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2 years ago

6

A TV has a listed price of $708.99 before tax. If the sales tax rate is 9.75% , find the total cost of the TV with sales tax inc

luded.
Round your answer to the nearest cent, as necessary.

1 answer:

lakkis [162]2 years ago

3 0

Answer:

$778.12

Step-by-step explanation:

Before Tax Price: $708.99

Sale Tax: 9.75% or $69.13

After Tax Price: $778.12

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Can someone thoroughly explain this implicit differentiation with a trig function. No matter how many times I try to solve this,

Anton [14]

Answer:

$\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)(1+\sec^2(x-y)(8+x^2))}$

Step-by-step explanation:

So we have the equation:

$\tan(x-y)=\frac{y}{8+x^2}$

And we want to find dy/dx.

So, let's take the derivative of both sides:

$\frac{d}{dx}[\tan(x-y)]=\frac{d}{dx}[\frac{y}{8+x^2}]$

Let's do each side individually.

Left Side:

We have:

$\frac{d}{dx}[\tan(x-y)]$

We can use the chain rule, where:

$(u(v(x))'=u'(v(x))\cdot v'(x)$

Let u(x) be tan(x). Then v(x) is (x-y). Remember that d/dx(tan(x)) is sec²(x). So:

$=\sec^2(x-y)\cdot (\frac{d}{dx}[x-y])$

Differentiate x like normally. Implicitly differentiate for y. This yields:

$=\sec^2(x-y)(1-y')$

Distribute:

$=\sec^2(x-y)-y'\sec^2(x-y)$

And that is our left side.

Right Side:

We have:

$\frac{d}{dx}[\frac{y}{8+x^2}]$

We can use the quotient rule, where:

$\frac{d}{dx}[f/g]=\frac{f'g-fg'}{g^2}$

f is y. g is (8+x²). So:

$=\frac{\frac{d}{dx}[y](8+x^2)-(y)\frac{d}{dx}(8+x^2)}{(8+x^2)^2}$

Differentiate:

$=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}$

And that is our right side.

So, our entire equation is:

$\sec^2(x-y)-y'\sec^2(x-y)=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}$

To find dy/dx, we have to solve for y'. Let's multiply both sides by the denominator on the right. So:

$((8+x^2)^2)\sec^2(x-y)-y'\sec^2(x-y)=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}((8+x^2)^2)$

The right side cancels. Let's distribute the left:

$\sec^2(x-y)(8+x^2)^2-y'\sec^2(x-y)(8+x^2)^2=y'(8+x^2)-2xy$

Now, let's move all the y'-terms to one side. Add our second term from our left equation to the right. So:

$\sec^2(x-y)(8+x^2)^2=y'(8+x^2)-2xy+y'\sec^2(x-y)(8+x^2)^2$

Move -2xy to the left. So:

$\sec^2(x-y)(8+x^2)^2+2xy=y'(8+x^2)+y'\sec^2(x-y)(8+x^2)^2$

Factor out a y' from the right:

$\sec^2(x-y)(8+x^2)^2+2xy=y'((8+x^2)+\sec^2(x-y)(8+x^2)^2)$

Divide. Therefore, dy/dx is:

$\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)+\sec^2(x-y)(8+x^2)^2}$

We can factor out a (8+x²) from the denominator. So:

$\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)(1+\sec^2(x-y)(8+x^2))}$

And we're done!

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3 years ago

What adds to 12 and multiplies to 8

Ipatiy [6.2K]

X+y= -12 xy=8 y=8/x x+8/x=-12 x^2+12x+8=0 This has no integral

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3 years ago

Based on the table of values below, find the slope between points where x = 5 and

aleksklad [387]

Answer:

Slope = 1

Step-by-step explanation:

The table gives the values of y corresponding to the values of x.

At x =5, y = 2.

At x = 7, y = 6 and

At x = 10, y = 7

Now, we have to determine the slope between points where x = 5 and where x = 10.

Now, the two concerned points are (5,2) and (10,7) and we have to find the slope between those two points.

Now, slope, $m = \frac{7 - 2}{10 - 5} = 1$ (Answer)

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3 years ago

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EastWind [94]

Answer:

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Step-by-step explanation:

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3 years ago

Which factorization is equivalent to this expression?

grigory [225]

Answer:

$10(3x+7)$

Step-by-step explanation:

we have the expression:

$30x + 70$

To factor this expression we need to indentify the components that are common in both terms.

At first glance there is nothing in common, but we can notice that 30 and 70 are multiples of 10, that is:

$10*3=30\\10*7=70$

so we can substitute this into the expression:

$10*3x+10*7$

and now that we have the common term (the number 10) we can factorize it, that is, take out the common term and include a parentheses:

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