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.
One way is to factor and group and get every 3
729=3 times 3 times 3 times 3 times 3 times 3
so we group the ones that happen 3 times
729=(3*3*3) times (3*3*3)
we know that we can take the cube root of each group and multiply the result
729=
![( \sqrt[3]{3*3*3})( \sqrt[3]{3*3*3})](https://tex.z-dn.net/?f=%28%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D%29%28%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D%29)
=(3)(3)=9
the answer is 9
Question 4 of 5 Page 4 Question 4 (1 point) f(x) - 0.5x + 3 The function is used to estimate the number of pounds of potatoes a caterer plans to make depending on the number of people being served, X. The mathematical domain for the function is the set of real numbers. Which statement describes the limitation for the reasonable domain compared to the mathematical domain? O O O a b C d The reasonable domain contains only real numbers greater than 3. The reasonable domain contains only positive whole numbers The reasonable domain contains only rational numbers greater than 3. the reasonable domain contains only negative whole numbers Next Page Back were to search
The square root of 36/100 is c. -6/10 and 6/10
You can get this by using a calculator.
@
[email protected]
General equation for a circle
(x - a)² + (y - b)² = r²
with (a,b) represents the center, (x,y) represents one of the points lie on the circle, and r represents the radius
Determine r² by substituting the points into the general equation
(x - a)² + (y - b)² = r²
(5 - (-1))² + (-4 - 2)² = r²
(5 + 1)² + (-6)² = r²
6² + 36 = r²
36 + 36 = r²
72 = r²
Determine the equation of the circle
(x - a)² + (y - b)² = r²
(x - (-1))² + (y - 2)² = 72
(x + 1)² + (y - 2)² = 72 (This is the equation of the circle)
