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3 years ago

Alan has forgotten his 4-digit PIN code.

2 answers:

5 0

200

If the number is divisible by 5, then the last digit should be either 5 or 0.

First digit is fixed.

Second digit can be 10 ways.

Third digit can be 10 ways.

Fourth digit can be 2 ways.

So total number of digits 1 x 10 x 10 x 2 = 200

My name is Ann [436]3 years ago

5 0

The answer Probably 200

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3 years ago

Consider the right cone and right triangular prism below. Suppose that all measurements are labeled in centimeters.

Musya8 [376]

Answer:

The prism has a volume about 340 cubic centimeters larger than the cone.

Step-by-step explanation:

<u />

<u>Formulas</u>

$\sf Surface\:area\:of\:a\:cone=\pi r \left(r+\sqrt{h^2+r^2}\right)$

$\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h$

where:

r = radius of circular base
h = height perpendicular to the base

Given:

r = 3 cm
h = 6 cm

Substitute the given values into the formulas:

$\begin{aligned}\sf Surface\:area\:of\:cone & =\pi (3) \left(3+\sqrt{6^2+3^2}\right)\\ & = 3 \pi \left (3+\sqrt{36+9}\right)\\ & = 3\pi (3+\sqrt{45})\\ & = 3\pi(3+3\sqrt{5})\\ & = 91.5 \:\: \sf cm^2\:(1\:d.p.)\end{aligned}$

$\begin{aligned}\textsf{Volume of cone} & =\dfrac{1}{3} \pi (3)^2 (6)\\& = \dfrac{54}{3} \pi \\ & = 18 \pi \\ & = 56.5\:\: \sf cm^3 \:(1 \: d.p.)\end{aligned}$

<h3><u>Prism</u></h3>

<u>Formulas</u>

<u /> $\textsf{Surface area of a prism}=\textsf{Total area of all the sides}$

$\textsf{Volume of a prism}=\sf \textsf{Area of base} \times height$

$\textsf{Area of a triangle}=\sf \dfrac{1}{2} \times base \times height$

$\textsf{Area of a rectangle}=\sf width \times length$

Given:

Height of triangular base = 10 cm
Base of triangular base = 8 cm
Height of prism = 10 cm

Find the <u>area of the triangular base</u> of the prism:

$\begin{aligned}\textsf{Area of the base} & = \dfrac{1}{2} \times 8 \times 10\\& = 40\:\: \sf cm^2\end{aligned}$

Find the third edge of the triangular base by using <u>Pythagoras Theorem</u>:

$\begin{aligned}a^2+b^2 & = c^2\\\implies 8^2+10^2 & = c^2\\164 & = c^2\\c & = \sqrt{164}\\c & = 2\sqrt{41}\end{aligned}$

Use the found values and the formulas to find the surface area of volume of the prism:

$\begin{aligned}\textsf{Surface area of prism} & = \sf 2\:triangles+3\:rectangles\\& = 2\left(40\right) + (10 \times 10)+(10 \times 8)+ (10 \times 2\sqrt{41})\\& = 80 + 100 + 80 + 20\sqrt{41}\\& = 388.1 \:\: \sf cm^2\:(1\:d.p.)\end{aligned}$

$\begin{aligned}\textsf{Volume of prism} & = 40 \times 10\\& = 400\:\:\sf cm^3 \:(1 \:d.p.)\end{aligned}$

<h3><u>Conclusion</u></h3>

The surface area and volume of the prism is <u>larger</u> than that of the cone.

<u>Difference between surface areas</u>:

388.1 - 91.5 = 296.6 ≈ 300 cm²

<u>Difference between volumes</u>:

400 - 56.5 = 343.5 ≈ 340 cm³

Therefore:

The prism has a surface area about 300 square centimeters larger than the cone.
The prism has a volume about 340 cubic centimeters larger than the cone.

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3 years ago

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step below. Question 1 Hexagon AGHBGHCGHD GHEGHFGH is a reflected image of hexagon ABCDEF. The midpoints of the sides of hexagon

Anuta_ua [19.1K]

Answer:

Hexagon AGHBGHCGHDGHEGHFGH coincides with hexagon ABCDEF when GH passes through the midpoints of opposite sides; that is, it is a perpendicular bisector of the two sides. HexagonAGHBGHCGHDGHEGHFGH also coincides with hexagon ABCDEF when the line of reflection joins a pair of vertices opposite one another on the hexagon. There are three perpendicular bisectors and three pairs of opposite vertices. In all, there are six lines of reflection that will map the hexagon back onto itself.

Step-by-step explanation:

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3 years ago