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4 years ago

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A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula? –12, –18

, –27, ... –20, 30, –45, ... –18, –16.5, –15, ... –16, –17.5, –19, ...

1 answer:

AlexFokin [52]4 years ago

4 0

It is -16, 17.5, -19, ...

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A 15-ft ladder leans against a wall. The lower end of the ladder is being pulled away from the wall at the rate of 1.5 ft/sec. L

Aleks [24]

Answer:

The top of the ladder is sliding down at a rate of 2 feet per second.

Step-by-step explanation:

Refer the image for the diagram. Consider $\Delta ABC$ as right angle triangle. Values of length of one side and hypotenuse is given. Value of another side is not known. So applying Pythagoras theorem,

$\left ( AB \right )^{2}+\left ( BC \right )^{2}=\left ( AC \right )^{2}$

From the given data, $L=15\:ft=AC$ , $y=9\:ft=AB$ and $x=BC$

Substituting the values,

$\therefore \left ( 9 \right )^{2}+\left ( x \right )^{2}=\left ( 15 \right )^{2}$

$\therefore 81+x^{2}=225$

$\therefore x^{2}=225-81$

$\therefore x^{2}=144$

$\therefore \sqrt{x^{2}}=\sqrt{144}$

$\therefore x=\pm 12$

Since length can never be negative, so $x= 12$ .

Now to calculate $\dfrac{dy}{dt}$ again consider following equation,

$\left ( y \right )^{2}+\left ( x \right )^{2}=\left ( l \right )^{2}$

Differentiate both sides of the equation with respect to t,

$\dfrac{d}{dt}\left(y^2+x^2\right)=\dfrac{d}{dt}\left(l^2\right)$

Applying sum rule of derivative,

$\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(l^2\right)$

$\dfrac{d}{dt}\left(y^2\right)+\dfrac{d}{dt}\left(x^2\right)=\dfrac{d}{dt}\left(225\right)$

Applying power rule of derivative,

$2y\dfrac{dy}{dt}+2x\dfrac{dx}{dt}=0$

Simplifying,

$y\dfrac{dy}{dt}+x\dfrac{dx}{dt}=0$

Substituting the values,

$9\dfrac{dy}{dt}+12\times1.5=0$

$9\dfrac{dy}{dt}+18=0$

Subtracting both sides by 18,

$9\dfrac{dy}{dt}=-18$

Dividing both sides by 9,

$\dfrac{dy}{dt}= - 2$

Here, negative indicates that the ladder is sliding in downward direction.

$\therefore \dfrac{dy}{dt}= 2\:\dfrac{ft}{sec}$

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Step-by-step explanation:

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Danielle is x years old. Her sister is 5 years older and her brother is half Danielle's age. Write an expression in simplest for

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The expression is 2.5x + 5

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PLS HELP ME I WILL GIVE BRAINLIEST

Ronch [10]

Answer:

78°

Step-by-step explanation:

The angular distance of an arc is twice the angle that forms it if that angle lies of the edge of the circle.

By this, Arc AK has angular distance 158°.

Arc JL = 202°.

Arc KL = 122°.

By subtracting these we get 80° for Arc JK.

Arc KA = 158°.

Arc AJ = KA - JK

AJ = 158-80

AJ = 78°

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