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1 year ago

(x² + 6x-5) + (x²-8x-4)

Mathematics

1 answer:

leonid [27]1 year ago

8 0

Answer: 2x^2-2x-9

Step-by-step explanation:

subtract the numbers

x^2 + 6x-5+x^2-8x-4

X^2+6x-9+x^2-8x

then your gonna combine like terms

x^2+6x-9=x^2-8x

2x^2+6x-9-8x

combine like terms

2x^2+6x-9-8x

2x^2-2x-9

solution

2x^2-2x-9

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Step-by-step explanation:

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Moving along the the shoreline when it is 1 km from P.

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From the above statement light makes seven revolutions per minute.

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$\frac{d\theta}{dt}=\frac{7\times 2\pi\ rad}{1\ min} = 14\pi\ rad/min$

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From the given figure.

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Substitute x = 1

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Now, first we differentiate both side with respect to t.

$\frac{d(tan\theta)}{dt} = \frac{d}{dt}.(\frac{x}{3})$

Using chain rule.

$\frac{d(tan\theta)}{dt}.\frac{d\theta}{dt} = (\frac{1}{5})\frac{dx}{dt}$

$sec^{2} \theta.\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

$(1+tan^{2} \theta).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

Substitute $tan\theta=\frac{1}{5}$ from equation 1.

$(1+(\frac{1}{3})^{2} ).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

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Substitute $\frac{d\theta}{dt}=14\pi$

$\frac{10}{9}.14\pi = \frac{1}{5}.\frac{dx}{dt}$

Applying cross multiplication rule.

$\frac{dx}{dt}= \frac{700\pi }{9}$

$\frac{dx}{dt}= 77.78\pi$

Therefore, light is moving along the shore at the speed of 77.78 km/min

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