MATHEMATICS HIGH SCHOOL

The town of gettysburg, PA, plans to shoot a live cannon as part of their annual Gettysburg Civil War Battle Reenactment. The organizers want to make sure that when they fire the cannon, it lands in a location that does not injure any participants or spectators. The slope of the field they are firing into can be represented by the equation y=0.15x. Let x represent horizontal distance, and y represents vertical distance.. if the cannon fires the cannon ball at an arc denoted by the equation y=-0.5x^2+2.5x+1, at what distance will the cannonball land. -I know i'm supposed to set -0.5x^2+2.5x+1=.15x and use distance formula BUT I KEEP GETTING DIFFERENT ANSWERS.

Answers

Answer 1

Answer:

Answer:

The cannonball lands at approximately 5.093 unit distance from the point of fire

Step-by-step explanation:

The given parameters are;

The arc denoting the equation of motion of the cannon is y₁ = -0.5·x² + 2.5·x + 1

The slope of the field where in the direction the cannon is fired is y₂ = 1.5·x

The points where the cannonball land on the slopping field is given as rightly pointed by equating the two equations, the cannonball path path and the field path as follows;

At the point of contact of the cannonball and the field, the y-values of both equation will be equal

y₁ = y₂

∴ -0.5·x² + 2.5·x + 1 = 0.15·x

Which gives;

-0.5·x² + 2.5·x - 0.15·x + 1 = 0

-0.5·x² + 2.35·x + 1 = 0

-(-0.5·x² + 2.35·x + 1) = 0.5·x² - 2.35·x - 1 = 0

0.5·x² - 2.35·x - 1 = 0

The above equation is in the general form of a quadratic equation, which is given as follows;

a·x² + b·x + c = 0

By the quadratic equation, we have;

$x = \frac{-b\pm \sqrt{b^(2)-4\cdot a\cdot c}}{2\cdot a}$

Plugging in the values, gives;

$x = \frac{2.35\pm \sqrt{(2.35)^(2)-4\cdot (0.5)* (-1)}}{2\cdot (0.5)} = (2.35\pm √(7.5225))/(1) =2.35 \pm √(7.5225)$

∴ x ≈ 5.093 or x ≈ -0.393

Therefore, the cannonball will takeoff at x ≈ -0.393 and land at x ≈ 5.093

The height from which they fire the cannon is given by the substituting the value of x ≈ -0.393 into the equation for the path of the cannonball, to give;

$y_((initial))$ = -0.5·(-0.393)² + 2.5·(-0.393) + 1 = -0.0597

$y_((initial))$ ≈ -0.0597.

However, the actual initial height from which the cannonball is fired given by placing x = 0, which gives y = 1, which is the reason for the other (negative) value for x. Please see the attached graph created with Microsoft Excel.

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A company makes a product and has no way to determine which ones are faulty until an unhappy customer returns it. Three percent of the products are faulty and will cost the company $200 each in customer service and repairs. If the company does not refund the customer when repairing the item, how much should the company charge to make a profit of $2.00 per item? $6.00 $6.19 $8.00 $8.25

Answers

(x) - (0.03)(200) = 2.00
Let x be the company charge to make the profit

solving for x gives 8$

Answer: $8.00

Step-by-step explanation:

Given: Percent of products which are faulty=3%=0.03

Cost of each faulty product =$200

Let x be the company charge to make the profit .

According to the question,

$x-0.03*200=2.00\n\Rightarrow\ x-6.00=2.00\n\Rightarrow\ x=2.00+6.00\n\Rightarrow\ x=$8.00$

Hence, the company should charge $ 8.00 to make a profit of $2.00 per item.

What is 1725 with a 15% markup

Answers

$\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\n \cline{1-1} \n \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \n\n \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 1725}}{\left( \cfrac{15}{100} \right)1725}\implies 258.75~\hfill~\underset{ \textit{marked up} }{\stackrel{ 1725~~ + ~~258.75 }{\text{\LARGE 1983.75}}}$

Answer:

1983.75

Step-by-step explanation:

What is 1725 with a 15% markup?

15% = 0.15

We take

1725 + (1725 x 0.15) = 1983.75

So, the answer is 1983.75

Rewrite the multiplication problem using improper fractions.

1 5/6 x 2

Answers

22/6 is the result of the product of the expression.

Multiplication problem using improper fractions.

To rewrite the multiplication problem using improper fractions, we need to convert the mixed number 1 5/6 to an improper fraction.

1 5/6 = 11/6

Now, the multiplication problem can be expressed as:

1 5/6 x 2= 11/6 x 2

1 5/6 x 2 = 22/6

Therefore, the multiplication problem, using improper fractions, is 22/6

Learn more on multiplication of fraction here: brainly.com/question/30391645

#SPJ2

you'll convert 1 5/6 by multiplying the denominator to the whole number (6) then add the numerator 6 + 5 = 11. So the answer is

11/6 x 2

What are the possible values for x in the equation 4x²=641) x=0
2) x=4
3) x=4,-4
4) x=0,4,-4

Answers

$4x^2=64\n \n4x^2-64 =0 \ \ /:4 \n \n x^2-16 =0 \n \nx^2-4^2=0 \n \n (x-4)(x+4)=0 \n \n x-4=0 \ \ or \ \ x+4 =0 \n \n x=4 \ \ or \ \ x= -4 \n \nAnswer : \ 3) \ \ x=4,-4$

$3z - 2 = 4 \n z =$
what does z equal

Answers

The answer that I found was z=2

David's car could cover one lap of the Indy 500 in about 90 seconds. Chris' car could cover one lap in about 54 seconds. If both cars left the same starting point at the same time, after how many seconds would they meet again at the starting point?

Answers

After 270 seconds, both cars will meet again at the startingpoint.

To find the time at which both cars meet again at the starting point, we need to find the least common multiple (LCM) of their lap times. The LCM is the smallest positive integer that is divisible by both lap times.

David's car lap time = 90 seconds

Chris' car lap time = 54 seconds

Now, let's calculate the LCM:

Find the prime factors of each lap time:

90 = 2 × 3² × 5

54 = 2 × 3³

Take the highest power of each prime factor:

LCM = 2 × 3³ × 5

= 2 × 27 × 5

= 270 seconds

So, after 270 seconds, both cars will meet again at the startingpoint.

To learn more on Number system click: