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4 years ago

Use long division to determine the decimal equivalent to 5/9

Mathematics

2 answers:

likoan [24]4 years ago

6 0

5/9 is equal to.5555555555

kumpel [21]4 years ago

5 0

I researched and found that it is in fact a repeating decimal and would round to 0.55555556.

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Please help Ladder question!!

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

Which would most likely be graphed using a continuous graph? Check all that apply.

valentina_108 [34]

speed of a car, s, as it accelerates over time

decrease in outside temperature

one evening over time, t

6 0

3 years ago

Read 2 more answers

A man stands on a balcony 140 feet up and sees a bus stop at a 75 degree angle How far is the bus stop to the man in nearest fee

lakkis [162]

D = 140 sec Θ models the distance from the man
<span>to any object given his angle of sight theta.
</span>after working it out you will find out that the awnser is <span>541 feet</span>

4 0

4 years ago

Read 2 more answers

Help pls i don't know how to solve this

choli [55]

Answer:

x = - 8 and (- 8, 0 )

Step-by-step explanation:

Given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the equation of the axis of symmetry which is also the x- coordinate of the vertex is

x = - $\frac{b}{2a}$

y = x² + 16x + 64 ← is in standard form, with

a = 1 and b = 16, then

x = - $\frac{16}{2}$ = - 8

Equation of axis of symmetry is x = - 8

Substitute x = - 8 into the quadratic and evaluate for y

y = (- 8)² + 16(- 8) + 64 = 64 - 128 + 64 = 0

vertex = (- 8, 0 )

6 0

3 years ago

Lisa says that 43 is a 2-digit odd number that is composite us she correct

kogti [31]

Yes Lisa is correct 43 is a 2 digit number 4 is one digit and 3 is a digit so it makes two digits 43 is a prime number because 43 has no positive divisors rather than 1 and itself.

SO answer is YES

7 0

3 years ago

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