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Svetach [21]
3 years ago
5

The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by

a receiver 78 yards directly downfield at a height of 4 feet. The pass is released at an angle of 75 degrees with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.
Mathematics
1 answer:
motikmotik3 years ago
8 0

Answer:

t = 25.1seconds

Step-by-step explanation:

X(t)= 16cos75°t

Y(t)= 6 + (Vosin75°t - 16t^2)

Converting 78 yards to feet :

1 yard = 3 feet

78feet =?

78×3=234 feet

Y(t)= number of feet above the ground at t seconds

VoCos75° t = 234

t = 234/(VoCos75°)

At this time,4 = y(234/VoCos75°)

4 = 6 + VoSin75°(234/VoCos75) - 16(234/VoCos75°)^2

Vo= 140.66ft/s

Time,t= 234/(140.66× Cos75°)

t = 25.087seconds

t= 25.1 seconds (1 decimal place)

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QUESTION 1
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Answer:

1)

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

2)

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

Step-by-step explanation:

Question 1)

The given inequality is:

\frac{5}{12}-\frac{x-3}{6} \leq  \frac{x-2}{3}

<u>Step 1: Making the denominators common for all fractions</u>

\frac{5}{12}-\frac{2}{2} \times \frac{x-3}{6} \leq \frac{4}{4} \times \frac{x-2}{3}

This step is done correctly in the given solution.

<u>Step 2: Simplifying </u>

\frac{5}{12}-\frac{2x-6}{12}\leq \frac{4x-8}{12}

This step is done correctly in the given solution

<u>Step 3: Multiplying both sides by 12, and simplifying.</u>

5-(2x-6)\leq 4x-8\\\\ 5-2x+6\leq 4x-8

First error is made in this step. While opening the brackets, the negative sign should be distributed inside the bracket, which will change the signs.

<u>Step 4: Simplification:</u>

11-2x\leq 4x-8

<u>Step 5: Moving Common terms to one side and simplifying</u>

-2x-4x\leq -8-11\\\\ -6x\leq -19

Error was made in this step. When a number is moved to other side, its sign will be changed.

<u>Step 6: Dividing both sides by -6</u>

x\geq \frac{19}{6}

Conclusion:

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

Question 2:

In the Equation 2: 12=-4(-6x-3), when -4 will be multiplied inside the brackets, the 12 on eft hand side will cancel the 12 that will appear on right hand side, giving a result that will lead to x = 0.

Same is the case with Equation 6: x+5=-5x+5, 5 on both sides will cancel out leaving x = 0.

So, 2nd and 6th equations will have the same solution.

In Equation 1, on expanding the bracket and moving 7 to other side, we get a relation: 4x = 16

In Equation 3, on simplifying the right hand side, and carrying common terms to one side, we get the relation: - 9x = -36

In Equation 5, on expanding the bracket and simplifying the relation is reduced to 4 = x

It can be observed that all these 3 equations have the same solution i.e. x = 4

So, the following set of Equations have the same solution:

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

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3 years ago
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Answer:

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Step-by-step explanation:

green marbles = 9r

red marbles = r

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10r = 40

r = 4 = red marbles

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Answer:(350+12x)/x

Step-by-step explanation:

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Then, divide that by the number of hours worked in a week (x).

Then, set it equal to 22 (the average hours worked).

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Answer:

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Step-by-step explanation:

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