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.
Answer:
The dimensions of the herb garden on the scale drawing are 2.4 by 6 inches
Step 1 (finding the scale factor):
12/10 (inches/feet) or 1.2 (inches/feet)
(1.2 inches<em> </em>in the <em>drawing</em> represent 1 foot in real life)
Step 2 (finding the dimensions of the herb garden on the scale drawing):
Real life dimensions are 2ft by 5ft so we multiply by the <em>scale factor</em>:
2ft = 2 x 1.2 = 2.4 inches
5ft = 5 x 1.2 = 6 inches
So the dimensions of the herb garden on the scale drawing are 2.4 by 6 inches.
Slope = Y2-Y1/X2-X1 = 7-(-3)/3-(-2)= 10/5 = 2
