MATHEMATICS HIGH SCHOOL

A surveyor find that the cross section of the bottom of a circular pound has the shape of a parabola. The pond is 24 feet in diameter. The middle of the pond is the deepest part at 8 feet deep. At a point 2 feet from shore the water is 3 feet deep. How deep is the pond at a point 6 feet from shore?

Answers

Answer 1
Answer:

Answer:

2.32 feet

Step-by-step explanation:

Given;

The cross section of the bottom of a circular pound has the shape of a parabola

Now,

For the circular parabola, the equation is given as:

y² = 4ax

here,

y is the depth

x is the horizontal distance from the center

a is the constant

also,

at diameter of the pond = 24 feet

and,

at x = 0 ; y = 8 feet

now,

the point 2 feet from the shore with respect to the center of the pond = radius of the pond - The distance from the shore

= \frac{\textup{24}}{\textup{2}} - 2 = 10 feet

thus,

at x = 10 feet ; y = 3 feet

thus,

we have

the equation as:

3² = 4a × 10

or

0.9 = 4a

or

a =  0.225

therefore,

we get the equation as;

y² = ( 4 × 0.225 ) × x

and, for point  6 feet away from the shore, i.e \frac{\textup{24}}{\textup{2}} - 6 = 6 feet away from the center

we have

y² = ( 4 × 0.225 ) × 6

or

y² = 5.4

or

y = 2.32 feet   (negative value is neglected as the depth cannot be negative)
Answer 2
Answer:

Answer:

I wanna say 48 squared feet

Step-by-step explanation:

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If a point is on the perpendicular bisector of a segment, then it is:A. the midpoint of the segment.
B. equidistant from the endpoints of the segment.
C. equidistant from the midpoint and one endpoint of the segment.
D. on the segment.

Answers

To create a perpendicular bisector of a segment, it is a line drawn through the midpoint of the segment. Although one would immediately think that (A) would be the answer, just because a point is found on the perpendicular bisector, doesn't mean that it is immediately the midpoint. Although the midpoint is definitely found on the segment, there are numerous other points found on the segment. The midpoint is a point equidistant to both endpoints. Since the bisector passes through the midpoint, then any point on the bisector is equidistant to both endpoints. Therefore, the correct answer is B.

Answer:

B

Step-by-step explanation:

Jerry makes $40,000 a year working at a nearby factory. He gets two weeks paid vacation per year, plus five other paid holidays. He wants to figure out his per-diem (daily) pay, so he divides 40,000 by 365, which yields $109.59. Is this the correct answer?

Answers

Answer:

Vacation pays are not included in salaries. Therefore, Jerry's calculation is wrong.

Step-by-step explanation:

Given is :

Jerry makes $40,000 a year working at a nearby factory.

He gets two weeks paid vacation per year, plus five other paid holidays.

So total paid holidays become = 14+5=19 days

Subtracting 19 from 365 days and assuming that Jerry works for 365 days a year.

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So, his per day salary will be = (40000)/(346)= 115.60

Vacation pays are not included in salaries. Therefore, Jerry's calculation is wrong.

What is the value of the expression below?

|-12|

Answers

Answer:

the absolute value is 12

Step-by-step explanation:

the absolute value is 12 since that is the distance from 0.

Answer:

12

Step-by-step explanation:

The absolute value is the distance of a number to zero, which is always a positive number. |-12| is 12 units away from zero and therefore, the answer is 12.

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

Answers

The answer is 4x cm < h < 10x cm.

The third side of the triangle is greater than the difference of the lengths of the other two sides (h > 7x cm - 3x cm) and it is less than the sum of the lengths of the other two sides (h < 7x cm + 3x cm). Therefore:
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This can be expressed as:
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4. A Plane

Answers

Answer:

2) An angle is the correct option.

Step-by-step explanation:

Given  :  Two rays that intersect at a common endpoint.

To find : Which represents two rays that intersect at a common endpoint.

Solution : We have given

Two rays that intersect at a common endpoint.

Angle : An angle is the space between two lines that meet each other ,When two lines meet at a point.

Therefore, 2) An angle is the correct option.
From my understanding of mathematics I got the 2nd answer to be correct. Sorry, if I got this wrong I'm new at this.

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Answers

Hello There!

Mean: Average number in a set of data.

STEP 1: Add up all the numbers in the set of data. In this case, we would add

66 + 85 + 98 = 249

STEP 2: Divide the sum by the number of digits you added. We would divide 249 "sum of numbers" by 3 "number of digits" and would get a quotient of 83.

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83; add all the numbers,divide that by 3
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