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.

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;

[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]

Plugging in the values, gives;

[tex]x = \dfrac{2.35\pm \sqrt{(2.35)^{2}-4\cdot (0.5)\times (-1)}}{2\cdot (0.5)} = \dfrac{2.35\pm \sqrt{7.5225}}{1} =2.35 \pm \sqrt{7.5225}[/tex]

∴ 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;

[tex]y_{(initial)}[/tex] = -0.5·(-0.393)² + 2.5·(-0.393) + 1 = -0.0597

[tex]y_{(initial)}[/tex] ≈ -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.

PLEASE HELPPPP!! The options are
DC= AB
AC=AC

Write an
explicit formula for An, the nth term of the sequence 15, 8, 1, ....

Find one or more sequences of rigid motions and dilations that will map ABC to DEF Often, there is more than one sequence that will
nap a prelmage to a similar image. The table below provides spaces for two different sequences.
Begin by setting the scale factor of each dilation equal to the ratio you computed in question 1. Then find the rigid transformations needed to
complete the mapping Perform the transformations in GeoGebra to check your sequences.

What is the value (in degrees) of angle Z1?
55°
<1
mZ1
-
HELP

what is the y - intercept

What is the slope of this line? ​

Help me pleaseeeeee!!!!

What is the equation in slope-intercept form of the line that passes through the points (−4, 2) and (12, 6)?

One tub of dried cranberries costs $4. How many tubs can you buy for $12?

how do I solve "at 1:00., you have 24 megabytes of a movie. at 1:15., you have 96 megabytes. what is the download rate in megabytes per minute?"​

Brianna jogs 15 minutes more on Sunday than Saturday. She jogged 26 minutes on Saturday.
a.
How many minutes does she jog on Sunday?

b) Given that BC = 5 cm,
work out the perimeter of the triangle.
​

Cary is having a party and can only afford to spend no more than $40 on food. She wants to order at least 3 pizzas which cost $6 a pie, and at least 2 orders of wings that cost $8 per order. Select all the inequalities she would have to graph to determine how many pizzas and wings she could order. Let x stand for the number of pizzas and y stand for the number of wings.
y ≥ 2
x ≥ 3
3 x + 8 y ≤ 40
6 x + 8 y ≤ 40
x ≤ 3
y ≤ 2
((You can select more than one))

:( I am very dumb please help

Question 3) What is a markup? *
O A a percent of increase
B the sale price of an item
O C a discount on an original price
D the amount of money borrowed or invested

HELP ASAP PLEASE
Given that these two triangles are similar, what is the measure of A?

A)20°

B)35°

C)55°

D)90°

Is -7 greater or less than 15,771??

2x + 3(1/5x+3/4) simplify expression

I need help will mark BRAINLIEST if right!!!!!!!!

help me fast please I give brainliest answer ​

PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((

What is the slope of the line parallel to 7x + 4y = -16?

Give the percent equation AND answer for.......... 89% of what number is 14?

(10 POINTS) Rectangle ABCD is dilated with center at (0, 0) and scale factor 2. Select the three statements that are true about the dilation.

me puede ayudar porfavor sequel nole entiendo nada a nandq​

simplify x X x^5 divided by x^2 X x

what is 111 × 111 ÷ 14 ​

Air Pods are on sale for 25% off. If AirPods originally cost $120, what is the sale price?

5 stars and a thank you

In what country would one be able to see a fjord? A. Argentina B. Suriname C. Colombia D. Brazil