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4 years ago

All of the following solid figures except _____ have two congruent, parallel bases.

Mathematics

1 answer:

Tatiana [17]4 years ago

8 0

Answer:
rectangular pyramid

Explanation:
1- rectangular pyramid:
A rectangular pyramid has only one base that has a rectangle shape. Slanting sides meet at a vertex in the top.

2- Heptagonal prism:
A prism whose two bases are heptagons (7-sided polygons). The two bases are parallel and congruent

3- Cylinder:
A prism whose two bases are circles. The two bases are parallel and congruent

4- Cube:
A prism whose two bases are squares. The two bases are parallel and congruent

I have attached figures of the all 4 options for better illustration.

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Solve cos(2x)=1-sin(x)

Vedmedyk [2.9K]

Given:

$cos(2x)=1-sin(x)$

Expanding using double angle formula,

$1 - 2 \sin^{2} (x) = 1 - \sin(x)$

Rearranging into a single equation,

$1 - 2 \sin^{2}(x) - 1 + \sin(x) = 0$

Combining like terms,

$- 2 \sin^{2} (x) + \sin(x) = 0$

Now multiplying each term by -1,

$2 \sin^{2} (x) - \sin(x) = 0$

Factor greatest common factors out,

$\sin(x)(2 \sin(x) - 1) = 0$

Applying Zero property rule,

$\sin(x) = 0 \: or \: 2 \sin(x) - 1 = 0$

• Solve the trignometric equation to find a particular solution,

$x = 0 \: or \: x = π$

$= > x = 2nπ \: or \: x = π + 2nπ$

• Find the union of the solution sets,

$x = nπ$ }

• Rearrange unknown terms to the left side,

$2 \sin(x) = 1$

• Divide both sides of the equation by the coefficient of variable,

$\sin(x) = \frac{1}{2}$

• Solve the trignometric equation to find a particular solution,

$x = \frac{π}{6} \: or \: x = \frac{5π}{6}$

$= > x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

}

☆ Now finding the union of both sets

$x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

Hence, the answer is $x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

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3 years ago

Mrs Perry shares out 15 biscuites between Gemma and Zak in the ratio 1:4 How many biscuites do they get each? Gemma: Zak

kotykmax [81]

Number of biscuits shared by Mrs Perry = 25
ratio in which the biscuits were shared between Gemma and Zak = 1:4
Let us assume the common ratio = x
then
x + 4x = 15
5x = 15
x = 3
Then
The number of biscuits that Gemma got = 3
The number of biscuits that Zak got = 4x
= 4 * 3
= 12
So
Gemma: Zak = 3:12
I hope the procedure is clear enough for you to understand.

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