Answer:
r = the radius, in your case, it's 4 cm. So. Area = π ×r2. = π× (4 cm)2. = 16π cm2 ≈ 50.24 cm2.
Step-by-step explanation:
B
Step-by-step explanation:
because the figure is based on the graphic law
9514 1404 393
Answer:
2 2/3
Step-by-step explanation:
Let the number be represented by x. Then the problem statement is telling you ...
4 5/9 = 2 1/3 + (5/6)x
You can isolate the x term by subtracting 2 1/3 from both sides of the equation. (The properties of equality require that the same operation be performed on both sides of the equation.)
(4 5/9) - (2 3/9) = (2 3/9) -(2 3/9) +(5/6)x
2 2/9 = (5/6)x
The definition of the multiplicative inverse tells you that the coefficient of x can be made to be 1 if the term is multiplied by (6/5). We must do that to both sides of the equation.
(6/5)(2 2/9) = (6/5)(5/6)x
(6/5)(20/9) = x . . . . simplify
120/45 = x . . . . . . do the multiplication
8/3 = x = 2 2/3 . . . . . . . reduce the fraction
The number is 2 2/3.
_____
<em>Additional comment</em>
The number we're looking for is multiplied by 5/6 and the result has 2 1/3 added to it. To find the number, we "undo" these operations, in reverse order. We undo the addition by subtracting the amount that was added. We undo the multiplication by multiplying by the inverse of that factor.
This is the sort of logic that you would use to fill in the blank for ...
7 = 1 + 3×___
You probably recognize that this breaks down into two problems:
7 = 1 + ___ . . . . . (6 goes in the blank)
and
6 = 3×___
You may notice that for all of these problems, a good knowledge of addition and multiplication facts is useful.
Answer:
1) the football already reached the ground
2) t = 0.625 seconds
3) t = 1.46 seconds
Step-by-step explanation:
<u>Data</u>
- initial velocity, Vi = 20 ft/s
- initial height, Hi = 5 feet.
- gravitational acceleration, g = 32 ft/s²
1) time, t = 2.25 s
To relate these variables we need to use the next equation:
H = Hi + Vi*t - 1/2*g*t²
H = 5 + 20*2.25 - 1/2*32*2.25²
H = -31 ft
that is, 31 ft under the line of reference. This means that the football already reached the ground
2) At the highest point the final velocity (Vf) is zero.
To relate these variables we need to use the next equation:
Vf = Vi - g*t = 0
Vi = g*t
t = Vi/g
t = 20/32
t = 0.625 s
3) When the football hits the ground, ΔH = -5 ft. Then:
ΔH = Vi*t - 1/2*g*t²
-5 = 20*t - 1/2*32*t²
0 = -16t² + 20t + 5
Using quadratic formula:
The first result is discarded because it doesn't have physical sense. So, the football hit the ground after 1.46 seconds
Answer:
24 ways
Step-by-step explanation:
By the Fundamental Counting Principle,
Number of permutations = 4 ⋅ 3 ⋅ 2 ⋅ 1
= 4!
= 24
There are 24 different ways the teacher can order the student presentations.