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3 years ago

6

How much do you earn per week if your annual salary is $40,716?

1 answer:

Sidana [21]3 years ago

4 0

Answer:

783

Step-by-step explanation:

There are 52 weeks in a year. Divide 40,716/52 and you get $783 weekly.

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In my coin purse. I have six times as many nickels as quarters. If I took away 15 nickels. I would have an equal number of quart

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3 quarters and 18 nickels

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Convert the Cartesian equation x^2 + y^2 = 16 to a polar equation.

RideAnS [48]

Answer:

Problem 1: $r=4$

Problem 2: $r=-2\sin(\theta)$

Problem 3: $r\sin(\theta)=3$

Step-by-step explanation:

Problem 1:

So we are going to use the following to help us:

$x=r \cos(\theta)$

$y=r \sin(\theta)$

$\frac{y}{x}=\tan(\theta)$

So if we make those substitution into the first equation we get:

$x^2+y^2=16$

$(r\cos(\theta))^2+r\sin(\theta))^2=16$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)=16$

Factor the $r^2$ out:

$r^2(\cos^2(\theta)+\sin^2(\theta))=16$

The following is a Pythagorean Identity: $\cos^2(\theta)+\sin^2(\theta)=1$ .

We will apply this identity now:

$r^2=16$

This implies:

$r=4 \text{ or } r=-4$

We don't need both because both of include points with radius 4.

Problem 2:

$x^2+y^2+2y=0$

$(r\cos(\theta))^2+(r\sin(\theta))^2+2(r\sin(\theta))=0$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)+2r\sin(theta)=0$

Factoring out $r^2$ from first two terms:

$r^2(\cos^2(\theta)+\sin^2(\theta))+2r\sin(\theta)=0$

Apply the Pythagorean Identity I mentioned above from problem 1:

$r^2(1)+2r\sin(\theta)=0$

$r^2+2r\sin(\theta)=0$

or if we factor out r:

$r(r+2\sin(\theta))=0$

$r=0 \text{ or } r=-2\sin(\theta)$

r=0 is actually included in the other equation since when theta=0, r=0.

Problem 3:

$y=3$

$r\sin(\theta)=3$

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4 years ago

Solve for b. ax+3b=2f

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b = $\frac{2f}{3}$ - $\frac{ax}{3}$

hope this helps <3

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Isolate the variable by dividing each side by factors that don't contain the variable.
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What is the x intercept of the line defined by 2x-3y=12

I am Lyosha [343]

Answer:

x- intercept = 6 or (6, 0 )

Step-by-step explanation:

to find the x-intercept, that is where the graph crosses the x-axis, let y = 0 in the equation and solve for x

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