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pantera1 [17]
3 years ago
12

A bridge constructed over a bayou has a supporting arch in the shape of an inverted parabola. Find the equation of the parabolic

arch of the length of the road over the arch is 100 meters and the maximum height of the arch is 40 meters.
Mathematics
1 answer:
babymother [125]3 years ago
6 0

Answer: f(x) = -0.016x² + 1.6x

Step-by-step explanation:

If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.

So, we have

(0,0) (50,40) (100,0)

A quadratic function is always on the form: f(x) = ax² + bx + c

0 = a0² + b0 + c

40 = a50² + b50 + c

0 = a100² + b100 + c

0 = a0² + b0 + c → c = 0 ∴

40 = a50² + b50

0 = a100² + b100

_________________________

2500a + 50b = 40 (*2)

10000a + 100b = 0

_________________________

5000a + 100b = 80

10000a + 100b = 0 (-)

__________________________

-5000a = 80

-a=80/5000

a=-0.016

∴

2500a + 50b = 40

2500.(-0.016) + 50b = 40

-40 + 50b = 40

50b = 80

b = 80/50

b = 1.6

This way f(x) = -0.016x² + 1.6x

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algol13

Answer:

Step-by-step explanation:

Remark

The formula for this is

Heat = m * c * Δt

Givens

Heat = unknown

m = 200 grams

c = 4.184 Joules / grams oC

Δt = the change in temperature = 35.7 - 22.3 = 13.4

Solution

Heat = 200 * 4.184 * 13.4

Heat = 11213 Joules

Heat = 11.2 Kj

It's hard to get the correct number of sig digs because the 200 is not qualified in any way.

Part 2.

This can really puzzle you until you know that heat given up = the heat taken on. The heat taken on was 11.2 Kj. The Butane lighter must have given that heat on.

Heat of Combustion = Heat Given Up / Number grams burned.

Heat of Combustion = 11.2 Kj / 0.23 grams

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8 0
3 years ago
Which equation does the graph represent?
Art [367]

Answer:

It is the second answer

Step-by-step explanation:

The standard form of an ellipse is

x^2/a^2 + y^2/b^2  or x^2/b^2 + y^2/a^2 = 1

If the x is the main axis we use the first form.  If the y is the main axis we use the second form.  We will use the second form.

our a is 3 and our b is 4

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3 0
2 years ago
Diana sold $150.00 worth of products and earns a commission of 3.5%. How much did she earn in commission?
ioda

Answer:

$5.25

Step-by-step explanation:

Take $150.00 times 3.5% to get $5.25

150(.035) = 5.25

4 0
3 years ago
Read 2 more answers
Write the equation of the line that passes through the point (3,5) and is perpendicular to the line y=3.
3241004551 [841]

Answer:

x = 3

Step-by-step explanation:

y = 3 is the equation of a horizontal line parallel to the x- axis.

A line perpendicular to it must therefore be a vertical line parallel to the y- axis with equation

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (3, 5) with x- coordinate 3 , thus

x = 3 ← equation of perpendicular line

6 0
3 years ago
What is the solution of the following system
AleksAgata [21]

Step-by-step explanation:

8x + 14y = 4 ...1

-6x - 7y = -10 ...2

...2 × 2 in 2 sides of the equation

-12x -14y = -20 ...3

...1 + ...3

8x + 14y +(-12x -14y) = 4 +(-20)

8x + 14y - 12x -14y = 4 - 20

-4x = -16

x = (-16)/(-4)

= 4

replace x in ...1 or ...2 you will reserve y value

and answer in the term of (x,y)

4 0
3 years ago
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