The owner of an automotive shop devotes 90% of his workweek to supervising, sales and accounting tasks. In one week, the owner spent 36 hours of his workweek on supervising, sales and accounting tasks. How many hours did he work that week? Group of answer choices

Answer:

I hope this helps.

Step-by-step explanation:

h(t) = -16t2 + 108t + 28

(a)

Maximum height occurs at the vertex of the height-vs.-time parabola, which is at

t = -108/[2(-16)] sec = ? sec

Evaluate h(t) at this value of t to get hmax.

(b)

Set h(t) = 0 and solve the quadratic equation for t.  You will get a positive and a negative solution.  Discard the negative solution, since time starts at t = 0.

The quadratic function, h = -16t + 136t + 72, gives us:

a) The maximum height of the ball is 360 feet.

b) The time taken by the ball to hit the ground is 9 seconds.

A quadratic function is a function over a quadratic expression, that is, over an expression having degree 2.

In the question, we are informed that a person standing close to the edge of a 72-foot building throws a ball vertically upward. The quadratic function h = -16t² + 136t + 72 models the ball's height above the ground, h in feet, t seconds after it was thrown.

We solve the following:-

a) What is the maximum height of the ball?

The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.

Differentiating both sides. we get:

[tex]\frac{\delta h}{\delta t} = -32t + 136[/tex] .

To get point of inflection, we equate this to 0, to get:

[tex]\frac{\delta h}{\delta t} = -32t + 136 = 0[/tex],

or, -32t + 136 = 0,

or, t = 136/32 = 4.5.

To check whether the value of h is maximum/minimum at t = 4.5, we differentiate [tex]\frac{\delta h}{\delta t} = -32t + 136[/tex] again, to get:

[tex]\frac{\delta^{2} h}{\delta t^{2} } = -32[/tex] , which is < 0, which that implies, h is maximum at t = 4.5.

Now, we calculate the maximum height, by putting in t = 4.5, in the equation, to get:

h = -16(4.5)² + 136(4.5) + 72,

or, h = -16(20.25) + 612 + 72,

or, h = -324 + 684 = 360.

Therefore, The maximum height of the ball is 360 feet.

b) How many seconds does it take until the ball hits the ground?

The time taken can be calculated by putting the value of h = 0, and solving the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.

Therefore, it can be written as:

0 = -16t² + 136t + 72.

or, 16t² - 136t - 72 = 0.

Solving this using the quadratic equation, we get:

[tex]t = \frac{-(-136)\pm \sqrt{(-136)^{2} - 4(16)(-72)}}{2(16)}[/tex] ,

or, [tex]t = \frac{136\pm \sqrt{18496 + 4608}}{32}[/tex] ,

or, [tex]t = \frac{136\pm \sqrt{23104}}{32}[/tex] ,

or, [tex]t = \frac{136\pm 52}{32}[/tex]

Therefore, either t = (136+152)/32 = 9,

or, t  (136 - 152)/32 = -0.5.

Since t represents time, we won't take the negative value, and hence t = 9.

Therefore, The time taken by the ball to hit the ground is 9 seconds.

Learn more about quadratic equations at

https://brainly.com/question/15340389

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Answer:

429.7

Step-by-step explanation:

Answer:

429,710

Step-by-step explanation:

Answer:

(2, 1)

Step-by-step explanation:

To do this add 2 to the x-value and subtract 3 from the y-value.

(0+2, 4-3) = (2, 1)

Answer:

(2,1)

Step-by-step explanation:

0+2=2

4-3=1

look at the graph and move ur mose however many counter to the right if its the right left if its left and then down if its down then up if its up

Answer:

A) 2x = -20 and C) x = -10

Step-by-step explanation:

2/5x = -4

5 •  2/5x = 5(-4)        Multiply terms to eliminate the denominator

2x = -20       Cancel the multiplied terms

2x/2 = -20/2      Divide

x = -10

Hope this helps

Answer:

x=3

Step-by-step explanation:

subtract 2x from both sides then you are left with 3=4x-9

add 9 to both sides then you have 12=4x then divide both sides by 4 and x=3

Answer:

x=3

Step-by-step explanation:

2x+3=6x-9

subtract 3 both sides

2x=6x-12

subtract 6 x both sides

-4x=-6

divide 4 both sides

-x=-3 simplify (divide both sides by -1)

x=3

Answer:

0

Step-by-step explanation:

Answer:

the answer is A <_______________^______________

Answer:

D.y-4=-5/7(X=3)

Hope this helps!!!

///////////////////////////////////////////////////////////////////////////////////////////////////////////////

Answer:

0.111111

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution

=2×3/3×3-5×1/9×1

=6/9-5/9

=6-5/9

=1/9

Please mark me brainliest.Ok

Answer:

50/100

Step-by-step explanation:

it is a half becaus 50 is half of 100 1 is hal of 2

Answer:

it will compare unit to some quanlity to a different number of units of a different queality.

Step-by-step explanation:

a/b=c/d proportions are two fractions that are equal example: 1/2=2/4

Answer:

d = √[(-2 - 3)2 + (1 - 1)2] = √25 = 5 units

Answer:

-4.4c+1.1

Step-by-step explanation:

Answer:

5y + 4z

Step-by-step explanation:

hope that helps :)

Answer:

15

Step-by-step explanation: so i did 8/3 x 15/4 x 3/2 and got 15

Answer:

$4,000

Step-by-step explanation:

10% of $20,000 is $2,000, which means the price of the car is decreasing by $2,000 each year. After 8 years, the price of the car has decreased by $16,000 ($2,000 times 8 years). The totals cost of the car is now $4,000, as it was originally $20,000, but decreased by $16,000. (20,000-16,000=4,000).

Answer:

62b+27nb-12n-12

Step-by-step explanation:

u gotta combine like terms

Answer:

-0.7 .................

12/15 and 1/15 is the prob

Answer:

is answer is 8,340

Step-by-step explanation:

add 280 and 415 and get 695

then multiply by 5 and get 3,475

then multiply 695 by 12 and get 8,340

Answer:

Boxes at the top are as follows

Monomial. 1. 4x

Binomial. 2. 4x+2

Trinomial. 3.

Polynomial. More than 3.

[tex] {5x}^{4} + {2x}^{3} + {12x}^{2} + 135 [/tex]

This would be an example of a polynomial ^

Omit the next highest term to get a trinomial etc

1. 4th degree. Leading term:

[tex] {x}^{4} [/tex]

Leading coefficient: x

2. 2nd degree. Leading term:

[tex] - {7x}^{2} [/tex]

Leading coefficient: -7x

It's a little confusing to read but that should be everything. Sorry it's not organized better

Answer:

6

Step-by-step explanation:

Answer:

3 cans cost 2

1 can cost 2/3                    

 I wrote 2/3 to make it easier so you don't have to write in cents

2/3 can be spend to buy 1 can

12 can be spend to buy (2/3)(12) can

(2/3)(12)=8 cans

So the answer is 8 cans

You can buy 8 cans of tuna with 12 dollars

Answer:

wow um ok ill try?(if that counts)

Step-by-step explanation:

8x to 30y?

Answer:

7 and 9

Step-by-step explanation:

Variables:

x = smaller number

y = larger number

We can set up two equations with the information given:

5x + 3y = 62

and

y = x + 2

We get the second equation with the information that the two numbers are consecutive and both odd. therefore the smaller number is two less than the larger number, and the larger number is two greater than the smaller number.

Next, we need to replace our y in the first equation with the y in the second:

5x + 3y = 62

5x + 3 (x+2) = 62

5x + 3x + 6 = 62

8x = 56

x (smaller number) = 7

Finally, we solve for the larger number by placing it back into the second equation:

y = x + 2

y = 7 + 2

y (larger number) = 9

I hope this helps!

-TheBusinessMan