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2 years ago

6

why is it that when you have a power to a power situation, why do you multiply the exponents ? create an example as part of your

explanation

1 answer:

loris [4]2 years ago

6 0

Step-by-step explanation:

For example, (2^4) is 2x2x2x2 or 16

(2^4)^3 Would be 16^3 or 2x2x2x2 3 times so 12 times in a row which is 4x3

Because exponents are for repeating multiplication they multiply when used together

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Démontrer que x²-4x+5=(x-2)²+1 ; En déduire que x²-4x+5=0 n'a pas de solution

iragen [17]

1st: toute valeur de x rend I'<span>équation vraie
tous les nombres r</span><span>éels

2nd: r</span><span>ésoudre l'équation pour x en trouvant a, b et c du quadratique puis en appliquant la formule quadratique
x = 2 ± i</span>

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3 years ago

If a silver alloy that costs $6.50 an ounce

bearhunter [10]

6.8 ounces would be used?

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3 years ago

On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or

almond37 [142]

Answer:

a) $\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$ , b) $\theta = \frac{\pi}{4}$ , c) $y_{max} = 84.375\,m$ , $t = 3.75\,s$ .

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

$\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j$

The particular expression for the cannonball is:

$\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$

b) The components of the position of the cannonball before hitting the ground is:

$x = (90\cdot \cos \theta)\cdot t$

$0 = 90\cdot \sin \theta - 6\cdot t$

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

$0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta} \right)$

$0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x$

$0 = 4050\cdot \sin 2\theta - 6\cdot x$

$6\cdot x = 4050\cdot \sin 2\theta$

$x = 675\cdot \sin 2\theta$

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

$\frac{dx}{d\theta} = 1350\cdot \cos 2\theta$

$1350\cdot \cos 2\theta = 0$

$\cos 2\theta = 0$

$2\theta = \frac{\pi}{2}$

$\theta = \frac{\pi}{4}$

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

$\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta$

$\frac{d^{2}x}{d\theta^{2}} = -2700$

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

$y = 45\cdot t - 6\cdot t^{2}$

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

$\frac{dy}{dt} = 45 - 12\cdot t$

$45-12\cdot t = 0$

$t = \frac{45}{12}$

$t = 3.75\,s$

Now, the second derivative is used to check if such solution leads to a maximum:

$\frac{d^{2}y}{dt^{2}} = -12$

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

$y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}$

$y_{max} = 84.375\,m$

7 0

3 years ago

a test for a certain drug has a 0.1% probability of producing a false positive. if a company hired 500 drug-free employees, what

Natasha_Volkova [10]

The probability of obtaining at least 1 false positive if the number of employees is 500 is 0.5

Probability

In the statistics concept, the probability refers the possible number of way of happening the particular event.

Given,

A test for a certain drug has a 0.1% probability of producing a false positive.

Here we need to find the probability of obtaining at least 1 false positive if a company hired 500 drug-free employees.

In the given question, we have the following values,

=> number of employees = 500

=> Probability of false positive = 0.1%

So, the probability of obtaining at least 1 false positive is calculated as,

=> 500 x 0.1/100

=> 5 x 0.1

=> 0.5

Therefore, the probability of obtaining at least 1 false positive is 0.5.

To know more about Probability here.

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6 0

1 year ago

Is this right ? Plz help mee

sasho [114]

6.32 is the final answer! :)

6 0

2 years ago

Read 2 more answers