The straight line 2x + 3y = 7 meets the curve

Mathematics

1 answer:

NISA [10]3 years ago

5 0

Step-by-step explanation:

xy + 10 = 0. => y = -10/x.

2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.

When -10/x = -2/3 x + 7/3,

-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.

=> 2x² - 7x - 30 = 0

=> (2x + 5)(x - 6) = 0

=> x = -2.5 or x = 6.

dy/dx = d/dx [-10/x] = 10/x².

When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.

When x = 6, dy/dx = 10 / (6)² = 5/18.

Hence the gradients at the points are 1.6 and 5/18.

You might be interested in

What interest rate is implicit in a $1,000 par value zero-coupon bond that matures in 6 years if the current price is $470.

avanturin [10]

Answer:

The formula for calculating the yield to maturity on a zero-coupon bond is:

Yield To Maturity=(Face Value/Current Bond Price)^(1/Years To Maturity)−1

For a $1,000 zero-coupon bond that has six years until maturity, the bond is currently valued at $470, the price at which it could be purchased today. The formula would look as follows: (1000/470)^(1/6)-1. When solved, this equation produces a value of 0.134097, which would be rounded and listed as a yield of 13.41%.

Step-by-step explanation:

4 0

3 years ago

Find the value of xxx in the isosceles triangle shown below.

Ivahew [28]

Answer:

$x=10\ units$