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nadya68 [22]
3 years ago
5

3√6-4√6 Please simplify

Mathematics
1 answer:
Eva8 [605]3 years ago
3 0

Answer:

= -√6

Step-by-step explanation:

1) collect like terms by subtracting coefficients:

3√6 - 4√6

(3-4)√6

2) calculate (3-4):

(3-4)√6

-1√6

3) the coefficient of -1 does not have to be written, but the negative sign remains:

-1√6

-√6

so therefore:

-√6 is your answer

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Jason and Alison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of
Shalnov [3]

Answer:

Owl= 67.14ft

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}

22^{\circ} 8'6'' = 22.135^{\circ}

30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}

30^{\circ} 40'30'' = 30.675^{\circ}

Considering Jason's position:

tan(22.135^{\circ}) = \frac{H}{x + 48}

Where x = distance between the tree and Alison

Make H the subject

H = (x + 48)tan(22.135^{\circ})

Considering Alison's position

tan(30.675^{\circ}) = \frac{H}{x}

Make H the subject

H = xtan(30.675^{\circ})

H = H

(x + 48)tan(22.135^{\circ}) = xtan(30.675^{\circ})

(x + 48) *0.4068 = x* 0.5932

Open bracket

x *0.4068 + 48 *0.4068 = 0.5932x

0.4068x + 19.5264 = 0.5932x

Collect Like Terms

-0.5932x+0.4068x = -19.5264

-0.1864x = -19.5264

0.1864x = 19.5264

Make x the subject

x = \frac{19.5264}{0.1864}

x = 104.76

Substitute 104.76 for x in H = xtan(30.675^{\circ})

H = 104.76 * tan(30.675^{\circ})

H = 104.76 * 0.5932

H = 62.14

The above represents the height of the tree.

The height of the owl is:

Owl= H + 5

Owl= 62.14 + 5

Owl= 67.14ft

7 0
2 years ago
Y=-x+4 <br>y=x-4<br>the picture gives instructions<br>​
Soloha48 [4]

Answer:

This equation has <u>No Solutions. </u>

Step-by-step explanation:

It is parrel because it has the same x. When equations have the same x it is always parrel or it always has no solutions.

<em>I hope it helps! Have a great day!</em>

<em>Lilac~ </em>

8 0
2 years ago
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The circle passes through the point (-4,-1). What is its radius?
liubo4ka [24]

Answer:

c is the correct answer for this question

Step-by-step explanation:

c is the correct answer for this question

А

1.5

2.5

© 2

V3

Hope this helps.

4 0
3 years ago
The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for eac
olya-2409 [2.1K]

Answer:

a) \frac{74}{10025}

b) \frac{3x-2}{x(8x+1)}

c) \frac{-24x^2+32x-2}{(8x^2+x)^2}

Step-by-step explanation:

For total cost function c(x), average cost is given by \frac{c(x)}{x} i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., \left ( \frac{c(x)}{x} \right )'

Given:c(x)=\frac{3x-2}{8x+1}

Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

a)

At x = 50 units,

\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}

b)

Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

c)

Marginal average cost:

Differentiate average cost with respect to x

Take f=3x-2\,,\,g=8x^2+x

using quotient rule, \left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}

Therefore,

\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}

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3 years ago
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jeka57 [31]

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4 0
3 years ago
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