Find the 9th term of the geometric sequence 8, 32, 128, ...

A company is looking to hire a lawyer. One law rm states that their legal fees can be determined using the

melisa1 [442]

Answer:

100 hours

Step-by-step explanation:

Law firm A = 350x + 22,000,

Law firm B = 410x+16,000

Where,

x = number of hours of legal assistance

What number of hours of legal assistance makes the equation 350x+22,000 = 410x+16,000 true?

Equate the legal fees of the two law firms

350x + 22,000 = 410x + 16,000

Collect like terms

350x - 410x = 16,000 - 22,000

-60x = -6,000

Divide both sides by -60

x = -6,000 / -60

= 100

x = 100 hours

The number of hours of legal assistance makes the equation true is 100 hours

3 0

3 years ago

A suspension bridge has two main towers of equal height. A visitor on a tour ship

Scilla [17]

Answer:

The Height of the tower is 188.67 ft

Step-by-step explanation:

Given as :

The angle of elevation to tower = 15°

The distance travel closer to tower the elevation changes to 42° = 497 ft

Now, Let the of height of tower = h ft

The distance between 42° and foot of tower = x ft

So, The distance between 15° and foot of tower = ( x + 497 ) ft

So, From figure :

In Δ ABC

Tan 42° = $\frac{perpendicular}{base}$

Or , Tan 42° = $\frac{AB}{BC}$

Or, 0.900 = $\frac{h}{x}$

∴ h = 0.900 x

Again :

In Δ ABD

Tan 15° = $\frac{perpendicular}{base}$

Or , Tan 15° = $\frac{AB}{BD}$

Or, 0.267 = $\frac{h}{( x + 497 )}$

Or, h = ( x + 497 ) × 0.267

So, from above two eq :

0.900 x = ( x + 497 ) × 0.267

Or, 0.900 x - 0.267 x = 497 × 0.267

So, 0.633 x = 132.699

∴ x = $\frac{132.699}{0.633}$

Or, x = 209.63 ft

So, The height of tower = h = 0.900 × 209.63

Or, h = 188.67 ft

Hence The Height of the tower is 188.67 ft Answer

3 0

3 years ago

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.

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

7 0

3 years ago

Please help im timed how would you solve 17=w/4?

max2010maxim [7]

Answer:

Solution for 17=w-4 equation:

17=w-4

We simplify the equation to the form, which is simple to understand

17=w-4

We move all terms containing w to the left and all other terms to the right.

-1w=-4-17

We simplify the left and right sides of the equation.

-1w=-21

We divide both sides of the equation by -01 to get w.

w=21

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Please help, is it 7.8?

Ivahew [28]

Answer:

yes, it says on the pic, lol

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers