Solve these absolute value inequalities. 1<|2x +2|

Mathematics

1 answer:

inessss [21]3 years ago

8 0

1<|2x2|= 1<4

Nei valori assoluti non importa il segno che c'è davanti al numero, esso sarà sempre positivo, però qua non c'è neanche un meno perciò basta fare 2x2 (boh, non spiego bene)

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Caroline has a unique pet chimpanzee that is relatively likely to have twins. Each pregnancy is independent, and

mrs_skeptik [129]

Answer: 2=.36, 3=.48, 4=.16

Step-by-step explanation:

If we let "S" represent 1 baby and "D" represent 2 babies, the sample space for the chimpanzee's 2 pregnancies is {SS, SD, DS, DD}.

We can find the probability of each possible outcome by multiplying the probability of the independent events leading to that outcome.

Outcomes:. Probability:

SS. .60 x .60 = .36

SD. .60 x .40 = .24

DS. .40 x .60 = .24

DD. .40x .40 =.16

Total. 1.00

Lastly group the similar outcomes. SD+DS= .48

4 0

3 years ago

(1 point) Find the length traced out along the parametric curve x=cos(cos(4t))x=cos⁡(cos⁡(4t)), y=sin(cos(4t))y=sin⁡(cos⁡(4t)) a

Mazyrski [523]

The length of a curve $C$ given parametrically by $(x(t),y(t))$ over some domain $t\in[a,b]$ is

$\displaystyle\int_C\mathrm ds=\int_a^b\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt$

In this case,

$x(t)=\cos(\cos4t)\implies\dfrac{\mathrm dx}{\mathrm dt}=-\sin(\cos4t)(-\sin4t)(4)=4\sin4t\sin(\cos4t)$

$y(t)=\sin(\cos4t)\implies\dfrac{\mathrm dy}{\mathrm dt}=\cos(\cos4t)(-\sin4t)(4)=-4\sin4t\cos(\cos4t)$

So we have

$\displaystyle\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=16\sin^24t\sin^2(\cos4t)+16\sin^24t\cos^2(\cos4t)=16\sin^24t$

and the arc length is

$\displaystyle\int_0^1\sqrt{16\sin^24t}\,\mathrm dt=4\int_0^1|\sin4t|\,\mathrm dt$

We have

$\sin(4t)=0\implies4t=n\pi\implies t=\dfrac{n\pi}4$

where $n$ is any integer; this tells us $\sin(4t)\ge0$ on the interval $\left[0,\frac\pi4\right]$ and $\sin(4t)$ on $\left[\frac\pi4,1\right]$ . So the arc length is