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IrinaVladis [17]
3 years ago
10

The following expression represents the population of colony of penguins in Antarctica: P,= 17.2.3 P, is the penguin population,

and r is time in days. a. What is the population after 6 days? b. When will P, be 650 penguins?​
Mathematics
1 answer:
nikdorinn [45]3 years ago
6 0
55 hours is your answer
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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
3 years ago
B is located at (−5, 2).
Harman [31]

When (-5, 2) is reflected across the y-axis then it becomes (5, 2). When (-5, 2) is reflected across the x-axis, it becomes (-5, -2)

I hope this helps out!

6 0
3 years ago
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24. 17 is 40% of what number?
EastWind [94]

Answer:

9.7

Step-by-step explanation:

6 0
3 years ago
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What is the volume of thiss figure ?
allochka39001 [22]

Answer:

18 ft³

Step-by-step explanation:

7 0
3 years ago
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How do you solve 7n-2=6n-2n
pantera1 [17]
First combine like terms:
6n-2n = 4n
7n-2=4n
subtract 7n from both sides
7n-2=4n
-7n    -7n
-2=-3n
divide -2 on both sides.
n=1.5
7 0
3 years ago
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