Triangle FGH is an equilateral triangle.FH=6x+1,FG=3x+10,and GH=9x-8

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

Laurie buys four bags of candy with 10 pieces of candy in each bag. Her father then gives her 5 more pieces of candy. Laurie wan

lina2011 [118]

Answer:

3 pieces left over

Step-by-step explanation:

Laurie has a total of 45 pieces of candy, if she has 6 friends, you can do

$45 \div 6 = 7.5$

each friend can get 7 pieces of candy

$7 \times 6 = 42$

if each friend gets 7 pieces, you have used 42 pieces out of you total 45

$45 - 42 = 3$

which leaves 3 pieces left over.

3 0

3 years ago

A painting has an area of 108 square inches. The dimensions of the painting are 12 and x + 3. What is the perimeter of the paint

slega [8]

Answer:

108 divide 12 and i got 9

then i did 9-3 and i got 6.

12+12+9+9=42

So the perimeter is 42

Welp i don't know if it is correct or not

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

the sum of four times the first number and three times the second number is 15. the difference of three times the first number a

Nana76 [90]

Hey there!

Let's create a systems of equations using x and y.

4x+3y=15

3x-2y=7

We need to solve this using elimination. First, we need to multiply the first equation by 2/3 so that we can cancel out the y's when combining our equations.

2 2/3x+2y=10

3x-2y=7

Now we combine the equations...

5 2/3x=17

x=3

Now we can plug our x into the first equation to find y.

12+3y=15

y=1

Our numbers are 3 and 1.

I hope this helps!

3 0

3 years ago

Solve the following quadratic equation using the quadratic formula.

sdas [7]

$ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}$

<span> $5x^2-8x+5=0\to a=5;\ b=-8;\ c=5\\\\\Delta=(-8)^2-4\cdot5\cdot5=64-100=-36\\\\\sqrt\Delta=\sqrt{-36}=6i$

$x_1=\dfrac{-(-8)-6i}{2\cdot5}=\dfrac{8-6i}{10}=\dfrac{4-3i}{5}\\\\x_2=\dfrac{-(-8)+6i}{2\cdot5}=\dfrac{8+6i}{10}=\dfrac{4+3i}{5}$
</span>

6 0

3 years ago

Read 2 more answers