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2 years ago

Three Texas drovers met on a highway and began to dicker as follows:

Mathematics

1 answer:

Alik [6]2 years ago

5 0

Answer:

Jim's: 7
Duke's: 21
Hank's: 11

Step-by-step explanation:

Let J, D, and H represent the drove sizes of Jim, Duke, and Hank.

2(H -6 + 1) = (J +6 -1) . . . . . Hank's offer

3(D -14 +1) = (H +14 -1) . . . . Duke's offer

6(J -4 +1) = (D +4 -1) . . . . . . Jim's offer

These equations can be simplified to ...

2H - J = 15

3D - H = 52

6J - D = 21

Solution

Adding twice the second equation to the first gives ...

2(3D -H) +(2H -J) = 2(52) +(15)

6D -J = 119

Adding 6 times the third equation to this one gives ...

6(6J -D) +(6D -J) = 6(21) +(119)

35J = 245

J = 7

Using this value in the third equation gives ...

6(7) -D = 21

42 -21 = D = 21

Using the value of J in the first equation gives ...

2H -7 = 15

H = (15 +7)/2 = 11

Then the solution is (J, D, H) = (7, 21, 11).

Jim's drove had 7 animals; Duke's drove had 21 animals; Hank's drove had 11 animals.

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Dada la sucesión an = 1700 + 4,1· n2 + 304,9· n

shutvik [7]

Concluimos que la opción correcta es "Solo II".

Una expresión es una sucesión aritmética si y solo si existe entre dos elementos consecutivos cualesquiera de la serie la misma diferencia. La sucesión aritmética es definida por una expresión de la forma:

$a_{n} = a + b\cdot n$ , $n\in \mathbb{N}$ (1)

Donde $a,b$ son coeficientes de la sucesión.

Asimismo, una expresión es una sucesión geométrica si y solo si entre dos elementos consecutivos cualesquiera de la serie existe la misma razón. La sucesión geométrica es definida por una expresión de la forma:

$a_{n} = a\cdot r^{b\cdot n}$ , $n\in \mathbb{N}$ (2)

Donde $a, b, r$ son coeficientes de la sucesión.

Por último, una expresión es una sucesión monótona creciente si dados dos elementos consecutivos de una serie, el elemento posterior es siempre mayor que el elemento anterior. Matemáticamente, debe satisfacerse la siguiente condición:

$\frac{a_{n+1}}{a_{n}} > 1, n\in \mathbb{N}$ (3)

Esta claro por inspección directa que la sucesión dada no es aritmética ni geométrica y cabe comprobar si es monótona creciente. Valiéndonos de (3), realizamos las operaciones algebraicas pertinentes:

$r = \frac{1700 + 4,1\cdot (n+1)^{2}+304,9\cdot (n+1)}{1700 + 4,1\cdot n^{2}+304,9\cdot n}$

$r = \frac{1700+4,1\cdot (n^{2}+2\cdot n +1) +304,9\cdot (n+1)}{1700 + 4.1\cdot n^{2}+304,9\cdot n}$

$r = \frac{1700+4,1\cdot n^{2}+304,9\cdot n+4,1\dot (2\cdot n +1) +304.9}{1700+4,1\cdot n^{2}+304,9\cdot n}$

$r = 1 + \frac{8,2\cdot n +309}{1700 + 4,1\cdot n^{2}+304,9\cdot n}$

Como puede apreciarse, $r > 1$ . Por tanto, la sucesión es monótona y creciente.

En consecuencia, concluimos que la opción correcta es "Solo II".

Invitamos cordialmente a leer esta pregunta sobre sucesiones: brainly.com/question/21709418

4 0

3 years ago

Jernel has to figure out the area of her square garage. she knows that one side of the garage is equal to the length of her rabb

Readme [11.4K]

Answer: 100 square units.

Step-by-step explanation:

Given: Jernel has to figure out the area of her square garage.

She knows that one side of the garage is equal to the length of her rabbit pen.

Now, the length of the rabbit pen = 10 units

Then , the length of the garage will be 10 units

Now, Area of square = $\text{(side)}^2=10^2=100\text{units}^2$

Hence, the area of the garage = 100 square units.

4 0

3 years ago

How much interest will she earn in 3 years?

alekssr [168]

For this, the equation is
90× 1.13³=y
X was replaced with y. Since she is gaining, you have to remember she is going to have 100 percent of what he had before, she will not lose any.
90× 1.13= 129.86
Now, we need to find the amount of interest she gained, so we have to subtract 90 from the total.
129.86-90=39.86
We can also find the answer by completing a small chart.
The first column will be the year. The second will be the amount. The third will be the interest for the year.
1 90 11.7
2 101.7 13.22
3 114.92 14.94
The total would round to 39.86, so her interest for the 3 year would be 39.86, with her having 129.86 altogether.

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3 years ago

Read 2 more answers

Find the value of k so that the

BaLLatris [955]

Answer:

$gradient = - 3 \\ - 3 = \frac{(8 + 1)}{( - 2 - k)} \\ 3(2 + k) = 9 \\ 2 + k = 3 \\ k = 1$