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:
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.
Related Questions
1. If f(x) = 4x + 5, what is the value of f(-3)? *
Answers
Answer:
-7
Step-by-step explanation:
Plug the value in.
4(-3)+5=-12+5=-7
Hope I helped!
Over the past 10 years, the high school football team averaged 24.8 points per game with a standard deviation of 8.5. At the homecoming game, the team scored 52 points. Find and interpret the z-score.
Answers
Answer:
3.2 i think
Step-by-step explanation:
7. Estimote the following percentages of 60.
10% =
25% =
50% =
20% =
Answers
Answer:
10% of 60 = 6
25% of 60 = 15
50% of 60 = 30
20% of 60 = 12
Step-by-step explanation:
Answer:
10% = 6
25% = 15
50% = 30
20% = 12
Step-by-step explanation:
10 % just drop the 0 from 60. 1/10 of 60 is 6
25% is 1/4. Divide: 60/4 =15
50% is half. Divide 60/2 = 30
20% is 1/5 Divide 60/5 =12
9 of 9
A glass is 1/3 full. Then 75cm3 of orange juice is poured in.
The glass is now 3/4 full. What is the total volume of the glass?
Answers
Step-by-step explanation:
1/3 divide by 75cm3=?
divide and see what u get
help please please
Answers
If i just knew the answer i would tell you buti dont know sorrry
Answer:
1. A. 9
B. - 51
2. A. (-3,2)
B. (5,-2)
3. A. (11,-3) B. (11,1) C. They have the same x
The local newspaper has letters to the editor from 50 people. If this number represents 2% of all of the newspaper's readers, how many readers does the newspaper have?
Answers
Answer: The newspaper has 2500 readers.
Step-by-step explanation:
Given: The local newspaper has letters to the editor from 50 people.
This is the 2% of all newspaper readers.
Let x be the number of all newspaper readers.
Then. 2% of x= 50
[tex]\Rightarrow\ 0.02x=50\ \ [\text{To remove }\% \text{we divide number by 100}]\\\\\Rightarrow\ x=\dfrac{50}{0.02}=\dfrac{5000}{2}=2500\\\\\Rightarrow x=2500[/tex]
Hence, the newspaper has 2500 readers.
BRAINLIEST!!! Correct and fastest answer!
Answers
Answer:
whats the question?????
Step-by-step explanation:
a scale drawing of a rectangular room measures 3 1/2 inches by 11/2 inches the scale is 1/4 inches the scale 1/4 inch = 2 feet carpeting cost $10 per square foot how much will it cost to buy enough carpenter to cover the floor of this room
Answers
Answer:
$1540
Step-by-step explanation:
3/2 x 11/2 = 19 1/4
19 times 4 to find how many 1/4s fit in 19 = 76
Add 1/4 = 77
77 x 2 = 154 feet
154 x 10 = $1540
Answer:
1,120
Step-by-step explanation:
I don’t really know but it’s 1,120
After converting the equation 5x + 2y = 10 to slope-intercept form. What would be the slope and the y-intercept? a) m = -2/5 and b = 5 b) m = 5/2 and b = 2 c) m = -5/2 and b = 5 d) m = 2/5 and b = 2 Inc.
Answers
Answer:
the answer is C
Simplify.
312+18
358
3210
368
334
Answers
The sum of 312+18 is 330.
To simplify the sum of 312 + 18, we add the two numbers together:
When three hundred twelve is added with eighteen we get three hundred thirty.
312
+18
________
330
Hence, the value of 312+18 is 330.
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A biker cycles 9 miles in 2/3 of an hour.
a
Make a chart and fill it in to show how far he will bike if he maintains the same pace for 2 hours, 3 hours, 3.5 hours
Answers
Answer:
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
He rides 27 miles in two hours, 81/2 miles in 3 hours, and 189/4 in 3.5 hours.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A biker cycles 9 miles in 2/3 of an hour.
∴ He rides (9×3/2) is (2/3)×(3/2) hours.
He rides 27/2 miles in 1 hour.
So, He rides (27/2)×2 in 2 hours.
27 miles in 2 hours.
He rides (27/2)×3 miles in 3 hours.
81/2 miles in 3 hours.
He rides (27/2)×(7/2) miles in 7/2 hours.
189/4 miles in 7/2 hours.
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The length of a square is 6 2/3 inches. What is the Perimeter of the square?
Answers
Answer:
26 2/3 inches
Step-by-step explanation:
P=4s
P= 4 × 6 2/3
P= 26 2/3 inches
Ms. Sakai rode her bike 7.25 miles on Friday. She then rode 12.3 miles on Saturday and then 7.3 miles on Sunday. How many total miles did she ride over those three days?
Answers
Answer:26.85 miles
Step-by-step explanation: 7.25+12.3+7.3=26.85
what fraction altogether is 5/12 and 4/12
Answers
Answer:
20/12 or 20/24
Step-by-step explanation:
Answer:
9/12
Step-by-step explanation:
5 4 9
_ _ = _
12 12 12
When both denominators are the same keep it. Then add the top no matter what. if it says 6+3 add that then you would get 9
_
12
So here you go the answer is 9/12
A baker in 70 minutes iced 40 cupcakes and in 49 minutes he iced 28 cupcakes what is the constant of proportionality? express your awnser in decimal form.
Answers
Answer:
1 cupcake is made in 1.75 minutes.
1.75 minutes
Step-by-step explanation:
Divide 70 by 40 = 1.75.
49/28=1.75
The constant of proportionality of the given data is 0.57.
What is constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value.
Now it is given that,
Time taken for icing 40 cupcakes = 70 minutes
∴ Icing of cupcakes in 1 minute = 40/70
= 0.57
Time taken for icing 28 cupcakes = 49 minutes
∴ Icing of cupcakes in 1 minute = 28/49
= 0.57
⇒ constant of proportionality = 0.57
Thus, the constant of proportionality of the given data is 0.57.
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Two forces of 17.3 pounds and 42.5 pounds act on a body with an angle of 21.9 degrees between them. The force of 42.5 pounds acts on the body in the horizontal direction. Choose the correct approximation for the direction angle the resultant vector makes with the horizontal force.
a. 6.3
b. 21.9
c. 15.7
d. 10.9
Answers
The resultant vector makes a 6.3-degree angle with the horizontal force, the correct option is A.
What is the formula for determination of angle of the resultant vector ?The resultant angle between the vectors is given by
[tex]\rm \theta = tan^{-1} \dfrac{B sin\theta}{A +B cos\theta}[/tex]
The two forces have magnitude of 17.3 and 42.5 pounds.
The angle of the resultant vector is
[tex]\rm \rm \theta = tan^{-1} \dfrac{17.3\; sin\; 21.9}{42.5 +17.3 cos\;21.9}[/tex]
[tex]\rm \theta = tan^{-1}[/tex] (6.453/58.55)
[tex]\rm \theta[/tex] = 6.2886 degree = 6.3 degree.
Therefore, the resultant vector makes a 6.3-degree angle with the horizontal force.
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Answer:
6.3 on edge
Step-by-step explanation:
NEED HELP PLEASE.............
Answers
E
(Maybe B, but not 100% sure though)
HELP ASAP!!!! WILL GIVE BRAINLIEST! Tamara bought yarn for $39 and 2 pairs of knitting needles. Her total cost for the yarn and knitting needles was $69. Tamara writes an equation that represents the cost of each pair of knitting needles. If k represents the cost of each pair of knitting needles, which statements about verifying the value of k are true?
CHECK ALL THAT APPLY
A.) Tamara should substitute k = 30 into the equation 39 + 2 k = 69.
B.) After she substitutes the correct value for k into the equation, Tamara should find that the left side of the equation is equal to the right side.
C.) Tamara should substitute k = 15 into the equation 39 + 2 k = 69.
D.) After she substitutes the correct value for k into the equation, Tamara should find that the left side of the equation is not equal to the right side.
E.) To verify the solution to the equation, Tamara multiplies the solution by 2 and then adds it to 39. Then, she checks that it is equal to 69.
F.) To verify the solution to the equation, Tamara adds the solution to 2 and then adds it to 69. Then, she checks that it is equal to 39.
Answers
Answer:
2,3,5
Step-by-step explanation:
Answer:
B. C. E
Step-by-step explanation:
(2/3)m tm= a + r, for m
Answers
Answer:
m = √ 6 t ( a + r )/ 2 t m = − √ 6 t ( a + r )/ 2 t
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Which pair of triangles can be proven congruent by SAS?
Answers
Which statement about rigid transformations is true?
A.
A rigid transformation preserves only the side lengths of a polygon.
B.
A rigid transformation preserves only the angle measures of a polygon.
C.
A rigid transformation preserves both the side lengths and the angle measures of a polygon.
D.
A rigid transformation preserves neither the side l
Answers
Answer:
The answer is B because it is only the measure of the polygon
HELP ASPCA PLZ
How long is the flight from Baltimore to Miami?
2 hours 25 minutes
O 2 hours 35 minutes
O 3 hours 25 minutes
o 3 hours 35 minutes
Answers
What is the difference of 4 cubed and 25????
Answers
Answer:
39
Step-by-step explanation:
4 cubed is 64 and 64-25 is 39
*15 Points* need help quickly plz
Answers
Answer:
Both of these statements are correct.
Step-by-step explanation:
Adjacent means next to each other, vertical angles are like angles 2 and 5, where they are right across from each other.
I hope this helps/ makes sense!!!
What is the perimeter of this shape
Answers
Answer:
40.9
Step-by-step explanation:
8+10+8.9+10+4=40.9
hope this helps :3
if it did pls mark brainliest
Answer:
40.9 ft
Step-by-step explanation:
Perimeter is the sum of lengths of all outer sides of the shape. Since the rectangle has two pairs of parallel lines of the same length... It is safe to assume that the unmarked side length is 10 ft (just like it's parallel counterpart)
Now it is a simple matter of adding all of the outer sides.
8ft + 10 ft + 10 ft + 8.9 ft + 4 ft = 40.9 ft
In △ABC, BM is a median, △BMC is equilateral and MC = 3cm. Through M is drawn line l∥AB that intersects CB at point N. Find:
- m∠ABC
- The distance from C to AB
- The distance from l to AB
Answers
Answer:
m∠ABC = 60°
The distance from C to AB = 3 cm
The distance from l to AB = 1.5 cm
Step-by-step explanation:
The median of ΔABC = BM
The length of MC = 3 cm
Type of triangle given as ΔBMC = Equilateral triangle
Line MN is parallel to AB and passes through M intersecting CB at N
Given that BM is a median, we have;
MC = AM = 3 cm
BM = MC = CB = 3 cm, from ΔBMC = Equilateral triangle
CN = NB by midpoint theorem
∴ CB = CN + NB = 2·CN = 3 cm
The distance from C to AB = CB = 3 cm
The distance from C to AB = 3 cm
CN = 3/2 = 1.5
CN = NB = 1.5
The distance from l to AB = CN = 1.5 cm
The distance from l to AB = 1.5 cm
m∠ABC = m∠BMC = m∠MBC = 60° Interior angles of an equilateral triangle.
m∠ABC = 60°
3/4 divided by what equals 12
Answers
Answer:
0.05357142
Step-by-step explanation:
!!20 POINTS!! BRAINLIEST TO CORRECT ANSWER!!
Select the correct answer.
Which ratio is equal to 27:81?
А.1:9
B.2:9
C.3:9
D. 3:27
E.9:12
Answers
Answer:
3:9
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
27:81
= 27/81
=3/9
=3:9
it could be reduced to 1:3 but because the alternatives does not include, it 3: 9
please reward me by marking me as the brainliest.
At a sale this week, a sofa is being sold for $527. This is a 32% discount from the original price. What is the original price?
Answers
527 times 0.32 then add that to 527
Write an equation in slope-intercept form of the line that passes through (3,8) and (1,-2)
Answers
Step-by-step explanation:
let eqn be y = mx + b.
m = (-2 - 8)/(1 - 3) = 5
sub (3, 8):
8 = 5(3) + b
b = -7
therefore equation of the line is y = 5x - 7
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Answer:y = 5x - 7
Step-by-step explanation: /
