Given:
The equation of a circle is
![x^2+y^2=169](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D169)
A tangent line l to the circle touches the circle at point P(12,5).
To find:
The gradient of the line l.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is
![m_1=\dfrac{5-0}{12-0}](https://tex.z-dn.net/?f=m_1%3D%5Cdfrac%7B5-0%7D%7B12-0%7D)
![m_1=\dfrac{5}{12}](https://tex.z-dn.net/?f=m_1%3D%5Cdfrac%7B5%7D%7B12%7D)
We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.
Product of slopes of two perpendicular lines is always -1.
Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.
![m\times m_1=-1](https://tex.z-dn.net/?f=m%5Ctimes%20m_1%3D-1)
![m\times \dfrac{5}{12}=-1](https://tex.z-dn.net/?f=m%5Ctimes%20%5Cdfrac%7B5%7D%7B12%7D%3D-1)
![m=-\dfrac{12}{5}](https://tex.z-dn.net/?f=m%3D-%5Cdfrac%7B12%7D%7B5%7D)
Therefore, the gradient or slope of the tangent line l is
.
Answer:
its blurry for me sorry
Step-by-step explanation:
1st problem:
A = 630 cm
2nd problem:
A = 104 cm
All I can see on the picture you provided.
I beleive it is a because both variable could change
Answer:” use
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal
Let x be the fluid ounces of milk does Monica use.
As per the statement:
Monica uses 3 tablespoons of milk in her custard recipe.
It is also given that:
The ratio of tablespoons to fluid ounces is 2 : 1.
by proportion definition we have;
by cross multiply we have;
3 = 2x
Divide both sides by 2 we have;
therefore, fluid ounces of milk does Monica use.”
Step-by-step explanation: