Which answer choice shows 25.077 rounded to the nearest hundredth?

PIT_PIT [208]

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is

$x^2+y^2=c^2$ where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$ and dividing everything by 2 to simplify a bit:

$x\frac{dx}{dt}+y\frac{dy}{dt}=0$ . Upon analyzing that equation, it looks like we need values for x, y, $\frac{dx}{dt}$ , and $\frac{dy}{dt}$ . And here's what we were given:

$\theta=45$ and $\frac{dx}{dt}=.5$ In the greater realm of things, that's nothing at all.

BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to

Find $\frac{dy}{dt}$ at the instant that $\frac{dx}{dt}$ = .5.

Solving for x and y:

$tan45=\frac{x}{6}$ and

6tan45 = x ( and since this is a 45-45-90 triangle, y = x):

$6(\frac{\sqrt{2} }{2})=x=y$ so

$x=y=3\sqrt{2}$ and now we can fill in our derivative. Remember the derivative was found to be

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

$3\sqrt{2}(\frac{1}{2})+3\sqrt{2}\frac{dy}{dt}=0$ and

$\frac{3\sqrt{2} }{2}+3\sqrt{2} \frac{dy}{dt}=0$ and

$3\sqrt{2}\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}$ and multiplying by the reciprocal of the left gives us:

$\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}(\frac{1}{3\sqrt{2} })$ so

$\frac{dy}{dt}=-\frac{1}{2}\frac{m}{s}$

8 0

3 years ago

u 1. Consider the sequence: 192, 144, 108,81 ... a. Is this sequence arithmetic or geometric? Explain, geomethe becose hoy sonet

GarryVolchara [31]

Answer:

fydysotsstodhydfhgsodxhphddyhd

6 0

3 years ago

What is 7 * 3? this is very important so plz help

vampirchik [111]

The answer to your question is 21.

7 * 3 = 21

4 0

4 years ago

Read 2 more answers

Shane is a salesperson. He earns an hourly wage of $8.00 per hour, plus he receives a commission of 7% on sales he makes. Write

Arisa [49]

Answer:

8X+.07Y=W

Step-by-step explanation:

x is your hours and y is your sales

he makes 8 an hour, hence 8X or 8 x X

7 percent written as a decimal is .07 and his commission for sales, so .07Y

add them together and you get your equation:

8X+.07Y=W

7 0

3 years ago

Tark each location described.<br> 1) Mark the location of<br> of 6/3

Alinara [238K]

Answer: Chet aero marine

Step-by-step explanation: (this is the only thing I will say and warn this) The contents of the report reflects the views of the authors who are responsible for the fact of the accuracy of the data presented herein. Although the contents do not necessarily reflect policy of the department of transportation. This report does not constitute a standard, specification, or regulation. The united states government does not endorse products or manufacturers. Trade or manufacturer's names appear herein only because they are considered essential to the object of the document. :I hope this helps have a uwu or great day! ✍(◔◡◔)

7 0

3 years ago