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expeople1 [14]
3 years ago
13

A waterfall has a height of 1900 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 12 feet p

er second. The height, h, of the pebble after t seconds is given by the equation h=-16t^2+12t+1900. How long after the pebble is thrown will it hit the ground?
Mathematics
1 answer:
saw5 [17]3 years ago
7 0

Answer:

Step-by-step explanation:

h is the height of the pebble after a certain amount of time has gone by. Since we are told to find that time when the pebble is on the ground, we say that h = 0 since the height of something on the ground has no height at all. Then factor the quadratic.

-16t^2+12t+1900=0

Throw that into the quadratic formula or however you were taught to factor irrational quadratics (maybe completing the square?) to get that

t = 11.27869 sec and t = -10.52869 sec

Since we all know that time will never carry a negative value, we will disregard it and go with 11.27869 seconds. Not sure to where you are told to round.

You might be interested in
1/8-(-5+3/4)=x+(-1/4)
-BARSIC- [3]

Answer:

x = 37 /8

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in:
Studentka2010 [4]

Answer:

$1500

6% interest

use the formula...

P(1+(r/100))^n

where P=initial amount

r=interest rate

t=time period elapsed

so ... for 5 years we get

$1500(1+(6/100))^5 = $1500(1.06)^5 = 2007.3383664

for 10 years

1500(1.06)^10 = 2686.271544814228043264

468 months = 39 years

1500(1.06)^39=14555.261231781943250017719606544

3 0
2 years ago
Read 2 more answers
Find the diameter of the circle with the given circumference use 3.14 C=18
algol [13]
The formula for the circumference of a circle is pi * r * 2

First we solve for r (the radius)
pi*r*2 = C
pi*r*2 = 18

Divide 18 by 2
pi*r = 9

Then divide 9 by 3.14
pi= 9/3.14 which is 2.866

The diameter is 2 times length of the radius so multiply 2.866 by 2
The diameter is about 5.732
(And you can round of course)

Hope that helped
3 0
3 years ago
A salesman is paid a salary of $2500 per month and a commission of 10% on all sales above $7000. Calculate his gross salary if h
Verizon [17]

Answer:

$4150

Step-by-step explanation:

Given data

Salary= $2500

Commission= 10%

Sales=  $16500

Let us find the amount of the commission made

=10/100*16500

=0.1*16500

=$1650

Hence the total amount made for the month is

=commission + salary

=1650+2500

=$4150

3 0
2 years ago
Can someone give me an example on a Riemann Sum and like how to work through it ? I want to learn but I don’t understand it when
Georgia [21]

Explanation:

A Riemann Sum is the sum of areas under a curve. It approximates an integral. There are various ways the area under a curve can be approximated, and the different ways give rise to different descriptions of the sum.

A Riemann Sum is often specified in terms of the overall interval of "integration," the number of divisions of that interval to use, and the method of combining function values.

<u>Example Problem</u>

For the example attached, we are finding the area under the sine curve on the interval [1, 4] using 6 subintervals. We are using a rectangle whose height matches the function at the left side of the rectangle. We say this is a <em>left sum</em>.

When rectangles are used, other choices often seen are <em>right sum</em>, or <em>midpoint sum</em> (where the midpoint of the rectangle matches the function value at that point).

Each term of the sum is the area of the rectangle. That is the product of the rectangle's height and its width. We have chosen the width of the rectangle (the "subinterval") to be 1/6 of the width of the interval [1, 4], so each rectangle is (4-1)/6 = 1/2 unit wide.

The height of each rectangle is the function value at its left edge. In the example, we have defined the function x₁(j) to give us the x-value at the left edge of subinterval j. Then the height of the rectangle is f(x₁(j)).

We have factored the rectangle width out of the sum, so our sum is simply the heights of the left edges of the 6 subintervals. Multiplying that sum by the subinterval width gives our left sum r₁. (It is not a very good approximation of the integral.)

The second and third attachments show a <em>right sum</em> (r₂) and a <em>midpoint sum</em> (r₃). The latter is the best of these approximations.

_____

<u>Other Rules</u>

Described above and shown in the graphics are the use of <em>rectangles</em> for elements of the summation. Another choice is the use of <em>trapezoids</em>. For this, the corners of the trapezoid match the function value on both the left and right edges of the subinterval.

Suppose the n subinterval boundaries are at x0, x1, x2, ..., xn, so that the function values at those boundaries are f(x0), f(x1), f(x2), ..., f(xn). Using trapezoids, the area of the first trapezoid would be ...

  a1 = (f(x0) +f(x1))/2·∆x . . . . where ∆x is the subinterval width

  a2 = (f(x1) +f(x2))/2·∆x

We can see that in computing these two terms, we have evaluated f(x1) twice. We also see that f(x1)/2 contributes twice to the overall sum.

If we collapse the sum a1+a2+...+an, we find it is ...

  ∆x·(f(x0)/2 + f(x1) +f(x2) + ... +f(x_n-1) + f(xn)/2)

That is, each function value except the first and last contributes fully to the sum. When we compute the sum this way, we say we are using the <em>trapezoidal rule</em>.

If the function values are used to create an <em>approximating parabola</em>, a different formula emerges. That formula is called <em>Simpson's rule</em>. That rule has different weights for alternate function values and for the end values. The formulas are readily available elsewhere, and are beyond the scope of this answer.

_____

<em>Comment on mechanics</em>

As you can tell from the attachments, it is convenient to let a graphing calculator or spreadsheet compute the sum. If you need to see the interval boundaries and the function values, a spreadsheet may be preferred.

8 0
3 years ago
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