Step-by-step explanation:
a rectangular prism (like this brick) has the same basic structure as a cube (like a die) : it has 6 sides.
while a die has 6 equal sides, a rectangular prism has 3 pairs of equal sides :
top and bottom
left and right
front and back
all we have to do is calculate the areas of the 6 rectangles and add them up. that's it.
your remember, the area of a rectangle is
length × width
in our case we have
top and bottom : 2.5×11.5 × 2 = 28.75×2 = 57.5 in²
left and right : 2.5×5 × 2 = 12.5×2 = 25 in²
front and back : 11.5×5 × 2 = 57.5×2 = 115 in²
so, the total surface area of the whole block is
57.5 + 25 + 115 = 197.5 in²
(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where

then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,

(b) The velocity after 3 seconds is

(c) The particle is at rest when its velocity is zero:

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.
(e) The total distance traveled is given by the definite integral,

By definition of absolute value, we have

In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as

and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to

Answer:
6574900
Step-by-step explanation:
A goes between -1 and -1/2
Answer:
f(-5) = -81
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = -x² + 10x - 6
f(-5) is x = -5
<u>Step 2: Evaluate</u>
- Substitute: f(-5) = -(-5)² + 10(-5) - 6
- Exponents: f(-5) = -(25) + 10(-5) - 6
- Multiply: f(-5) = -25 - 50 - 6
- Subtract: f(-5) = -75 - 6
- Subtract: f(-5) = -81