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3 years ago

What is the exact value of the expression the square root of 72 − the square root of 8 + the square root of 128?

Mathematics

2 answers:

kotykmax [81]3 years ago

7 0

The answer is
$12 \times \sqrt{2}$

Romashka [77]3 years ago

4 0

Answer:

Option B is correct.

Step-by-step explanation:

Given Expression is $\sqrt{72}-\sqrt{8}+\sqrt{128}$

Simplify the given expression,

72 = 2 × 2 × 2 × 3 × 3 ⇒ √72 = 6√2

8 = 2 × 2 × 2 ⇒ √8 = 2√2

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 ⇒ √128 = 8√2

⇒ $\sqrt{72}-\sqrt{8}+\sqrt{128}=6\sqrt{2}-2\sqrt{2}+8\sqrt{2}$

$=12\sqrt{2}$

Therefore, Option B is correct.

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3 years ago

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3 years ago

the figure below shows a circle centre of radius 10 cm the chord PQ=16cm calculate the area of the shaded region

m_a_m_a [10]

Step-by-step explanation:

OPQ originally forms a sector, the formula for sector is

$\frac{x}{360} \pi {r}^{2}$

where x is the degrees of rotation between the two radii.

We know three sides length and is trying to find an angle between the radii so we can use law of cosines which states that

$16 = \sqrt{10 {}^{2} + 10 {}^{2} - 2(100) \times \cos(o) }$

This isn't the standard formula, it's for this problem

$16 = \sqrt{200 - 200 \times \cos(o) }$

$16 = \sqrt{200 - 200 \cos(o) }$

$256 = 200 - 200 \cos(o)$

$56 = - 200 \cos(o)$

$- \frac{7}{25} = \cos(o)$

$\cos {}^{ - 1} ( - \frac{7}{25} ) = \cos {}^{ - 1} ( \cos(o) )$

$106.26 = o$

So we found our angle of rotation, which is 106.26

Now, we do the sector formula.

$\frac{106.26}{360} (100)\pi$

$\frac{10626}{360} \pi$

is the area of sector.

Now let find the area of triangle, we can use Heron formula,

The area of a triangle is

$\sqrt{s(s - a)(s - b)(s - c)}$

where s is the semi-perimeter.

To find s, add all the side lengths up, 10,10,16 and divide it by 2.

Which is

$\frac{36}{2} = 18$

$\sqrt{18(18 - 10)(18 - 10)(18 - 16)}$

$\sqrt{18(8)(8)(2)}$

$\sqrt{(36)(64)}$

$6 \times 8 = 48$

So our area of the triangle is 48. Now, to find the shaded area subtract the main area,( the sector of the circle) by the area of the triangle so we get

$\frac{10626}{360} - 48$

Which is an approximate or

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2 years ago

Determine the domain and range:

Luda [366]

Answer:

Option B is correct.

Step-by-step explanation:

Recall that the domain is the set of (unique) inputs and the range is the set of outputs (which do not have to be unique).

The set of inputs of the given relation is {-1, 9, -10, 1}, and this set is also found in Option B. The set out outputs is {7, 2, 6, -6|, which is in Option B.

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3 years ago