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2 years ago

Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1).

1 answer:

6 0

Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way: $y'= \frac{x(0)-3(1)}{x^2}$ so $y'=- \frac{3}{x^2}$ . The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is: $y'=- \frac{3}{3^2}=- \frac{3}{9}=- \frac{1}{3}$ . So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b. $1=- \frac{1}{3}(3)+b$ so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is $y=- \frac{1}{3}x+2$

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Find the difference between the cash price and the payment plan and calculate the interest rate for the following questions.

vagabundo [1.1K]

Answer:

1).

Difference = $6

Interest rate= 4.03%

2).diffrence = $97

Interest rate = 14.37%

3). Difference = $7

Interest rate= 4.67%

4). difference= 191

Interest rate= 9.6%

5). Difference= 2.25

Interest rate= 3%

6). Difference=$ 302

Interest rate=9.12%

Step-by-step explanation:

1).$10 per months for 15 months

= 10*15=$150

PLus a down payment of $5= $155

Interest = 155-149= $6

Interest rate = 6/149*100= 4.03%

2.)$120.00 per month for 6 months

= 120*6=$ 720

Plus a down payment of $52=$772

Interest= 772-675= $97

Interest rate = 97/675 *100= 14.37%

3). $12.00 per month for 11 months

= 12*11= 132 plus down payment of $25

= $157

Interest= 157-150= $7

Interest rate=7/150 *100= 4.67%

4).$74.00 per month for 24 months

= 74*24=$1776

Plus a down payment of $400=$ 2176

Interest= 2176-1985= 191

Interest rate= 191/1985*100= 9.6%

5).$4.75 per week for 11 weeks

= 4.75*11=$52.25

Plus a down payment if $25

= 25+52.25=$ 77.25

Interest= 77.25-75= 2.25

Interest rate= 2.25/75 *100= 3%

6).$300 a month for 10 months

= 300*10= $3000

Plus a down payment of $600

= $3600

Interest=3600-3298= 302

Interest rate= 302/3298 *100=9.12%

5 0

1 year ago

On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes thr

Nitella [24]

Answer:

x + 2y = 8.

Step-by-step explanation:

Line goes through (-4, 0) and (4, -4).

The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.

Since we are looking for the equation of the line parallel to that line, the slope will be the same.

We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.

3 = (-1/2) * 2 + b

b - 1 = 3

b = 4.

So, we have y = -1/2x + 4.

1/2x + y = 4

x + 2y = 8.

Hope this helps!

8 0

2 years ago

Read 2 more answers

The necklace charm shown has two parts, each shaped like a trapezoid with identical dimensions. What is the total area, in squar

pashok25 [27]

The area of the trapezoid can be calculated through the equation,
A = (b₁ + b₂)h / 2
where b₁ and b₂ are the bases and h is the height. Substituting the known values from the given,
A = (25mm + 32mm)(15 mm) / 2
A = 427.5 mm²
Since there are two trapezoids in the necklace, the area calculated is to be multiplied by two to get the total area.
total area = (427.5 mm²)(2)
<em>total area = 855 mm²</em>

3 0

2 years ago

Read 2 more answers

Lucy wants to have a fun-filled day without spending too much money. The local zoo charges a $25 entry fee and a parking fee of

ehidna [41]

Answer:

The required system of equations is,

$y=25+x$