Solve 12y^-4z^-2/6z^2y^-1

Which shows all the critical points for the inequality x2-4/x2-5x+6<0

Hoochie [10]

Answer:

x = ±2, 3 are the critical points of the given inequality.

Step-by-step explanation:

The given inequality is $\frac{(x^{2}- 4)}{x^{2}-5x+6}$

To find the critical points we will equate the numerator and denominator of the inequality to zero.

For numerator,

$x^{2}-4=0$

(x - 2)(x + 2) = 0

x = ±2

For denominator,

x² - 5x + 6 = 0

x² - 3x -2x + 6 = 0

x(x - 3) -2(x - 3) = 0

(x - 3)(x - 2) = 0

x = 2, 3

Therefore, critical points of the inequality are x = ±2, 3 where the sign of the inequality will change.

7 0

3 years ago

Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec

julia-pushkina [17]

Answer:

$(2,6,6) \not \in \text{Span}(u,v)$

$(-9,-2,5)\in \text{Span}(u,v)$

Step-by-step explanation:

Let $b=(b_1,b_2,b_3) \in \mathbb{R}^3$ . We have that $b\in \text{Span}\{u,v\}$ if and only if we can find scalars $\alpha,\beta \in \mathbb{R}$ such that $\alpha u + \beta v = b$ . This can be translated to the following equations:

1. $-\alpha + 3 \beta = b_1$

2. $2\alpha+4 \beta = b_2$

3. $3 \alpha +2 \beta = b_3$

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for $\alpha,\beta$ and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

$-\alpha + 3 \beta = 2$

$2\alpha+4 \beta = 6$

whose unique solutions are $\alpha =1 = \beta$ , but note that for this values, the third equation doesn't hold (3+2 = 5 $\neq$ 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

$-\alpha + 3 \beta = -9$

$2\alpha+4 \beta = -2$

whose unique solutions are $\alpha=3, \beta=-2$ . Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

4 0

2 years ago

A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius o

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

r - radius

H - height

We have r = 1cm and H = 21cm. Substitute:

$V=\pi(1^2)(21)=21\pi\ cm^3$

The formula of a cone:

$V=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have V = 21π cm³ and H = 7cm. Substitute:

$\dfrac{1}{3}\pi(r^2)(7)=21\pi$ <em>divide both sides by π</em>

$\dfrac{1}{3}(7)(r^2)=21$ <em>divide both sides by 7</em>

$\dfrac{1}{3}r^2=3$ <em>multiply both sides by 3</em>

$r^2=9\to r=\sqrt9\\\\r=3\ cm$

5 0

3 years ago

Read 2 more answers

Avery has 2 blue marbles. one sixth of avery's marbles are blue. how many marbles does avery have mama 2 6 8 12

kodGreya [7K]

I don't understand Can you type it again?

5 0

3 years ago

A biologist has been observing a tree's height. This type of tree typically grows by 0.22 feet each month. Fifteen months into t

Lyrx [107]

Data:

x: number of months

y: tree's height

Tipical grow: 0.22

Fifteen months into the observation, the tree was 20.5 feet tall: x=15 y=20.5ft (15,20.5)

In this case the slope (m) or rate of change is the tipical grow.

m=0.22

To find the line's slope-intercep equation you use the slope (m) and the given values of x and y (15 , 20.5) in the next formula to find the y-intercept (b):

$\begin{gathered} y=mx+b \\ 20.5=0.22(15)+b \\ 20.5=3.3+b \\ 20.5-3.3=b \\ 17.2=b \end{gathered}$

Use the slope(m) and y-intercept (b) to write the equation:

$\begin{gathered} y=mx+b \\ \\ y=0.22x+17.2 \end{gathered}$ A) This line's slope-intercept equation is: y=0.22x+17.2

B) To find the height of the tree after 29 months you substitute in the equation the x for 29 and evaluate to find the y:

$\begin{gathered} y=0.22(29)+17.2 \\ y=6.38+17.2 \\ \\ y=23.58 \end{gathered}$ Then, after 29 months the tree would be 23.58 feet in height

C) In this case as you have the height and need to find the number of moths you substitute the y for 29.96feet and solve the equation for x, as follow:

$\begin{gathered} 29.96=0.22x+17.2 \\ 29.96-17.2=0.22x \\ 12.76=0.22x \\ \frac{12.76}{0.22}=x \\ \\ 58=x \end{gathered}$ Then, after 58 months the tree would be 29.96feet tall

3 0

1 year ago