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goldfiish [28.3K]
4 years ago
11

The length of a car is 4.5 m. A model of it is made and the length of the model is 12.5 cm.

Mathematics
2 answers:
kvv77 [185]4 years ago
5 0

Answer: 9:25 ?

Step-by-step explanation:

4.5 × 2 = 9

12.5 × 2 = 25

4.5:12.5 ratio simplified is 9:25

Sphinxa [80]4 years ago
3 0
4.5 m = 4.5 × 100 = 450 cm
450 ÷ 12.5 = 36
12.5 ÷ 12.5 = 1
450:12.5
ratio simplified is 36:1
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In the xy plane, what is the y intercept of the graph of the equation y=2 (x+3)(x+4)?
olga2289 [7]
The y-intercept is the value of y when the graph intersects the y-axis.  Graphs intersect the y-axis when x=0, so we just substitute in x=0 to get:

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Base Surface Area = 2π×22 = 25.132741228718 feet2
Lateral Surface Area = 2π×2×15 = 188.49555921539 feet2
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3 years ago
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find the coordinates of the point P on the parabola y=1-x^2 with domain 0≤x≤1 that minimize the area of the triangle enclosed by
coldgirl [10]

Let point P be with coordinates (x_0,y_0). Find the equation of the  tangent line.

1. If y=1-x^2, then y'=-2x.

2. The equation of the tangent line at point P is

y-y_0=-2x_0(x-x_0).

Find x-intercept and y-intercept of this line:

  • when x=0, then y=y_0+2x_0^2;
  • when y=0, then x=\dfrac{y_0}{2x_0}+x_0=\dfrac{y_0+2x_0^2}{2x_0}.

The area of the triangle enclosed by the tangent line at P, the x-axis, and y-axis is

A=\dfrac{1}{2}\cdot (2x_0^2+y_0)\cdot \left(\dfrac{y_0+2x_0^2}{2x_0}\right)=\dfrac{(y_0+2x_0^2)^2}{4x_0}.

Since point P is on the parabola, then y_0=1-x_0^2 and

A=\dfrac{(1-x_0^2+2x_0^2)^2}{4x_0}=\dfrac{(1+x_0^2)^2}{4x_0}.

Find the derivative A':

A'=\dfrac{2(1+x_0^2)\cdot 2x_0\cdot 4x_0-4(1+x_0^2)^2}{16x_0^2}=\dfrac{12x_0^4+8x_0^2-4}{16x_0^2}.

Equate this derivative to 0, then

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y_0=1-\left(\pm\dfrac{1}{\sqrt{3}}\right)^2=\dfrac{2}{3}.

Answer: two points: P_1\left(-\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right), P_2\left(\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right).

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