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3 years ago

Simplify 2[3-5(2+1)2+5] the last 2 is 2nd

Mathematics

2 answers:

mash [69]3 years ago

8 0

Answer:

-44 im pretty sure

Elena L [17]3 years ago

6 0

Answer:

uydfg

Step-by-step explanation:

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Four less than the square of a number is 0

marusya05 [52]

Answer:

± 2

Step-by-step explanation:

let the number be n , then

n² - 4 = 0 ( add 4 to both sides )

n² = 4 ( take square root of both sides )

n = ± $\sqrt{4}$ = ± 2

The number is - 2 or 2

5 0

3 years ago

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Help please question in the picture

cluponka [151]

Answer:

17.5

Step-by-step explanation:

The area of a triangle is (height*base)divided by two

(the eight is really unnecessary)

so 7=base

8=height

7*5=35

35/2=17.5

8 0

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

What expression is equivalent to x^2-10x+24

alexdok [17]

Answer:

(x-6)(x-4)

x=-6 , x=4

Step-by-step explanation:

5 0

3 years ago

*****BRAINLIEST AVAILABLE********

sweet-ann [11.9K]

Answer: C, D

Explanation:

Length: L = x + 3

width: x ≥ y + 2 ⇒ y ≤ x - 2

wheels: y

0.50(L * x) + 4(2.25y) ≤ 50

0.50(x + 3)(x) + 4(2.25y) ≤ 50

0.50(x² + 3x) + 9y ≤ 50

9y ≤ 50 - 0.50(x² + 3x)

9y ≤ 50 - 0.50x² - 1.5x

÷9 ÷9

y ≤ $\frac{50}{9}-\frac{1}{6}x-\frac{1}{18}x^{2}$

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15 per person is the rate

22 is the constant

y = 15x + 22

divide that by the number of people (x) to get:

y = $\frac{15x + 22}{x}$

8 0

4 years ago

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