Answer:
x = 41; B = 41°; A = 77°
Step-by-step explanation:
All of the angles add up to 180 so to solve for X you do (x) + (2x-5) + (62) = 180. Solve for X and you get 41. Lastly plut the answer back into the equation.
To find the maximum or minimum value of a function, we can find the derivative of the function, set it equal to 0, and solve for the critical points.
H'(t) = -32t + 64
Now find the critical numbers:
-32t + 64 = 0
-32t = -64
t = 2 seconds
Since H(t) has a negative leading coefficient, we know that it opens downward. This means that the critical point is a maximum value rather than a minimum. If we weren't sure, we could check by plugging in a value for t slightly less and slighter greater than t=2 into H'(t):
H'(1) = 32
H'(3) = -32
As you can see, the rate of change of the object's height goes from increasing to decreasing, meaning the critical point at t=2 is a maximum.
To find the height, plug t=2 into H(t):
H(2) = -16(2)^2 +64(2) + 30 = 94
The answer is 94 ft at 2 sec.
Answer:
6.1
Step-by-step explanation:
SOH-CAH-TOA
cos35=5/x
x=5/cos35
x=6.1m
<span>f(x) = x</span>² <span>+ 12x + 6 </span>→ y = x² + 12x + 6<span>
Let us convert the standard form into vertex form.
1) Complete the squares. Isolate x</span>² and x terms.
<span>y - 6 = x</span>² + 12x
<span>
2) Create the perfect square trinomial. Whatever number is added on one side must also be added on the other side.
y - 6 + 36 = x</span>² + 12x + 36<span>
y + 30 = (x + 6)</span>²
<span>y = (x + 6)</span>² - 30 ← Vertex form
<span>
To check:
y = (x + 6) (x + 6) - 30
y = x</span>² + 6x + 6x + 36 - 30
<span>y = x</span>² + 12x + 6<span>
The zero that could be added to the given function is 36, -36</span>
Answer:
12 years
Step-by-step explanation:
T + 5 = A
Therefore T =A - 5
In three years T = 3+ (A-5)
thus T = A - 2
Also in three years T = 2/3 (A+3)
Equating the two
A -2 = 2/3 (A+3)
3A - 6 = 2A + 6
3A - 2A = 6 + 6
Therefore A = 12
