Answer: x ≥ 1307
Explanation:
First, write the formula:
monthly fee: $14
minute rate: 7¢ or $0.07
total charge: $105.49
.07x + 14 ≥ 105.49 (the sign is this way because they said this price was the least she had been charged for a month.
You can solve for x just like you would in an equation by making the ≥ sign an equal sign
.07x + 14 = 105.49
- 14 -14
.07x = 91.49
÷ .07 ÷ .07
x = 1307 minutes
since you didn't divide by a negative number, the inequality sign stays the same:
x ≥ 1307
Answer:
(a). y'(1)=0 and y'(2) = 3
(b). 
(c). 
Step-by-step explanation:
(a). Let the curve is,
So the stationary point or the critical point of the differential function of a single real variable , f(x) is the value 
which lies in the domain of f where the derivative is 0.
Therefore, y'(1)=0
Also given that the derivative of the function y(t) is 3 at t = 2.
Therefore, y'(2) = 3.
(b).
Given function,
Differentiating the above equation with respect to x, we get
![y'(t)=\frac{d}{dt}[k \sin (bt^2)]\\ y'(t)=k\frac{d}{dt}[\sin (bt^2)]](https://tex.z-dn.net/?f=y%27%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bk%20%5Csin%20%28bt%5E2%29%5D%5C%5C%20y%27%28t%29%3Dk%5Cfrac%7Bd%7D%7Bdt%7D%5B%5Csin%20%28bt%5E2%29%5D)
Applying chain rule,
![y'(t)=k \cos (bt^2)(\frac{d}{dt}[bt^2])\\ y'(t)=k\cos(bt^2)(b2t)\\ y'(t)= kb2t\cos(bt^2)](https://tex.z-dn.net/?f=y%27%28t%29%3Dk%20%5Ccos%20%28bt%5E2%29%28%5Cfrac%7Bd%7D%7Bdt%7D%5Bbt%5E2%5D%29%5C%5C%20y%27%28t%29%3Dk%5Ccos%28bt%5E2%29%28b2t%29%5C%5C%20y%27%28t%29%3D%20kb2t%5Ccos%28bt%5E2%29)
(c).
Finding the exact values of k and b.
As per the above parts in (a) and (b), the initial conditions are
y'(1) = 0 and y'(2) = 3
And the equations were
Now putting the initial conditions in the equation y'(1)=0
2kbcos(b) = 0
cos b = 0 (Since, k and b cannot be zero)
And
y'(2) = 3
![$\therefore kb2(2)\cos [b(2)^2]=3$](https://tex.z-dn.net/?f=%24%5Ctherefore%20kb2%282%29%5Ccos%20%5Bb%282%29%5E2%5D%3D3%24)
Answer:
f(4) = 11
Step-by-step explanation:
To evaluate f(4) substitute x = 4 into f(x)
f(4) = 3(4) - 1 = 12 - 1 = 11
Answer:
B. DE = 58
Step-by-step explanation:
The base angles (<F and <E) of the ∆DEF are congruent/equal. This means that ∆DEF is an isosceles triangle.
This implies that, the two sides (DF and DE) that are opposite to the base angles are congruent/equal.
DE = 40 (given) => option B is INCORRECT
Therefore:
8x - 24 = 40
Solve for x
8x - 24 + 24 = 40 + 24
8x = 64
8x/8 = 64/8
x = 8 (option C is CORRECT)
Let's find DF and FE:
DF = 8x - 24
Plug in the value of x
DF = 8(8) - 24
DF = 64 - 24
DF = 40 (Option D is CORRECT)
FE = 6x + 10
FE = 6(8) + 10
FE = 48 + 10
FE = 58 (Option A is CORRECT)
The only incorrect statement is:
B. DE = 58
