It will take you 30 hours to build a perfect fort
Question is not well presented
The parabola y=x² is scaled vertically by a factor of 1/10.
What is the equation of the new parabola?
Answer:
The equation of the new parabola is 0.1x²
Step-by-step explanation:
Given
Parabola: y = x²
Scale = 1/10 = 0.1
The interpretation of this question is that; there's a need to scale the graph in ratio 1:10.
I.e; 1 unit on the parabola is being represented by 10 unit on the scale
So, x (on the new parabola) = 1/10 of old x.
So, the new equation of the parabola = 1/10x²
New equation = 0.1x²
Hence, the equation of the new parabola is calculated as 0.1x²
Answer:
7) 24 8) 75 9) .9
Step-by-step explanation:
You multiply the denominatior with the whole number.
Answer:
2 miles per hour
Step-by-step explanation:
1/4 x 4 = 1
1/2 x 4 = 2
1/4 is a quarter of 100, so you have to multiply it by 4 to get 100% or 1.
So 1/2 x 4 is 2, which is the mph.
Answer:
(a) y = -3/5 x + 13/5
(b) y = 5/3 x + 1/3
Step-by-step explanation:
(a) The slope of the tangent line is dy/dx. Use implicit differentiation:
x² + y² + 4x + 6y − 21 = 0
2x + 2y dy/dx + 4 + 6 dy/x = 0
2x + 4 + (2y + 6) dy/dx = 0
x + 2 + (y + 3) dy/dx = 0
(y + 3) dy/dx = -(x + 2)
dy/dx = -(x + 2) / (y + 3)
At the point (1, 2), the slope is:
dy/dx = -(1 + 2) / (2 + 3)
dy/dx = -3/5
Using point-slope form of a line:
y − 2 = -3/5 (x − 1)
Simplifying to slope-intercept form:
y − 2 = -3/5 x + 3/5
y = -3/5 x + 13/5
(b) The normal line is perpendicular to the tangent line, so its slope is 5/3. It also passes through the point (1, 2), so point-slope form of the line is:
y − 2 = 5/3 (x − 1)
Simplifying to slope-intercept form:
y − 2 = 5/3 x − 5/3
y = 5/3 x + 1/3
