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2 years ago

10

A tunnel is in the shape of a parabola. The maximum height is 31 m and it is 13 m wide at the base as shown below.

1 answer:

yan [13]2 years ago

6 0

Using the given values from the problem and the illustration, three points are known which are (0,0), (6.5,-31), (-6.5,-31). The first step in solving this problem is to determine the equation of the parabola.
y = ax²
-31 = a(6.5)²
-31 = 42.25a
a = -31/42.25
a = -124/169

Therefore, the equation of the parabola is y = (-124/169)x². The value 4.5 is then substituted in the equation as x to get the answer which is 16.14 meters.

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The following table shows the values of y for different values of x:

solmaris [256]

Answer:

Option B. It represents a nonlinear function because its points are not on a straight line.

Step-by-step explanation:

Let

$A(0,0),B(1,1),C(2,4)$

we know that

If point A,B and C are on a straight line

then

The slope of AB must be equal to the slope of AC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

<em>Find the slope AB</em>

$A(0,0),B(1,1)$

substitute in the formula

$m_A_B=\frac{1-0}{1-0}=1$

<em>Find the slope AC</em>

$A(0,0),C(2,4)$

substitute in the formula

$m_A_C=\frac{4-0}{2-0}=2$

so

$m_A_B\neq m_A_C$

Points A, B and C are not on a straight line

therefore

It represents a nonlinear function because its points are not on a straight line

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If 30% of a number equals 25, find 60% of that number.

suter [353]

Answer:

14.94

Step by step:

25/30 = 83.333

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Find the length of midsegment YZ in trapezoid ABCD when A(-5,-6) B(-6,-2) C(-4,0) and D(3,2)

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Answer:

Option C

Step-by-step explanation:

Since, Y and Z are the midpoints of sides AB and CD of the given trapezoid.

Segment YZ will the midsegment of trapezoid ABCD.

By the theorem of midsegment,

m(YZ) = $\frac{1}{2}(AD+BC)$

By using expression for the length of a segment between two points,

Length of a segment = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance between two points A(-5, -6) and D(3, 2),

AD = $\sqrt{(3+5)^2+(2+6)^2}$

AD = $\sqrt{64+64}$

AD = $\sqrt{128}$

AD = $8\sqrt{2}$

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BC = $\sqrt{(-6+4)^2+(-2-0)^2}$

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BC = $2\sqrt{2}$

Therefore, m(YZ) = $\frac{1}{2}(8\sqrt{2}+2\sqrt{2})$

= $\frac{1}{2} (10\sqrt{2})$

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Option C will be the answer.

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