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3 years ago

Please help / answer asap ! Is this correct and also what is the y-intercept ?

Mathematics

1 answer:

Vesna [10]3 years ago

8 0

Answer:

a. Slope (m): ⅓

b. y-intercept (b): 5

c. Equation: y = ⅓x + 5

Step-by-step explanation:

3a. Using two pairs from the table, say, (-3, 4) and (0, 5):

Slope = m = ∆y/∆x = (5 - 4)/(0 -(-3)) = 1/3

m = ⅓

b. y-intercept (b) is the value of y, when x = 0.

Thus, from the table, when x = 0, y = 5.

Therefore, y-intercept (b) = 5

c. Substitute m = ⅓, and b = 5 into y = mx + b

The equation is:

y = ⅓x + 5

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GaryK [48]

Answer:

x = 13

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3 years ago

A grasshopper jumps straight up from the ground with an initial vertical velocity of 8 feet per second. After how many seconds w

vlabodo [156]

Answer:

Problem 1 : After 0.25 s

Problem 2 : The squirrel doesn't reach the ground before the nut

Step-by-step explanation:

Problem 1

This is a standard physics problem

The equation that defines the movement of the grasshopper given the initial velocity, and the acceleration is the following

Distance = Do + Vo*t + 0.5*a*t^2

Where

Do is the initial distance.

(Do = 0, because the grasshopper is on the ground and we choose the reference system there)

Vo is the initial velocity = 8 feet/sec

a is the acceleration that is exerted on the body (in this case a = g = -9.8 m/s^2 = - 32.174 feet per second per second.)

t is the time

We substitute in the equation, and solve for t (time)

Distance = Do + Vo*t + 0.5*a*t^2

(1 foot)= (0)+ (8 feet/s)*t + 0.5*(-32.174 feet/s^2)*t^2

Solving this equation, we get that

t = 0.25 s

Problem 2

This problem is similar to the previous one

We apply the same formula

D = Do + Vo*t + 0.5*a*t^2

But in this case, we are going in the opposite direction, and we have an initial distance.

Do = 27 feet

Vo is the initial velocity of the nut = -6 feet/s

D = 0 (Ground)

We substitute in the equation, and solve for t (time)

(0) = (27) + (-6 feet/s)*t + 0.5*(-32 feet/s^2)*t^2

t = 1.125 s < 2s

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3 years ago

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Ede4ka [16]

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Start by simplifying the exponent.

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Artist 52 [7]

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salantis [7]

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3 years ago

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