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3 years ago

Frank is 8 years oldern than his sister. In 3 yrs he will be twice as old as she is. How old are they now?

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

8 0

Answer:

He is 13 & she is 5.

Step-by-step explanation:

In 3 years, he will be 16 & she will be 8.

This will make him twice her age.

In other words, 8+8=16 or you can use the equation 16÷2=8

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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

The following table represents a proportional relation. Find the missing values:

SCORPION-xisa [38]

Answer:16288.xy

Step-by-step explanation:

7 0

3 years ago

20 POINTS! Please help, best answer will recessive brainliest answer points as well as 5 stars and a thank you. :)

Kaylis [27]

Answer:

Step-by-step explanation:

Diagonals of a rhombus are perpendicular bisector.

Hence, triangle ABE so formed would be a right triangle right angled at E.

Therefore, by Pythagoras theorem:

$AB = \sqrt{AE^2 + BE^2 } \\ \\ \therefore \: AB = \sqrt{5^2 + 12^2 } \\ \\ = \sqrt{25 + 144} \\ \\ = \sqrt{169} \\ \huge \red { \boxed{ \therefore \: AB= 13}}$

8 0

3 years ago

William works at a nearby electronics store. He makes a commission of 6% on everything he sells. If he sells a computer for$764.

Sedaia [141]

Commission=0.06×764=$45.84

7 0

3 years ago

Helpppppppppppppppppp

makvit [3.9K]

Answer:

c. 25

Step-by-step explanation:

100/12 = 8.3

8.3 × 3 = 24.9

rounded up is 25

6 0

3 years ago