Mathematics, 29.07.2020 06:01 zayeboyd4971

A ball is thrown straight down from the top of a 435-foot building with an initial velocity of -27 feet per second. Use the position function below for free-falling objects. s(t) = -16t^2 + v_0t + s_0 What is its velocity after 2 seconds? v(2) = -91 ft/s What is its velocity after falling 364 feet? v = 1.61 ft/s Find an equation of the parabola y = ax^2 + bx + c that passes through (0, 1) and is tangent to the line y = 5x - 5 at (1, 0). Y = 5x + 10

Answers: 3

Show answers

Answers

a) The velocity of the ball after 2 seconds is -91 feet per second, b) The velocity of the ball after falling 364 feet is 155 feet per second, c) The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is $y = 6\cdot x^{2}-7\cdot x +1$ .

Step-by-step explanation:

a) The velocity function is obtained after deriving the position function in time:

$v (t) = -32\cdot t -27$

The velocity of the ball after 2 seconds is:

$v(2\,s) = -32\cdot (2\,s) -27$

$v(2\,s) = -91\,\frac{ft}{s}$

The velocity of the ball after 2 seconds is -91 feet per second.

b) The time of the ball after falling 364 feet is found after solving the position function as follows:

$435\,ft - 364\,ft = -16\cdot t^{2}-27\cdot t + 435\,ft$

$-16\cdot t^{2} - 27\cdot t + 364 = 0$

The solution of this second-grade polynomial is represented by two roots:

$t_{1} = 4\,s$ and $t_{2} = -5.688\,s$ .

Only the first root is physically reasonable since time is a positive variable. Now, the velocity of the ball after falling 364 feet is:

$v(4\,s) = -32\cdot (4\,s) - 27$

$v(4\,s) = -155\,\frac{ft}{s}$

The velocity of the ball after falling 364 feet is 155 feet per second.

c) Let consider the equation for a second order polynomial that passes through (0, 1) and its first derivative that passes through (1, 0) and represents the give equation of the tangent line. That is to say:

Second-order polynomial evaluated at (0, 1)

c = 1

Slope of the tangent line evaluated at (1, 0)

$5 = 2\cdot a \cdot (1) + b$

$2\cdot a + b = 5$

$b = 5 - 2\cdot a$

Now, let evaluate the second order polynomial at (1, 0):

$0 = a\cdot (1)^{2}+b\cdot (1) + c$

a + b + c = 0

If c = 1 and $b = 5 - 2\cdot a$ , then:

$a + (5-2\cdot a) +1 = 0$

-a +6 = 0

a = 6

And the value of b is: ( a = 6 )

$b = 5 - 2\cdot (6)$

b = -7

The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is $y = 6\cdot x^{2}-7\cdot x +1$ .

Answer from: Quest

add an image

step-by-step explanation:

Answer from: Quest

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

Another question on Mathematics

Mathematics, 21.06.2019 23:00

John has 1/2 pound of oranges to share with julie. if they share the oranges equally, how much will each of them have?

Answers: 1

Answer

Mathematics, 22.06.2019 01:30

The relative growth rate for a certain type of fungi is 60% per hour.a small culture has formed and in just 6 hours the count shows to be 20,273 fungi in the culture.what is the initial number of fungi in the culture?

Answers: 2

Answer

Mathematics, 22.06.2019 03:30

The monthly texting plan of all star cell is $11 per month and $0.25 per text. the monthly texting plan of top line cell is $14 per month and $0.15 per text. a student wants to set up a system of equations to find the number of texts for which the total monthly cost of the two companies is the same. he uses the variables x and y. he lets y represent the total monthly cost. what will x represent? x = number of texts x = cost of the total number of texts x = total monthly cost x = cost of each text

Answers: 1

Answer

Mathematics, 22.06.2019 04:00

Which of these lines passes through the point (1,-1) and has a slope of -3?

Answers: 1

Answer

You know the right answer?

A ball is thrown straight down from the top of a 435-foot building with an initial velocity of -27 f...

Questions