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4 years ago

4. A guardrail that runs along the

Mathematics

1 answer:

Vinvika [58]4 years ago

5 0

There are 50 sections.

Step-by-step explanation:

Given,

Length of section = 10 meters

Total length of guardrail = 0.5 km

We will convert this length in meters.

1 km = 1000 meters

0.5 km = 0.5*1000 = 500 meters

Now,

No. of sections = $\frac{Total\ length\ of\ guardrail}{Length\ of\ one\ section}$

No. of sections = $\frac{500}{10}$

No. of sections = 50

There are 50 sections.

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Simplify the expression. Write the answer using scientific notation. (9 x 10)^2(2 x 10)^10

Valentin [98]

Answer:

Step-by-step explanation:

To multiply scientific notation, multiply each part of the number.

(9 x 10)^2(2 x 10)^10 = (9*2) * (10^ 2 + 10) = 18 * 10 ^ 12

Since scientific notation can only have a digit in the ones place from 1-9. 18*10^12 becomes 1.8*10^13.

The solution is B.

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3 years ago

Find a unit vector that has the same direction as the given vector. 8i ? j + 4k

e-lub [12.9K]

Answer with Step-by-step explanation:

a.Let given vector

a=8i-j+4k

$\mid a\mid=\sqrt{(8)^2+(-1)^2+(4)^2}=9$

By using the formula

Magnitude of a vector= $\sqrt{x^2+y^2+z^2}$

Where x=Coefficient of i

y=Coefficient of j

z=Coefficient of k

Unit vector= $\hat{a}=\frac{a}{\mid a\mid}$

By using the formula

The unit vector= $\hat{a}=\frac{8i-j+4k}{9}=\frac{8}{9}i-\frac{1}{9}j+\frac{4}{9}k$

b.Let vector b=-2i+4j+2k

$\mid b\mid=\sqrt{(-2)^2+4^2+2^2}=2\sqrt 6$

$\hat{b}=\frac{-2i+4j+2k}{2\sqrt 6}$

Length of vector=6

Therefore, the vector in the direction of <-2,4,2> with length 6 is given by = $6\hat{b}=6\times \frac{-2i+4j+2k}{2\sqrt 6}$

The vector in the direction of <-2,4,2> with length 6 is given by = $-\sqrt 6(-i+2j+k)$

c. $\theta=\frac{\pi}{3}$

$\mid v\mid=8$

Let v= $v_x i+v_y j$

$v_x=\mid v\mid cos\theta$

$v_x=8cos\frac{\pi}{3}=8\times \frac{1}{2}=4$

$cos\frac{\pi}{3}=\frac{1}{2}$

$v_y=\mid v\mid sin\theta$

$v_y=8\times sin\frac{\pi}{3}=8\times \frac{\sqrt 3}{2}=4\sqrt 3$

$sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Therefore, the vector v in component form= $4i+4\sqrt 3j$

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3 years ago

20 POINTS! 1 question PERPENDICULAR LINES

garik1379 [7]

If the line is perpendicular, that means the slope has to be opposite, so it will have a slope of -1/2

Fill in the point that it has to pass through on y and x

1=-1/2(0) + b

1=0+b

1=b

Then go back to the standard form y=mx + b and fill in the slope and y intercept

Y= -1/2x + 1

8 0

3 years ago

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Urgent HELP PLS<br> I will give you brainliest!<br> #HardMathQuestion

vredina [299]

Kylie and jack ther lines both meet at 4,40

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2 years ago

Write the product of the reciprocal of 5 and 5g-20

Naddika [18.5K]

Answer:

$reciprocal \: of \: 5 = \frac{1}{5} \\ reciprocal \: of \: (5g - 20) = \frac{1}{5g - 20} \\ product \: of \: reciprocals = ( \frac{1}{5} )( \frac{1}{5g - 20 } ) \\ = \frac{1}{5(5g - 20)} \\ = \frac{1}{(25g - 100)} \\ divide \: by \: 25 \: on \: everything \: (optional) \\ = \frac{(1 \div 25)}{(25g \div 25) - (100 \div 25)} \\ = \frac{0.04}{g - 4}$

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3 years ago