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3 years ago

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Kathi starts with a number . She adds 3 to her number, then doubles the result. Finally , she subtracts 7. If she ended with 9,

what number did she start with ?

2 answers:

miss Akunina [59]3 years ago

8 0

The number she started with is 5.

nikklg [1K]3 years ago

5 0

Answer: The required number is 5.

Step-by-step explanation: Given that Kathi starts with a number, she adds 3 to her number and then doubles the result. Finally , she subtracts 7 and she ended with 9.

We are to find the number.

Let n represents the required number.

Then, according to the given information, we have

$2\times(n+3)-7=9\\\\\Rightarrow 2(n+3)=9+7\\\\\Rightarrow 2(n+3)=16\\\\\Rightarrow n+3=\dfrac{16}{2}\\\\\Rightarrow n+3=8\\\\\Rightarrow n=8-3\\\\\Rightarrow n=5.$

Thus, the required number is 5.

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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

triangle abc is reflected over the line y=x . triangle abc has points a (10,2) , b (9,5) and c (6,4) . what is the c' coordinate

Ghella [55]

The coordinates of C are 4,6 because thats the rule for y=x

7 0

3 years ago

Read 2 more answers

Maggie drew triangle and then triangle . Triangle is congruent to triangle only if ∠ is equal to what value?

Phantasy [73]

Answer:

Angle ABE = 58

Step-by-step explanation:

This would fulfill the AAA theorem, or 3 angles needing to be congruent. We got 58 by subtracting 89 and 62 from 180, then multiplying that answer by 2 (because it occupies both triangles).

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3 years ago

It takes one week for a crew of workers to pave 3/5 kilometer of a road. At that rate, how long will it take to pave 1 kilometer

Flauer [41]

Answer:

1.67 weeks

Step-by-step explanation:

Let X= time it will take to pave 1 kilometer?

1 week=3/5 kilometer

X week =1 kilometer

Cross multiply

3/5 X= 1

3X= 5

X= 5/3

1.67 weeks

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3 years ago

PLEASE ANSWER!!!!WILL MARK BRAINLIEST!!!

Setler79 [48]

Hope this is helpful

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3 years ago