Can you help me on this question -1+3(x+2)=5(1+8x)

[[-2,10],[0,4],[4,-8],[6,-14],[9,-23]]

BARSIC [14]

Answer:

- 24

Step-by-step explanation:

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3 0

3 years ago

The graphs of g(x) = x³- ax² + 6 and h(x) = 2x² + bx + 3 touch when x = 1. Therefore, the tangent to

Olegator [25]

Answer:

$(1,\, 10)$ .

Step-by-step explanation:

Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to $x$ . Make use of the power rule to find the following:

$g^\prime(x) = 3\, x^2 - 2\, a\, x$ .

$h^\prime(x) = 2\, (2\, x) + b = 4\, x + b$ .

The question states that the graphs of $g(x)$ and $h(x)$ touch at $x = 1$ , such that $g^\prime(1) = h^\prime(1)$ . Therefore:

$3 - 2\, a = 4 + b$ .

On the other hand, since the graph of $g(x)$ and $h(x)$ coincide at $x = 1$ , $g(1) = h(1)$ (otherwise, the two graphs would not even touch at that point.) Therefore:

$1 - a + 6 = 2 + b + 3$ .

Solve this system of two equations for $a$ and $b$ :

$\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}$ .

Therefore, $a = -3$ whereas $b = 5$ .

Substitute these two values back into the expression for $g(x)$ and $h(x)$ :

$g(x) = x^3 + 3\, x^2 + 6$ .

$h(x) = 2\, x^2 + 5\, x + 3$ .

Evaluate either expression at $x = 1$ to find the $y$ -coordinate of the intersection. For example, $g(1) = 1 + 3 + 6 = 10$ . Similarly, $h(1) = 2 + 5 + 3 = 10$ .

Therefore, the intersection of these two graphs would be at $(1,\, 10)$ .

6 0

3 years ago

Find the general term of sequence defined by these conditions.

disa [49]

Answer:

$\displaystyle a_{n} = (2)^{2n -1} - (3) ^{n-1 }$

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

$\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0 \: \: where : \: \:a_1 = 1 \: ,a_2 = 5,$

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

${x}^{n} = c_{1} {x}^{n - 1} + c_{2} {x}^{n - 2} + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}$

the steps for solving a linear homogeneous recurrence relation are as follows:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

${x}^{2} - 7x+ 12= 0$