h(t) = -46t² + 40t + 3
We can think this graph by t being the x-axis and h being y-axis
So we want the maximum value to y.
We know by math that the vertex of a parabola is (-b/2a, -Δ/4a)
So the y value of the vertex is -Δ/4a
Let's calculate:
Δ = b² - 4.a.c
Δ = 40² - 4.(-46).3
Δ = 2152
Yvertex = -2152/4.(-46)
Yvertex = 2152/184
Yvertex = 269/23
Now we have the value of y we need to equal it to the equation
269/23 = -46t² + 40t + 3
-46t² + 40t + 3 - 269/23 = 0
-46t² + 40t - 200/23 = 0
Δ = b² - 4.a.c
Δ = 40² - 4 . -46 . (-200/23)
Δ = 1600 - 4. -46 . (-200/23)
Δ = 0
There's 1 real root.
In this case, x' = x'':
x = (-b +- √Δ)/2a
x' = (-40 + √0)/2.-46
x'' = (-40 - √0)/2.-46
x' = -40 / -92
x'' = -40 / -92
x' = 0,43478260869565216
x'' = 0,43478260869565216
So, after approximately 0,4348 seconds the balloon will reach the highest point.
B) height after 2 seconds
h(2) = -46.2² + 40.2 + 3
h(2) = -46.4 + 80 + 3
h(2) = -184 + 83
h(2) = -101
Not sure how it's possible but it would be -101.
Im going to assume you know the formula.
sooo.
x= -11 +- √ (11)² -4 (1) (-15)
---------------------------------
2(1)
= -11 +- √121- (-60)
-------------------------
2
= -11 +- √181
-----------------
2
= -11 +- 13.45
-----------------
2
Either: Or:
X = -11 - 13.45
x = -11 + 13.45 ---------------
2
----- ----------
2
x = 1.23 x= -12.23
6. Call the length Marian bikes m. We have m/3+m=24, so 4m/3=24 and m=18, so Marian bikes 18 miles and Bin-Gee bikes the remaining 6 miles.
9. If 24 miles more than Jan's distance is three times Jan's distance, 24 is twice Jan's distance, so Jan drives 12 miles.
16. Call the amount of tied games t. We have: t+(t+1)+(t+1+2)=10, so 3t+4=10. As a result, 3t=6, so t=2. Therefore, two games were tied, 2+1=3 games were lost, and the remaining five games were won.
28. This problem is actually the same as problem 16! Do you see why? (Shortest piece is equal to games tied, middle is games lost, and largest is games won)
Answer:
-6 + 8d - 2c
-2c +8d -6
-2 (3 - 4d + c)
Step-by-step explanation:
hope this helps
Answer:
Divide both sides by 3
Step-by-step explanation:
Divide both sides by 3 to isolate x.
x = 81
