\frac{dR}{dx_2} = -16x_2-2x_1+116 =0$

From the first equation, we get, $x_2 = \frac{-10x_1+34}{2}$ .If we replace that in the second equation, we get

$-16\frac{-10x_1+34}{2} -2x_1+116=0= 80x_1-2x_1+116-272= 78x_1-156$

From where we get that $x_1 = \frac{156}{78}=2$ . If we replace that in the first equation, we get

$x_2 = \frac{-10\cdot 2 +34}{2}=\frac{14}{2} = 7$

So, the critical point is $(x_1,x_2) = (2,7)$ . We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that

$\frac{d^2R}{dx_1dx_2}= -2 = \frac{d^2R}{dx_2dx_1}$

$\frac{d^2R}{dx_{1}^2}=-10, \frac{d^2R}{dx_{2}^2}=-16$

We have the following matrix,

$\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right]$ .

Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is $(-10)\cdot (-16) - (-2)(-2) = 156>0$ and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum

8 0

3 years ago

Read 2 more answers

here is points my children <3 enjoy them just answer the question for the points: regards - drip king.

allochka39001 [22]

Answer:

thxs <3

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Need help quick please

Travka [436]

Answer:

line 2

Step-by-step explanation:

on line 2 the two minuses at the end turn into a + (where the -2 is there should be a +2) because - x - = +

4 0

3 years ago

The following is a rhombus, solve for x

lorasvet [3.4K]

Answer:

maybe since the rhombus is divided into triangles it'll be easier. x = 8

Step-by-step explanation:

the total degrees in a triangle would be 180 and the inner little angles would be 90 degrees so you would solve for (7x - 1) + (4x + 3) + 90 = 180 so 11x + 2 = 90 so 11x = 88 so x = 8

hope this helps!

7 0

3 years ago

How can you change the dimensions of the rectangle so that the ratio of the length to the width stays the same, but the perimete

Lady bird [3.3K]

Answer:

L = 62.5cm; B = 30cm

Step-by-step explanation:

P = 2 (L+W): L=25cm; W=12cm

=2 (25+12)

=50+24

P = 74cm

For a congruent rectangle with P = 185cm

A: 74 = 2 (25 + 12)

B: 185 = 2( ? + ?)

Since A/B are congruent;

185/75 = 2.5

B = 2 (2.5* (25 + 12)

= 2 ( 62.5 + 30)

= 125 + 60

= 185

Hence, B: L = 62.5cm; B = 30cm

185cm = 2 (62.5 + 30)

8 0

3 years ago