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Pavlova-9 [17]
3 years ago
15

A dart is thrown upward with an initial velocity of 66 ft/s at an angle of elevation of 54°. Consider the position of the dart a

t any time t. Neglect air resistance. (Assume t is in seconds.) Find parametric equations that model the problem situation.
Mathematics
1 answer:
givi [52]3 years ago
4 0

Answer:

Answer to the question:

Step-by-step explanation:

α= 54º

V= 66 ft/s

g= 9.8 m/s²

Vx= V * cos(54º) = 38.8 ft/s

Vy= V * sin(54º) = 53.4 ft/s

<u>PARAMETRIC EQUATIONS:</u>

x(t)= Vx * t

y(t)= Vy * t - (g * t²)/2

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*In ∆ABC, on the extension of the side BC , draw a line segment CD ≅ CA . Draw the segment AD . The line segment CE is the angle
Leya [2.2K]

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Step-by-step explanation:

In ∆ABC

  • On the extension of the side BC , draw a line segment CD ≅ CA
  • Draw the segment AD
  • The line segment CE is the angle bisector of ∠ACB
  • The line segment CF is the median towards AD in ∆ ACD

We want to prove that CF ⊥ CE

Look to the attached figure

In Δ ABC

∵ CE is the bisector of angle ACB

∴ ∠ACE ≅ ∠BCE

In Δ ACD

∵ CA = CD

∴ Δ ACD is an isosceles triangle

∵ AD is the median towards AD

- In any isosceles triangle the median from a vertex to its opposite

  side bisects this vertex

∴ AD bisects ∠ACD

∴ ∠ACF ≅ ∠DCF

∵ BCD is a straight segment

∵ CE , CA , CF are drawn from point C

∴ m∠BCE + m∠ACE + m∠ACF + m∠DCF = 180°

∵ m∠ACE ≅ m∠BCE

∵ m∠ACF ≅ m∠DCF

- Replace m∠BCE by m∠ACE and m∠DCF by m∠ACF

∴ m∠ACE + m∠ACE + m∠ACF + m∠ACF = 180°

∴ 2 m∠ACE + 2 m∠ACF = 180°

- Divide all terms by 2

∴ m∠ACE + m∠ACF = 90°

∴ EC ⊥ CF

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Learn more:

You can learn more about perpendicular lines in brainly.com/question/11223427

#LearnwithBrainly

7 0
3 years ago
Tell how to multiply two fractions give an example
mario62 [17]
Ex 1:
2/5 x 4/5
Multiply both the numerators together and then multiply both the denominators together. You would multiply 2x4 which is 8 and 5x5 which is 25. Which leaves you with 8/25 and it will stay that way because you cannot simplify it further.

Ex 2:
2/5 and 5/3
Multiply across 2x5/5x3 and you end up with 10/15 which can be simplified/reduced to 2/3 because they share a common factor of 5.
7 0
3 years ago
Tyler sells 20 of his records (r) and has 74 left. Which equation best<br> represents this scenario?
Anna71 [15]

Answer:

Equation: r-20=74

Step-by-step explanation:

So he started with 94. I got B

6 0
2 years ago
HELPP PLEASE GIVE EVIDENCE
ELEN [110]

Step-by-step explanation:

The value of k in the equation g(x) = f(x) + k comes out to be 8.

How the vertical shifting of a graph takes place?

If the graph of a function f(x) is shifted vertically by k units, f(x) becomes f(x)+k.

From the diagram, we can say that graph of f(x) has been shifted vertically by 8 units

If we shift f(x) vertically by 8 units f(x) becomes f(x)+8 and also coincides with the graph of g(x).

So, g(x) = f(x) + 8........(1)

Comparing (1) and g(x) = f(x) + k, we get k=8.

Hence, the value of k in the equation g(x) = f(x) + k comes out to be 8.

7 0
2 years ago
Read 2 more answers
Let m = 4 and n = 5
finlep [7]

the answer is c because 4(4)+4(5)=36 and 2(4)^2=16 that 36-16=20 and mn (4*5)=20 so that gives you answer c

 

4 0
3 years ago
Read 2 more answers
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