The path of a large arrow fired from a catapult can be modeled by y= -0.0044x^2+1.68x, where x is the distance the arrow traveled (in yards) and y is the height of the arrow (yards).
Give the height of the castle wall, find the safest distance from the wall to launch an arrow over the wall.
1. the height of the wall is 120 yards
2. the height of the wall is 100 feet.
Answers
Answer:
Step-by-step explanation:
Wwe can solve this in either of two ways: Differentiation or graphing.
Differentiation
y= -0.0044x^2+1.68x
y' = -0.0088x + 1.68
y' is an equation that tells us the slope of the line for any point x. We want to know when the arrow begins it's descent. That is the point of maximum height, and the slope of the line through that point will be zero. Set y' = 0 and solve for x:
0 = -0.0088x + 1.68
0.0088x = 1.68
x = 191
The maximum height is when the arrow has travelled 191 feet. Now put 191 feet into the equation to find the maximum height:
y= -0.0044x^2+1.68x
y(191) = feet
The maximum height is 160 feet
--
Graphing
See attachment.
Related Questions
Please help me with this
Answers
3/5 x 3 1/8 (25/8) = 1.875
1.875 as a fraction is 1 7/8
tatiana had $350. she spent $180 on herself ad the rest on presents for her family.writ an equation to express how much tatiana spent on her family.
Answers
Answer:
$350 - $180 = $170
$180 = T
$170 = F
T = Tatiana
F = Family
Step-by-step explanation:
Answer:
Equation to express how much Tatiana spent on her family
= $(350-180)
Directions: Tell whether the following is a quadratic inequality or not.
1. y = 4x2 + 3x + 9 = ____________________________
2. m + 4 > 0 = ____________________________
3. m2 + 3m + 2 < 0 = ____________________________
4. �� ≤ (x - 5) = ____________________________
5. b2 -14b -15 < 0 = ____________________________
6. (4d2-9) + (2d +3) > 0 = ____________________________
7. x > 8x = ____________________________
8. 0 > 2x2 - 262 = ____________________________
9. n2 +4n =21 = ____________________________
10. 15 – 4p ≥ 10p2 = ____________________________
Answers
Anser
(b2 – 4ac). sorry if this doesnt help it doesnt make sense on my screen it shows a weird equation
Step-by-step explanation:
Two consecutive numbers exist such that the sum of three times the first number and two less than the second number is equal to 144. What are third numbers
Answers
Step-by-step explanation:
two consecutive numbers means that one is larger by 1 than the other number.
so, we have to choices depending on whether the first number (multiplied by 3) is the larger one, or the second number.
to show what I mean, let's start with the second number being the larger one.
we are dealing therefore with x and (x+1).
3x + (x+1) - 2 = 144
4x - 1 = 144
4x = 145
x = 145/4
this is not an integer (but this is necessary to have 2 dedicated consecutive numbers).
so, it is actually not a valid solution.
therefore we are checking the other approach :
we are dealing therefore still with x and (x+1). but now we multiply the other number by 3.
3(x+1) + x - 2 = 144
4x + 1 = 144
4x = 143
x = 143/4
this is still not an integer (but this is necessary to have 2 dedicated consecutive numbers).
so, it is actually not a valid solution either.
and now I am beginning to think you left out some important information in the question.
could it be these 2 numbers are consecutive even or consecutive uneven numbers ?
because then the difference between the both of them is 2 and not 1.
we are dealing therefore with x and (x+2). first attempt to make the smaller number the "first" number :
3x + (x+2) - 2 = 144
4x = 144
x = 144/4 = 36
ah ! now that looks different !
36 and 38 are valid solutions under the changed assumptions. and we are dealing with consecutive even numbers.
let's check :
36×3 + 38 - 2 = 36×3 + 36 = 36×4 = 144
correct.
and fun fact, if we turn this around and make the larger number the "first" number, we are still dealing with x and (x+2), but now we multiply the larger number by 3 :
3(x+2) + x - 2 = 144
4x + 6 - 2 = 144
4x + 4 = 144
4x = 140
x = 140/4 = 35
35 and 37 are also valid solutions under the new assumptions and two consecutive uneven numbers ...
so, please check what your original question (and maybe the headlines and description around it) says. and then pick the right solution.
Marco is making rice but wants to decrease the recipe to make less.
Which fraction could he multiply his ingredient amounts by in order to produce less rice?
Answers
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
please help me :) there is a picture
Answers
Explanation: the ratio of the point (20,16) is 5/4 and the slope of the line is 5/4. You can also take the slope of (20,16) and (4,5) they also have the slope 5/4
What is mode in math.
Answers
Answer:
the number that appears the most in a data set
Step-by-step explanation:
example
3,4,5,2,3,3,3,7,7
Mode:3
HELP ME ANSWER THIS PLEASE
Answers
Answer:
I think it is -162
Step-by-step explanation:
Write a polynomial equation that has three real zeroes, and a y intercept of 250
Answers
Answer: Forget about imaginary roots.
Draw an x axis and a y-axis, at right angles.
Place a dot at y=250.
Place a dot at x=60 and place a dot at x=120.
Sketch a graph: in quadrant II, go left from the y-intercept of 250, downward and then curve upward before getting to the x-axis. You have created a local min in the 2nd quadrant.
In the first quadrant, curve smoothly fromthe y intercept down to 60 on the x axis, and continue toward the right and into the fourth quadrant, eventually curving upward and eventually crossing the x axis at 120. Continue upward indefinitely. You have created another local min, at about x=90.
The smooth polynomial curve will have a local max at(0,250).
Now y = a(x-60)(x-120)(x2+1) can represent this curve; it has two real zeros. Adjust "a" so that the y-intercept is 250.
Step-by-step explanation:
i hope this helps
5
x
:
8
=
7
:
2
Calculate the value of x
.
Give your answer in its simplest form.
Answers
Answer:
Step-by-step explanation:
5x:8=7:2
5x/8=7/2
By Cross Multiplication:
10x=56
x=56/10
x=28/5
If you need to ask any question,please let me know.
Let g (x) = 5x^2 + 3x and r (x) = 2x^2 + 6x - 13. Find g (x) - r (x)
-3x^2 - 3x + 13
-3x^2 + 3x + 13
-3x^2 + 3x - 13
-3x^2 - 3x - 13
Answers
Answer:
none
Step-by-step explanation:
[tex] = 5 {x}^{2} + 3x - 2 {x}^{2} - 6x + 13 \\ = 3 {x}^{2} - 3x + 13[/tex]
10000+2000003
ghsrhrs
Answers
- BRAINLIEST answerer
Answer: 2010003
Step-by-step explanation: because 10000+2000003= 2010003
3a-28-7a+10a
Someone PLEASE HELP
Answers
Answer:
6a - 28
Step-by-step explanation:
combine like terms
3a - 28 - 7a + 10a
3a - 7a + 10a = 6a
have a lovely day :)
Answer:
Step-by-step explanation:
the steps are on the pic
symbolab
tiger-algebra
and
geteasysolution
aregoof for math
Can someone help ?????
Answers
Accordingly the answer is Nineteen Fourths.
Q8. the distance between two villages is 12875km. Express the distance in standard form.
Answers
Answer:
1.2875 × 10^4
Step-by-step explanation:
Four equations are graphed on the coordinate grid: which set of equations has (-2,5) as its solution?
Answers
what is the equation of line that passes through(-6,-3) and is parrelel to the line 5x-3y=9
Answers
Answer:
y+3=5/3(x+6)
Step-by-step explanation:
Since it is parallel to 5x-3y=9, you need to find the slope of that line because then you would find the slope to your line.
5x-3y=9
5x=9+3y
5x-9=3y
y=5/3x-3, and the slope would be 5/3.
Now you can apply point slope form [tex]y-y_{1}=m(x-x_{1} )[/tex] to get an equation.
y+3=5/3(x+6)
Answer: [tex]\frac{5}{3}[/tex]x + 7
Step-by-step explanation:
Round 21.897 to the nearest hundredth.
Answers
Answer:
21.900 - 21.9
Step-by-step explanation:
if your rounding it its 21.900 or 21.9
Lee is creating a garden with the dimensions shown.
Lines are drawn inside a large triangle at each point to create smaller triangles. Line A B is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to A B is 36 degrees. Line Z Y is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to Z Y is 65 degrees. Line X Y is drawn to create a triangle that has 2 sides with a length of 8 feet. The angle opposite to X Y is 79 degrees.
He creates paths through the garden along Line segment A B, Line segment X Y, and Line segment Z Y. Which correctly compares the lengths of the paths?
The path along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B.
The path along Line segment A B is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment X Y.
The path along Line segment Z Y is longer than the path along Line segment X Y, and the path along Line segment X Y is longer than the path along Line segment A B.
The path along Line segment Z Y is longer than the path along Line segment A B, and the path along Line segment A B is longer than the path along Line segment X Y.
Mark this and return
Answers
Choose the numbers that is not a factor of 300.
A. 5
B. 6
C. 8
D.20
And explain!!
Answers
Answer:
C. 8
Step-by-step explanation:
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
8 is not a factor of 300.
Hope this helps :)
Find the slope of the line given the following point on the line:
(-1,-9) and (-5,1) with
Answers
Answer:
The slope with these points can only by (-2.5) or (-8/3)
Step-by-step explanation:
Solve the given equation
x – 1 + 5x = 23
Answers
Step-by-step explanation:
x - 1 + 5x = 23
6x - 1 = 23
6x = 23 + 1 = 24
6x = 24
x = 24/6
x = 4 ans.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE.
Use the exchange rate £1 = €1.13 to convert €339 into £.
Answers
Answer:
the answer is £300.
..........
Answer:
383.07
Step-by-step explanation:
All the info
£1 = €1.13 What are we trying to do? Turn €339 into £.
Therefore 339 X 0.13=44.07 So 44.07+339=£383.07 making £383.07 the exchanged sum
What is the slope of the given slide?
Answers
a^2 = b^2 + c^2
-15^2 + 18^2 = a^2
a^2 = 99
a = root of 99
[tex]\text{Slope,~} \tan \theta =\dfrac{15}{18}=\dfrac 56[/tex]
PLEASE HELP The mean life expectancy of a certain type of light bulb is 860 hours with a standard deviation of 22 hours.
What is the approximate standard deviation of the sampling distribution of the mean for all samples with n = 65?
0.34 h
0.75 h
2.73 h
2.95 h
Answers
Answer: The correct answer is: 2.73 h.
Step-by-step explanation:
I hope this helps! :)
hey does anyone know the answer to this equation
Answers
Answer:
it is D
UR WELCOME
Answer:
C
Step-by-step explanation:
Substitute the values of x into y and evaluate , that is
x = - 27 → y = [tex]\sqrt[3]{-27}[/tex] = - 3
x = 0 → y = [tex]\sqrt[3]{0}[/tex] = 0
x = 27 → y = [tex]\sqrt[3]{27}[/tex] = 3
The values of y that complete the table are
- 3, 0, 3 → C
simply the ratio 3:9
Answers
Answer:
1:3
Step-by-step explanation:
The ratio 3:9
3/9=1/3
=1:3
What is the perimeter of the quadrilateral that is the length of 7 height of 8
Answers
Answer:
30
Step-by-step explanation:
What you need to do is add all the sides when you want to find perimeter so for this one you would want to do 8+8+7+7 and that should give you 30. I hope I could help!!
Answer:
30 unitsStep-by-step explanation:
assuming it is a rectangle, there is no information on the shape of the quadrilateral, add all sides.
7 + 8 + 7 + 8 = 30 units
You need to raise a total of $1,000 for your trip. There are 20 days before you leave. You estimate that you will be able to sell 25 candy bars per day. How much should you charge for each candy bar?
Answers
Answer:
1,000 ÷25 = 40 so 40÷20= $2.00
your answer is $2.00 hope this helps
Which of the following can be the sides of a right angled triangle?
(i) 1.5 cm, 2 cm, 3 cm (ii) 6 cm, 1.1 cm, 6.1 cm
Answers
Answer:
(ii) 6 cm, 1.1 cm, 6.1 cm
Step-by-step explanation:
Knowing that all right triangles obey the Pythagorean Theorem, we can test both sets of numbers. The longest of the 3, the hypotenuse, is substituted to the c value of the equation a^2 + b^2 = c^2. If the equation is still true after substituting and simplifying both sides, that combination of triangle lengths is the correct answer. In this case, 6^2 + 1.1^2 and 6.1^2 are both equal to 37.21, so the second set is correct.
