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2 years ago

Which linear equation represents on the graph

Mathematics

1 answer:

s2008m [1.1K]2 years ago

4 0

Remember, rise/run is the easiest way to determine slope

y=mx+b is form

mx is slope, whilst b is y int

so, answer? y=-3x-2

Or A.

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Salmon often jump waterfalls to reach their breeding grounds. One salmon starts 2.00m from a waterfall that is 0.55m tall and ju

Law Incorporation [45]

Answer: 6.2 m/s

Explanation:

1) This is a projectile motion (parabolic)

2) Velocity:

i) initial velocity = V₀

ii) Horizontal component:

V₀x = V₀ cos α

The horizontal velocity is constant, so Vx = V₀x

ii) Vertical component:

V₀y = V₀ sin α

The vertical component is linear with acceleration = g ≈ 9.8 m/s²

Vy = V₀y - gt = V₀ sin α - gt

3) Displacement equations

i) Horizontal displacment:

x = V₀ cosα t

ii) Vertical displacement:

y = V₀ sin α t - g t² / 2

y ≈ V₀ sin α t - 4.9 t²

4) Solution

i) x = V₀ cosα t = V₀ cos(32°) t = 2.00 m ← salmon starts 2.00m from a waterfall

⇒ V₀ = 2 / [cos(32°) t ]

ii) y = V₀ sin α t - 4.9 t² = V₀ sin(32°) t - 4.9 t²

iii) Replace V₀ with 2 / [cos(32°) t ]

y = sin(32°) × 2 / [cos(32°) t ] × t - 4.9t² = 2 tan(32°) - 4.9t²

iv) Use jump's height (y = 0.55m) and solve

⇒ 0.55 = 2 tan(32°) - 4.9t²

t² = [2 tan(32°) - 0.55 ] / 4.9 = 0.143 s²

⇒ t = √ (0.143s²) = 0.38 s

v) Use V₀ = 2 / [cos(32°) t ] to find V₀

V₀ = 2 / [cos(32°) (0.38) ] = 6.2 m/s

8 0

1 year ago

Read 2 more answers

Consider the following expression -2m(m+n-4)+5(-2m+2n)+n(m+4n-5) which of the following is an equivalent expression

velikii [3]

The answer is:

-2m²+4n²-mn-2m+5n

aka letter c in algebra nation

3 0

2 years ago

The product of three integers is −5. Determine all of the possible values for the three factors.

tensa zangetsu [6.8K]

-1,1,5
-1,-1,-5
1,1,-5

6 0

2 years ago

Three highways connect city A with city B. Two highways connect city B with city C.

QveST [7]

(a) The probability that there is no open route from A to B is (0.2)^3 = 0.008.
Therefore the probability that at least one route is open from A to B is given by: 1 - 0.008 = 0.992.
The probability that there is no open route from B to C is (0.2)^2 = 0.04.
Therefore the probability that at least one route is open from B to C is given by:
1 - 0.04 = 0.96.
The probability that at least one route is open from A to C is:
$0.992\times0.96=0.9523$

(b)
α The probability that at least one route is open from A to B would become 0.9984. The probability in (a) will become: $0.9984\times0.96=0.95846$

β The probability that at least one route is open from B to C would become 0.992. The probability in (a) will become:
$0.992\times0.992=0.9841$

Gamma: The probability that a highway between A and C will not be blocked in rush hour is 0.8. We need to find the probability that there is at least one route open from A to C using either a route A to B to C, or the route A to C direct. This is found by using the formula:
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$0.9523+0.8-(0.9523\times0.8)=0.99$
Therefore building a highway direct from A to C gives the highest probability that there is at least one route open from A to C.

4 0

2 years ago

The histogram shows the number of vacation days taken by employees in the past year. Based on the histogram, which statement is

Serhud [2]

The correct answer is b

8 0

1 year ago