Francois earns a weekly salary of$475 a5.5%commission on sales at a gift shop how much would he earn in a week if he sold $700 g
1 answer:
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Answer:
R = 10 cm
Step-by-step explanation:
The area of a spherical shape is given by :
Where
r is the radius of the sphere
ATQ,
One large bubble separates into four small bubbles so that the total area of the small bubbles is equal to the area of the large bubble.
The radius of each small bubble is 5 cm
Using the given condition,
So, the radius of the large bubble is equal to 10 cm.
To give you a context on the problem, a tangent line is a line that intersects the parabola only at one single point. A parabola is a curve that forms an arc-shaped figure. A tangent line to a parabola is shown in the attached picture.
Now, we apply the concepts in calculus and analytical geometry. The first derivative of the equation is equal to the slope at the point of intersection. This slope must be equal to the slope of the tangent line.
y = x² - 5x + 7
dy/dx = slope = 2x -5
Since tangent lines must have the same slope with what they intersect with, we can determine the slope from the equation: y = 3x + c. This is already arranged in a slope-intercept form, where 3 is the slope and c is the y-intercept. So, we can equate the equation above to 3.
2x - 5 = 3
x = 4
Now, we substitute x=4 to the original equation of the parabola:
y = (4)² - 5(4) + 7
y = 3
Therefore, the point of intersection is at (4,3). Now, we use it to the equation of the tangent line to find c.
y = 3x + c
3 = 3(4) + c
c = -9
Now, we apply the concepts in calculus and analytical geometry. The first derivative of the equation is equal to the slope at the point of intersection. This slope must be equal to the slope of the tangent line.
y = x² - 5x + 7
dy/dx = slope = 2x -5
Since tangent lines must have the same slope with what they intersect with, we can determine the slope from the equation: y = 3x + c. This is already arranged in a slope-intercept form, where 3 is the slope and c is the y-intercept. So, we can equate the equation above to 3.
2x - 5 = 3
x = 4
Now, we substitute x=4 to the original equation of the parabola:
y = (4)² - 5(4) + 7
y = 3
Therefore, the point of intersection is at (4,3). Now, we use it to the equation of the tangent line to find c.
y = 3x + c
3 = 3(4) + c
c = -9