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weeeeeb [17]
4 years ago
13

Karen bought a jacket for$280.80 inclusive of an 8% sales tax.Find the price of the jacket before sales tax was applied.

Mathematics
1 answer:
Serhud [2]4 years ago
8 0

Answer:

$260

Step-by-step explanation:

Actual price + 8% of actual price=$280.80

Let x= actual price

8% of actual price=8/100 of x

=0.08x

x + 0.08x=$280.80

1.08x=$280.80

x=$280.80/1.08

x=$260

Price of the jacket before sales tax=$260

Check:

8% sales tax of $260

=8% of $260

=8/100×$260

=0.08×$260

=$20.8

Purchasing price= actual price+ sales tax

=$260+$20.8

=$280.80

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The slope of the the tangent line to a curve at a point. Calc derivative help
pickupchik [31]

Answer:

y = 108x + 216

Step-by-step explanation:

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y = 4x³ then \frac{dy}{dx} = 12x² = m_{tgt}

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equation of tangent in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept ), hence

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To find b substitute (- 3, - 108) into the equation

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5 0
3 years ago
Find the exact values of sin2 θ for cos θ = 3/18 on the interval 0° ≤ θ ≤ 90°
mote1985 [20]

Answer:

sin(2\theta)=\frac{\sqrt{35} }{18}

Step-by-step explanation:

Recall the formula for the sine of the double angle:

sin(2\theta)=2*sin(\theta)*cos(\theta)

we know that cos(\theta)=\frac{3}{18}, and that \theta is in the interval between 0 and 90 degrees, where both the functions sine and cosine are non-negative numbers. Based on such, we can find using the Pythagorean trigonometric property that relates sine and cosine of the same angle, what sin(\theta) is:

cos^2(\theta)+sin^2(\theta)=1\\sin^2(\theta)=1-cos^2(\theta)\\sin(\theta)=\sqrt{1-cos^2(\theta)} \\sin(\theta)=\sqrt{1-(\frac{3}{18} )^2}\\sin(\theta)=\sqrt{1-\frac{9}{324} }\\sin(\theta)=\sqrt{\frac{324-9}{324} }\\sin(\theta)=\sqrt{\frac{315}{324} }\\\\sin(\theta)=\frac{3}{18}\sqrt{35 }

With this information, we can now complete the value of the sine of the double angle requested:

sin(2\theta)=2*sin(\theta)*cos(\theta)\\sin(2\theta)=2*\frac{3}{18} \,\sqrt{35} \,\frac{3}{18}\\sin(2\theta)=\frac{2*3*3}{18*18}\,\sqrt{35} \\sin(2\theta)=\frac{\sqrt{35} }{18}

6 0
3 years ago
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