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3 years ago

Please help me with this quick :))))))))

Mathematics

1 answer:

vredina [299]3 years ago

6 0

Answer:

129.3 in²

Step-by-step explanation:

The shaded segment is calculated as

area of sector ABC - area of triangle ABC

area of sector = area of circle × fraction of circle

A = πr² × $\frac{60}{360}$

= π × 18² × $\frac{1}{6}$

= 324π × $\frac{1}{6}$ = 54π in²

area of Δ ABC = $\frac{1}{2}$ × 18 × 18 × sin60° ≈ 40.30 in²

Then

shaded area = 54π - 40.30 ≈ 129.3 in² ( to the nearest tenth )

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<img src="https://tex.z-dn.net/?f=%5Csqrt%7B%28-81%29x%5E%7B2%7D%20%7D" id="TexFormula1" title="\sqrt{(-81)x^{2} }" alt="\sqrt{(

SSSSS [86.1K]

Answer:

We conclude that:

$\sqrt{\left(-81\right)x^2}=9ix$

Step-by-step explanation:

Given the radical expression

$\sqrt{\left(-81\right)x^2}$

simplifying the expression

$\sqrt{\left(-81\right)x^2}$

Remove parentheses: (-a) = -a

$\sqrt{\left(-81\right)x^2}=\sqrt{-81x^2}$

Apply radical rule: $\sqrt{-a}=\sqrt{-1}\sqrt{a},\:\quad \mathrm{\:assuming\:}a\ge 0$

$=\sqrt{-1}\sqrt{81x^2}$

Apply imaginary number rule: $\sqrt{-1}=i$

$=i\sqrt{81x^2}$

Apply radical rule: $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0$

$=\sqrt{81}i\sqrt{x^2}$

$=9i\sqrt{x^2}$

Apply radical rule: $\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

$=9ix$

Therefore, we conclude that:

$\sqrt{\left(-81\right)x^2}=9ix$

7 0

3 years ago

What is the equation of y = x3 with the given transformations? horizontal translation right 10 units and vertical translation do

Nookie1986 [14]

A. y = (X - 10)^3 - 12

5 0

3 years ago

Read 2 more answers

Mr.davis, the volleyball coach, has 7 outstanding players. He will draw one name out of a jar to decide who stays on the bench.

Katen [24]

Answer:

7/1

Step-by-step explanation:

There are 7 players if the coach randomly draws a name that determines who stays on the bench there is a 1/7 chance Brianna will stay on the bench because there are 7 people and Brianna is 1 of them

5 0

3 years ago

A piece of cardboard measures 10 ft by 10 ft. Four equal squares of size x are removed from the corners. After removing the squa

Gnesinka [82]

Answer:

The value of x would be $\frac{5}{3}$

Step-by-step explanation:

Given,

The dimension of the cardboard = 10 ft by 10 ft,

∵ After removing four equal squares of size x ( in ft ) from the corners,

The dimension of the resultant box would be,

Length = ( 10 - 2x ) ft,

Width = ( 10 - 2x ) ft,

Height = x ft,

The volume of box,

$V=(10-2x)\times (10 - 2x)\times x=x(10-2x)^2 = x(100 - 40x + 4x^2)=100x - 40x^2 + 4x^3$

Differentiating with respect to x,

$V'=100 - 80x + 12x^2$

Again differentiating with respect to x,

$V''=-80 + 24x$

For maxima or minima,

$V'=0$

$\implies 100 - 80x + 12x^2 = 0$

$\implies 3x^2 - 20x + 25=0$

By quadratic formula,

$x=\frac{20\pm \sqrt{20^2-4\times 3\times 25}}{6}$

$x=\frac{20\pm \sqrt{400 - 300}}{6}$

$x=\frac{20\pm \sqrt{100}}{6}$

$x=\frac{20\pm 10}{6}$

$\implies x = \frac{10}{6}=\frac{5}{3}\text{ or } x = 5$

For x = 5/3, V'' = negative,

While for x = 5, V'' = Positive,

Hence, the value of x would be 5/3 ft for maximising the volume.

8 0

3 years ago

Slope pls help ASAP due tonight

kow [346]

Answer:

y=x+ -5

i think

4 0

3 years ago

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