I need to simplify

A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find

scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, $O(0,0)$ in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

$x^2=4ay\;\cdots(i)$

where $a$ is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is $A(83, -40)$ and $B(-83, -40).$

There is only one constant in the equation of the parabola, so, use either of one point to find the value of $a$ .

Putting $A(83,-40)$ in the equation (i) we have

$83^2=4a(-40)$

$\Rightarrow a=-43.05625$

So, on putting the value of $a$ in the equation (i), the equation of bridge is

$x^2=-172.225y$

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, $x=\pm 10$ feet, put this value in equation (i) to get the value of y.

$(\pm10)^2=-172.225y$

$\Rightarrow y=-1.72225$ feet.

The point $P_1(10,-1.72225)$ and $P_2(-10,-1.72225)$ represent the point on the bridge at a distance of 10 feet from its center.

The distance of these points from the x-axis is $d=1.72225$ feet and the distance of the base of the bridge from the x-axis is $h=40$ feet.

Hence, height from the base of the bridge at 10 feet from its center

$= h-d$

$=40-1.72225=38.27775$ feet.

8 0

2 years ago

In a horse race with 5 horses, you make a bet by predicting the ranking of all 5 horses. Suppose you place your bet at random. W

lapo4ka [179]

Answer:

P( top two horses are predicted incorrectly in incorrect order)

= $\frac{1}{2}$

Step-by-step explanation:

In the horse race the outcome can be predicted in 5! = 120 ways.

Now suppose the top two horses were predicted incorrectly in incorrect order. Now, the top horse can be predicted incorrectly in 4 ways.

Suppose the top horse was predicted to be in k-th position where k = 2, 3 ,4,5

so the second horse can be predicted to be in place from 1 to (k - 1)

So, the top two horses can be predicted incorrectly in incorrect order

in $\sum_{k =2}^{5}(k - 1)$ = 10 ways

and for each prediction of the two the remaining horses may be predicted in 3! = 6 ways.

Hence ,

P( top two horses are predicted incorrectly in incorrect order)

= $\frac{6 \times 10}{120}$

= $\frac{1}{2}$

8 0

2 years ago

(50 points)

kondor19780726 [428]

The answer is f(x) will eventually exceed g(x) because f(x) is an exponential function.

6 0

3 years ago

Evaluate the expression 4^3÷(7-3)×2

Serhud [2]

The answer should be 32

5 0

3 years ago

An expression is shown: martha evaluates the expression using these steps: step 1: step 2: step 3:

earnstyle [38]

Answer:Answer: D Step 3 ; f²k³

Explanation:

(k⁻¹)⁻³ = k³

Step-by-step explanation:

8 0

3 years ago

I need to simplify ​

I need to simplify