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Ugo [173]
3 years ago
13

A waterfall has a height of 900 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet pe

r second. The​ height, h, of the pebble after t seconds is given by the equation h equals negative 16 t squared plus 24 t plus 900. How long after the pebble is thrown will it hit the​ ground?
Mathematics
1 answer:
aliya0001 [1]3 years ago
7 0

Answer:

The pebble will hit the ground 8.29 second after it is thrown.

Step-by-step explanation:

Given that,

The height of the pebble after t seconds is given by the equation

h= -16t²+24 t+900.

When the pebble hit the ground, the height of the pebble will be zero.

So putting h=0 in the given equation.

0 = -16t²+24 t+900

⇒-4(4t²-6t-225)=0

⇒4t²-6t-225=0

Applying quadratic formula t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}, here a=4, b= -6 and c= -225.

\therefore t=\frac{-(-6)\pm\sqrt{(-6)^2-4.4.(-225)}}{2.4}

⇒ t = 8.29, -6.79

Since time can not negative.

∴t=8.29 seconds.

The pebble will hit the ground 8.29 second after it is thrown.

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An airplane climbs 100 feet during the first second after takeoff. In each succeeding second it climbs 100 feet more than it cli
tigry1 [53]

Answer:

15 seconds.

Step-by-step explanation:

∵ The distance covered by plane in first second = 100 ft,

Also, in each succeeding second it climbs 100 feet more than it climbed during the previous second,

So, distance covered in second second = 200,

In third second = 300,

In fourth second = 400,

............, so on....

Thus, the total distance covered by plane in n seconds = 100 + 200 + 300 +400......... upto n seconds

=\frac{n}{2}(2\times 100 + (n-1)100)  ( Sum of AP )

=\frac{n}{2}(200+100n-100)

=\frac{n}{2}(100+100n)

=50n+50n^2

Suppose the distance covered in n seconds is 12,000 feet,

\implies 50n+50n^2=12000

n+n^2=240

n^2+n-240=0

n^2+16n-15n-240=0

n(n+16)-15(n+16)=0

(n-15)(n+16)=0

\implies n=15\text{ or }n=-16

∵ n can not be negative,

Hence, after 15 seconds the plane will reach an altitude of 12,000 feet above its takeoff height.

6 0
3 years ago
Read 2 more answers
Two questions
melamori03 [73]

Use PEMDAS method to execute operations in the following order:

  1. Parentheses
  2. Exponents
  3. Multiplication
  4. Division
  5. Addition
  6. Subtraction

First equation:

12 + (38 - 18)2 = 12 + 20 × 2 = 52

Second equation:

(12)2 - 6(2 - 23) = 24 - 6(-21) = 24 + 126 = 150

Hope this helps.

5 0
3 years ago
Y=x^2+12x+35 into the form y=(x-h)^2+k
LiRa [457]

Answer:

y = (x + 6)² - 1

Step-by-step explanation:

So there are two ways of doing it, completing the square or partial factoring (which is what i prefer and will show)

so we will get x first:

x^2+12x

We are factoring x

x(x+12)

Now you do x=-12/2

x=-6

Now that you have x, you plg that back into the equation to get y

y= -6^2 +12(-6) +35

= 36-36+35

=-1

Put into vertex form

y = (x + 6)² - 1

4 0
2 years ago
By using sum or difference formulas, cos(π−x) can be written as
Liono4ka [1.6K]

We have cos( x - y ) = cosxcoy + sinxsiny <=> cos ( π - x ) = cosπcosx + sinπsinx <=> cos ( π - x ) = (-1)cosx + 0sinx = -cosx;

8 0
2 years ago
Justify the last two steps of the proof.
Georgia [21]
Statement 3:

NO and ON are the same line. They are congruent by the reflexive property (a line segment is a reflection of itself).

Statement 4:

Shape MNO and shape PON are congruent by side-side-side since:

side PN = side MO
side MN = side PO
side NO = side ON

Answer: Fourth option
3 0
3 years ago
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