The picture of the calendar is shown in the attached image.
Now, first we will get the volume of the calendar itself, we can note the calendar has the shape of a triangular prism.
Volume of triangular prism = area of base * depth
The area of base = area of triangle = 1/2 * base * depth
Therefore:
Volume of prism = 1/2 * base * height * depth
where:
base = 4 in
height is he height of the base = 6 in
depth is the depth of the calendar = 8 in
Therefore:
Volume of calendar = 1/2 * 4 * 6 * 8 = 96 in^3
Now, we are given that the volume of each candy is 2 in^3, this means that:
number of candies to fill the calendar = volume of calendar / volume of candy
= 96/2
= 48 candies
Hope this helps :)
Answer:
f(-3) = -12
g(-2) = -19
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = 3x - 3
g(x) = 3x³ + 5
f(-3) is <em>x</em> = -3 for function f(x)
g(-2) is <em>x</em> = -2 for function g(x)
<u>Step 2: Evaluate</u>
f(-3)
- Substitute in <em>x</em> [Function f(x)]: f(-3) = 3(-3) - 3
- Multiply: f(-3) = -9 - 3
- Subtract: f(-3) = -12
g(-2)
- Substitute in <em>x</em> [Function g(x)]: g(-2) = 3(-2)³ + 5
- Exponents: g(-2) = 3(-8) + 5
- Multiply: g(-2) = -24 + 5
- Add: g(-2) = -19
Answer:
<h3>f =27</h3>
Step-by-step explanation:

Collect like terms and simplify

Switch sides

Ok, so remember that the derivitive of the position function is the velocty function and the derivitive of the velocity function is the accceleration function
x(t) is the positon function
so just take the derivitive of 3t/π +cos(t) twice
first derivitive is 3/π-sin(t)
2nd derivitive is -cos(t)
a(t)=-cos(t)
on the interval [π/2,5π/2) where does -cos(t)=1? or where does cos(t)=-1?
at t=π
so now plug that in for t in the position function to find the position at time t=π
x(π)=3(π)/π+cos(π)
x(π)=3-1
x(π)=2
so the position is 2
ok, that graph is the first derivitive of f(x)
the function f(x) is increaseing when the slope is positive
it is concave up when the 2nd derivitive of f(x) is positive
we are given f'(x), the derivitive of f(x)
we want to find where it is increasing AND where it is concave down
it is increasing when the derivitive is positive, so just find where the graph is positive (that's about from -2 to 4)
it is concave down when the second derivitive (aka derivitive of the first derivitive aka slope of the first derivitive) is negative
where is the slope negative?
from about x=0 to x=2
and that's in our range of being increasing
so the interval is (0,2)
Answer:
f(2)=21
Step-by-step explanation:
f(2)=2^3+2*2-4+13=8+4-4+13=8+13=21