Answer:
Domain: (-5, 6]
Range: [-3, 6]
Step-by-step explanation:
Domain is all x-values that can be inputted into function f(x).
Range is all the y-values outputted by function f(x) when we plug in <em>x</em>.
We see that our x-values span from -5 to 6. Since -5 is a open dot, we cannot input -5. Therefore, we have:
Domain: (-5, 6]
Parenthesis on -5 shows that it is not included and bracket on 6 shows it is included.
We see that our y-values span from -3 to 6. Since both points are closed dots, we can include both. Therefore, we have:
Range: [-3, 6]
Brackets on both numbers signify that both values are included in the graph.
Answer/Step-by-step explanation:
Given that a and b are two corresponding sides of two similar figures, it follows that the ratio of their areas = a²/b².
We would use the above knowledge to solve the questions given as follows:
✔️The first pair similar of shapes:
Missing area = x cm²
Therefore,
x/9 = 8²/4²
x/9 = 64/16
x/9 = 4
Cross multiply
x = 4 × 9
x = 36 cm²
✔️The second pair similar of shapes:
Missing area = x cm²
Therefore,
x/240 = 8²/32²
x/240 = 64/1,024
Cross multiply
x*1,024 = 64*240
x*1,024 = 15,360
Divide both sides by 1,024
x = 15,360/1,024
x = 15 cm²
✔️The third pair similar of shapes:
Missing area = x cm²
Therefore,
x/40 = 3²/2²
x/40 = 9/4
Cross multiply
x*4 = 9*40
x*4 = 360
Divide both sides by 4
x = 360/4
x = 90 cm²
Answer:
The new volume will be 3 3/8 or maybe 27/8 of its original volume.
Step-by-step explanation:
Cone Volume = PI * radius^2 * height / 3
So if radius = 1 and height = 1 then volume = 1.0472
When radius = 3 and height = .375 then volume = 3.5343
Volume increases by 3.5343 / 1.0472 = 3 and 3/8
