<span>Highest point = 1406.25
Number of seconds = 9.375
We've been given the quadratic equation y = -16t^2 + 300t which describes a parabola. Since a parabola is a symmetric curve, the highest value will have a t value midway between its roots. So using the quadratic formula with A = -16, B = 300, C = 0. We get the roots of t = 0, and t = 18.75. The midpoint will be (0 + 18.75)/2 = 9.375
So let's calculate the height at t = 9.375.
y = -16t^2 + 300t
y = -16(9.375)^2 + 300(9.375)
y = -16(87.890625) + 300(9.375)
y = -1406.25 + 2812.5
y = 1406.25
So the highest point will be 1406.25 after 9.375 seconds.
Let's verify that. I'll use the value of (9.375 + e) for the time and substitute that into the height equation and see what I get.'
y = -16t^2 + 300t
y = -16(9.375 + e)^2 + 300(9.375 + e)
y = -16(87.890625 + 18.75e + e^2) + 300(9.375 + e)
y = -1406.25 - 300e - 16e^2 + 2812.5 + 300e
y = 1406.25 - 16e^2
Notice that the only term with e is -16e^2. Any non-zero value for e will cause that term to be negative and reduce the total value of the equation. Therefore any time value other than 9.375 will result in a lower height of the cannon ball. So 9.375 is the correct time and 1406.25 is the correct height.</span>
Answer:
x ≈ 4.8
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] cos∅ = adjacent over hypotenuse
Step-by-step explanation:
<u>Step 1: Identify Variables</u>
Angle measure = 58°
Adjacent side of angle = <em>x</em>
Hypotenuse = 9
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [cosine]: cos58° = x/9
- Isolate <em>x</em>: 9cos58° = x
- Evaluate: 4.76927 = x
- Rewrite: x = 4.76927
- Round: x ≈ 4.8
5^2 +12^2= diagonal^2
25+144=d^2
169= d^2
D= 13
To get the *percent increase* from week 1 to week 2, we calculate the change in distance from week 1 to week 2 (13.5 - 12.5 = 1 mile) over the week 1 distance (12.5 miles). Doing that, we find that Matthew increased his distance by
1/12.5 = 0.08, or 8%
We’re given that he’ll increase his distance by the same percentage from week 2 to 3, so to find his week 3 distance, we can find 8% of the week 2 distance and add that on. 8% of 13.5 miles is 0.08 x 13.5 = 1.08 miles, so by week 3, he’ll be running 13.5 + 1.08 = 14.58 miles.
9514 1404 393
Answer:
a) BE = 5; DE = 6; EF = 4
b) ∠EFC ≅ ∠DA.F ≅ ∠BDE or <em>b = e = f = i</em>
Step-by-step explanation:
Each short segment is the same length as the marked one it is parallel to.
E is the midpoint of BC, so BE = EC = 5.
ADEF is a parallelogram, so DE = A.F = 6.
D is the midpoint of AB, so AD = DB = 4. ADEF is a parallelogram, so ...
EF = AD = 4
__
As we have noted, AB║EF and DE║A.F, so corresponding angles and alternate interior angles are congruent. <em>b = e = f = i</em>
