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2 years ago

Find the area of a circle with a diameter of 8cm.

Mathematics

1 answer:

Elza [17]2 years ago

6 0

Answer:

50.24

Step-by-step explanation:

Area = r^2 x 3.14 (pi)

Radius = 8 ÷ 2 = 4

4² = 16

16 x 3.14 = 50.24

Area = 50.24 cm ²

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If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?

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The total number of students in Toby's grade is 200.

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Which expression is equivalent to (x superscript four-thirds baseline x superscript two-thirds Baseline ) superscript one-third

Andrei [34K]

<h3>The equivalent expression is:</h3>

$(x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = x^{\frac{2}{3}$

Solution:

Given expression is:

$\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}}$

We have to find the equivalent expression

We can simplify the above expression using law of exponents

Use the following law of exponents:

$a^m \times a^n = a^{m+n}$

Therefore,

$\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = (x^{\frac{4}{3}+\frac{2}{3}})^{\frac{1}{3}}\\\\Simplify\\\\\displaystyle (x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = (x^2)^\frac{1}{3}$

Use another law of exponent

$(a^m)^n = a^{mn}$

Therefore,

$(x^{\frac{4}{3}}x^{\frac{2}{3}})^{\frac{1}{3}} = x^{\frac{2}{3}$

Thus the equivalent expression is found

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3 years ago

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How many cubes with side lengths of 1/2 cm does it take to fill up the prism

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24 cubes can filled up the prism

Solution:

The image of the question is attached below.

Given data:

Length of the prism = 2 cm

Breadth of the prism = 1 cm

Height of the prism = $$\frac{3}{2}$ cm

Volume of the prism = length × breadth × height

$$=2\times 1\times \frac{3}{2}$

$=3$ cubic cm

Volume of the prism = 3 cubic cm

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Volume of the cube = side × side × side

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$$=\frac{1}{8}$ cubic cm

Volume of the cube = $\frac{1}{8}$ cm

$$\text{Number of cubes} =\frac{\text{Volume of the prism}}{\text{Volume of the cube}}$

$$=\frac{3}{\frac{1}{8} }$

$=3\times8$

$=24$

Number of cubes = 24

Hence 24 cubes can filled up the prism.

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