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3 years ago

I have never understood these. Help.

Mathematics

2 answers:

Reika [66]3 years ago

4 0

Answer:

5 sqrt(5)

Step-by-step explanation:

sqrt(125)

sqrt( 25*5)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(25) sqrt(5)

5 sqrt(5)

Mkey [24]3 years ago

3 0

Answer:

5√(5)

Step-by-step explanation:

Notice that 125 is 25×5

If you couldn't do it use the prime factorization.

Prime numbers are 2,3,5.....

125 isn't divisible by 2 and 3 so we'll go with 5.

● 125 ÷ 5 = 25

Againg 25 is divisible by 5

● 25÷5 = 5

5 is divisible by 5

● 5÷5=1

So 125= 5×5×5 = 5^2 × 5

● √(125)= √(5^2×5) = 5√(5)

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Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4?

mestny [16]

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We are given with a function , $f(x)=\frac{4x^2-16}{2x-4}$

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4 years ago

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A boat sails directly toward a 250-m skyscraper that stands on the

bazaltina [42]

a) The value of $\theta$ as a function of "x" is $\theta = tan^{-1}\frac{250}{x}$

b) The rate of change of the angle with respect to x is -0.000308rad/m

Find the complete question and diagram attached

Form the right-angled triangle shown:

Adjacent side = x

Opposite side = 250m

angle of elevation = $\theta$

Using the SOH CAH TOA identity

$tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}$

Hence the value of $\theta$ as a function of "x" is $\theta = tan^{-1}\frac{250}{x}$

b) If x = 450m

$\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\$

Differentiate both sides with respect to "x"

$sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}$

Substitute x = 450m and $\theta = 60^0$ into the resulting expression to have:

$\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308$

Hence the rate of change of the angle with respect to x is -0.000308rad/m

Learn more here: brainly.com/question/15580615

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3 years ago