Answer:
1. yes
2. no
3. yes
4. yes
5. no
Step-by-step explanation:
Answer:
The smallest model - bottom right - in the question diagram represents ![\sqrt[3]{64}=4](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B64%7D%3D4)
.
Step-by-step explanation:
Considering the radical expression
![\sqrt[3]{64}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B64%7D)
Lets simply this radical expression first
As
![=\sqrt[3]{4^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B4%5E3%7D)
![\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a,\:\quad \:a\ge 0](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aradical%5C%3Arule%7D%3A%5Cquad%20%5Csqrt%5Bn%5D%7Ba%5En%7D%3Da%2C%5C%3A%5Cquad%20%5C%3Aa%5Cge%200)
![\sqrt[3]{4^3}=4](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B4%5E3%7D%3D4)
Therefore,
Now, as we can determine that . So, the smallest model in the question diagram represents as each face of the cube of the smallest model in the diagram - bottom right - has 4 squares.
Therefore, the smallest model - bottom right - in the question diagram represents .
Keywords: square cube root, radical expression
Learn more about radical expression from brainly.com/question/13984232
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Answer:
Option A: P ≈ 38.7 in, A ≈ 63.7 in²
Step-by-step explanation:
We are told that △MNO ~△DEF. This means that they are similar triangles.
We can solve for this using scale factor.
a) Perimeter of △MNO
The scale factor of two similar triangles is equal to the ratio of the perimeter of the triangles
Scale factor(k) = ratio of the sides of the triangles
In the diagram we are given
Side of △MNO = 6.7in
Side of △DEF = 9in
Perimeter of △MNO = X
Perimeter of △DEF = 52in
Scale factor (k) = 6.7/9
Hence,
6.7/ 9 = X/52
Cross Multiply
9X = 6.7 × 52
X = 6.7 × 52/9
X = 38.711111111 inches
To the nearest tenth, Perimeter of △MNO = 38.7 inches
b) Area of △MNO
The square of the scale factor of two similar triangles is equal to the ratio of area of the triangles
Scale factor(k) = ratio of the sides of the triangles
In the diagram we are given
Side of △MNO = 6.7in
Side of △DEF = 9in
Area of △MNO = Y
Area of △DEF = 115in²
Scale factor (k) = 6.7/9
Hence,
(6.7/ 9)² = Y/115
6.7²/9² = Y / 115
Cross Multiply
9² × Y = 6.7² × 115
Y = 6.7²× 115 /9²
Y = 63.732716049 square inches
To the nearest tenth, Area of △MNO = 63.7 in²
Answer:
11.781 cubic inches (round accordingly)
Step-by-step explanation:
The formula for the volume of a cone is:
where r is the radius and h is the height.
For our ice cream cone:
d = 3 inches
r = 1.5 inches (the radius is half of the diameter)
h= 5 inches
So all we have to do is plug in our values and solve for the volume:
So our final answer is around 11.8 cubic inches.
