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DENIUS [597]
2 years ago
9

Perform the multiplication. Simplify the answers. 2 √30*( √5+ √6+ √10+ √15)

Mathematics
1 answer:
Delicious77 [7]2 years ago
3 0

The simplified expression of 2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})is 10\sqrt{6} +  6\sqrt{20}+  20\sqrt{3} +  30\sqrt{2}

The expression is given as:

2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})

Expand the expression

2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2\sqrt{30} \times \sqrt5+  2\sqrt{30} \times \sqrt6+  2\sqrt{30} \times \sqrt{10} +  2\sqrt{30} \times \sqrt{15}

Factor out 2

2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{30} \times \sqrt5+  \sqrt{30} \times \sqrt6+  \sqrt{30} \times \sqrt{10} +  \sqrt{30} \times \sqrt{15})

Combine the radicals

2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{150} +  \sqrt{180}+  \sqrt{300} +  \sqrt{450})

Expand the expression

2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{25 \times 6} +  \sqrt{9 \times 20}+  \sqrt{100 \times 3} +  \sqrt{225\times 2})

Evaluate the roots

2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(5\sqrt{6} +  3\sqrt{20}+  10\sqrt{3} +  15 \sqrt{2})

Expand

2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) =10\sqrt{6} +  6\sqrt{20}+  20\sqrt{3} +  30\sqrt{2}

Hence, the simplified expression of 2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})is 10\sqrt{6} +  6\sqrt{20}+  20\sqrt{3} +  30\sqrt{2}

Read more about simplified expressions at:

brainly.com/question/8008182

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mariarad [96]

Answer:

\boxed{x = 4}

Step-by-step explanation:

=> 5x-4+2(x-4) = 16

Expanding the brackets

=> 5x-4+2x-8 = 16

Combining like terms

=> 5x+2x-4-8 = 16

=> 7x - 12 = 16

Adding 12 to both sides

=> 7x = 16+12

=> 7x = 28

Dividing both sides by 7

=> x = 4

3 0
3 years ago
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A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin
Katen [24]

Answer:

Please red the answer below

Step-by-step explanation:

In order to determine the length of each cable you use the Newton second law for each component of the forces involved in the situation.

For the x component you have:

T_1cos\theta_1-T_2cos\theta_2=0           (1)

T1: tension of the first cable = 1500N

T2: tension of the second cable = 800N

θ1: angle between the horizontal and the first cable

θ2: angle between the horizontal and the first cable

For the y component you have:

T_1sin\theta_1+T_2sin\theta_2-W=0               (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2

Then, you sum the equations:

T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2        (3)

Next, you use the following identity:

sin^2\theta+cos^2\theta=1

and you obtain in the equation (3):

T_1^2=T_2^2-2WT_2sin\theta_2+W^2\\\\sin\theta_2=\frac{T_2^2-T_1^2+W^2}{2WT_2}=\frac{(800N)^2-(1500)^2+(1372N)^2}{2(800N)(1372N)}=0.066\\\\\theta_2=sin^{-1}0.066=27.23\°

With this values you can calculate the value of the another angle, by using the equation (1):

\theta_1=cos^{-1}(\frac{T_2cos(27.23\°)}{T_1})=cos^{-1}(\frac{(800N)(cos27.23\°)}{1500N})\\\\\theta_1=61.69\°

Now, you can calculate the length of each cable by using the information about the width of the football field. You use the following trigonometric relation:

l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\

d: distance to the right side of the field

By using the cosine law you can fins a system of equation and then you can calculate the values of l1 and l2.

3 0
3 years ago
A bird was perched on a tree at a height of 15 feet. The bird then saw food on a branch below and dropped down 61/3 feet. What i
natka813 [3]

The current height of the bird is -16/3

The bird perched at a height of 15 feet

The bird dropped to a height of 61/3 feet when it saw a food

The current height can be calculated as follows

= 15 - 61/3

= 45-61/3

= -16/3

Hence the current height of the bird is -16/3

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if there are 450 campers and 2/3 decides to come back next year how many campers will be coming back next year
DedPeter [7]

Answer:

So 452.3 campers will be coming back next year

Step-by-step explanation:

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Answer:271.66$

Step-by-step explanation:

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