How do i do #3? I dont know how to do the whole problem.

The position of an object along a vertical line is given by s(t) = −t3 + 3t2 + 7t + 4, where s is measured in feet and t is meas

saw5 [17]

Answer:

The maximum velocity of the object in the time interval [0, 4] is 10 ft/s.

Step-by-step explanation:

Given : The position of an object along a vertical line is given by $s(t) = -t^3+3t^2+7t +4$ , where s is measured in feet and t is measured in seconds.

To find : What is the maximum velocity of the object in the time interval [0, 4]?

Solution :

The velocity is rate of change of distance w.r.t time.

Distance in terms of t is given by,

$s(t) = -t^3+3t^2+7t +4$

Derivate w.r.t. time,

$v(t)=s'(t) = -3t^2+6t+7$

It is a quadratic function so its maximum is at vertex of the function.

The x point of the function is given by,

$x=-\frac{b}{2a}$

Where, a=-3, b=6 and c=7

$t=-\frac{6}{2(-3)}$

$t=-\frac{6}{-6}$

$t=1$

As 1 lie between interval [0,4]

Substitute t=1 in the function,

$v(t)= -3(1)^2+6(1)+7$

$v(t)= -3+6+7$

$v(1)=10$

Th maximum velocity is 10 ft/s.

Therefore, the maximum velocity of the object in the time interval [0, 4] is 10 ft/s.

8 0

3 years ago

Read 2 more answers

3х - 30 = у 7y - 6 = 3х

mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3x – 30 = y and the second is 7y – 6 = 3x

As I look, I see 3 ways to use substitution to solve this:

substitute 7y – 6 for 3x
substitute 3x – 30 for y
solve 3x – 30 = y for 3x and make it equal to 7y – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

Method 1:

3x – 30 = y

7y – 6 = 3x — initial system of equations

7y – 6 – 30 = y — substitute 7y – 6 for 3x

7y – 6 – 30 = y — marking like terms, bold for constants, underlined for variables

7y – 36 = y — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract y from both sides, divide by 6 OR subtract 7y from both sides and divide by –6 . For the sake of time, I'm subtracting 7y, though I don't like dealing with negatives.

7y – 7y – 36 = y – 7y — subtract 7y from both sides

–36 = –6y — simplify

–36 ÷ –6 = –6y ÷ –6 — divide by –6 on both sides

y = 6 — simplify

Again, we can diverge here: substitute y into 3x – 30 = y or substitute y into 7y – 6 = 3x

I'm going to choose 3x – 30 = y but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3x – 30 = y — initial equation

3x – 30 = 6 — substitute 6 for y

3x – 30 + 30 = 6 + 30 — add 30 to both sides to isolate 3x

3x = 36 — simplify the expression

3x ÷ 3 = 36 ÷ 3 — divide both sides by 3 to isolate x

x = 12 — simplify

So, we have x = 12 and y = 6 . We know they work for 3x – 30 = y but not if they work for 7y – 6 = 3x . Let's substitute those in to see if (12, 6) really is the solution point.

7y – 6 = 3x — original equation

7(6) – 6 ≟ 3(12) — substitute 6 for y and 12 for x

42 – 6 ≟ 36 — simplify by multiplying

36 = 36 ✔ — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0

3 years ago

A minor arc has a measure greater than 180° t or f

worty [1.4K]

the answer is true while a major arc reaches out past 180 and up to 360

8 0

3 years ago

Rational numbers that are not integers are?

Vladimir [108]

Any number that can be writen as a fraction example: 0.75, -15, 0, 9

6 0

3 years ago

Point (k, -3) lies on the line whose equation is x-2y=-2. What is the value of k?

natita [175]

Answer:

Substitute, y = -3 and x = k on the equation.

=> k - 2×(-3) = -2

=> k = -2 + (-6)

=> k = - 8

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<h2>HOPE U UNDERSTOOD</h2><h3>MARK AS BRAINLIEST ONE</h3>

Any Doubts? Please COMMENT

7 0

2 years ago