A waterfall has a height of 1700 feet. A pebble is thrown upward from the top of the falls with an initial velocity of  feet per second. The height of the pebble h in feet after t seconds is given by the equation h=-16t^2+24t+1700 . How long after the pebble is thrown will it hit the​ ground?


PLEASE HELPPPPP

Answers

Answer 1

Answer:

[tex]t = 11.085[/tex]

Step-by-step explanation:

The expression is given as:

[tex]h=-16t^2+24t+1700[/tex]

Required

Determine how long it will hit the ground

When the pebble is on the ground, this implies that h = 0

So, we have that:

[tex]h=-16t^2+24t+1700[/tex] becomes

[tex]0=-16t^2+24t+1700[/tex]

Reorder

[tex]-16t^2+24t+1700 = 0[/tex]

Multiply through by -1

[tex]16t^2-24t-1700 = 0[/tex]

Solve using quadratic formula [tex]ax^2 + bx + c = 0[/tex]:

[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

Where

[tex]a = 16[/tex]   [tex]b = -24[/tex]    [tex]c = -1700[/tex]

So, we have:

[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]t = \frac{-(-24) \± \sqrt{(-24)^2 - 4*16*(-1700)}}{2*16}[/tex]

[tex]t = \frac{24 \± \sqrt{576 + 108800}}{32}[/tex]

[tex]t = \frac{24 \± \sqrt{109376}}{32}[/tex]

[tex]t = \frac{24 \± 330.72}{32}[/tex]

[tex]t = \frac{24 + 330.72}{32}[/tex] or [tex]t = \frac{24 - 330.72}{32}[/tex]

[tex]t = \frac{354.72}{32}[/tex] or [tex]t = \frac{-306.72}{32}[/tex]

[tex]t = 11.085[/tex] or [tex]t = -9.585[/tex]

But time can't be negative.

So: [tex]t = 11.085[/tex]

Hence, it will take 11.085 seconds to hit the ground


Related Questions

Solve: 3x – 8 = 6(1 – 2x) + 16

Answers

Answer:

x=2

Step-by-step explanation:

3x-8=6-12x+16

3x+12x=22+8

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It's right bc I took the test and got it 100%

Solve the following system of equations.
2x+y = 3
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Answers

Answer:

y=1    x=1

Step-by-step explanation:

2x + y = 3

x = 2y - 1  

.

It looks like I could substitute the x=2y-1. Into 2x+y=3

2(2y-1)+y=3

4y-2+y=3

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Y =1

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Good luck!!

Rita charges $60 for 5 tutoring session. What is the cost per session?

Answers

Answer:

$12=$60÷5. 12dollars is the answer

simplify each of the following ratios.
e) 2/3 : 3/2 : 5/8​

Answers

Answer:

32/45

Step-by-step explanation:

2/3 : 3/2 : 5/8

Remember, a ratio and a fraction are both division. Therefore you can rewrite the problem like so:

2/3 ÷ 3/2 ÷ 5/8

Dividing fractions is the same as multiplying them by the reciprocal.

2/3 * 2/3 * 8/5

Now simplify:

32/45

32 and 45 have no common factor, hence the final answer is 32/45

Answer:

32/45

Step-by-step explanation:

2/3 : 3/2 : 5/8.

Remember, a ration and a fraction are both division. Therefore you can rewrite the problem like so:

2/3 ÷ 3/2 ÷ 5/8

Dividing fractions is the same as multiplying them by the reciprocal.

2/3 * 2/3 * 8/5

Now simplify:

32/45

32 and 45 have no common factor, hence the final answer is 32/45

May I have brainliest please? :)

Someone help me please.


Find the measure of 0.(to the nearest tenth)

Answers

Answer:

I don't believe any are correct, from what I know its 36.9.

Step-by-step explanation:

sorry I know this isn't help full good luck!

Calculate the TOTAL mechanical energy of a pendulum (mass 4 kg) as it swings from its highest point to its lowest point. Use your equations for gravitational potential energy and kinetic energy to determine these values based on the data given below. Total energy is the sum of gravitational potential energy and kinetic energy. In this problem, round gravity to: g = 10 m/s2.
**** BONUS POINTS ADDED FOR ANSWER****

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Answer: its should be 2.0 and 4.5 on it ✨

Step-by-step explanation: trusttt me

The graph models the path of a soccer ball, showing the vertical distance, in yards, as a function of the horizontal distance, in yards.

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let f(x)=-3x^3 + 21x^2 + 4x+4. what is the valu of f(-4)? can anyone answer this please

2 is less than or equal to x is less than or equal to 4

The State Furniture Company makes tables. The number of tables made on a given day is shown by the expression 20h , where h is the number of hours the company is open that day. What is a reasonable set of values for h?

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Answer:

z

Step-by-step explanation:

sdggsgsgdd

Answer:

im sorry

Step-by-step explanation:

i ned help on the same question

23) Solve for :
-3x + 14 > -13.

Answers

Answer:

x < 9

Step-by-step explanation:

-3x + 14 > -13

-3x > -13 - 14

-3x > -27

-x > -27 ÷ 3

-x > -9

x < 9

Answer:

explaination. a ah. is

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Jonathan bought 2 bagels and 5 muffins for
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Answers

Answer:

Bagels= 1$ and Muffins= 2$

Step-by-step explanation:

if Caleb bought 3 bagels for 1$ each that is 3$ and 2 muffins for 2$ each is 4$ and 4+3=7$

if Jonathan bought 2 bagels for 1$ each that is 2$ and 5 muffins for 2$ each is  10$ and 10+2=12$

Find the reciprocal of 4/11​

Answers

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The diameter of a circle is 20 centimeters. What is the radius?

Answers

Answer:

10

Step-by-step explanation:

radius is the middle point of a circle, therefore divide it in half.

Find the difference -1/8-(-6 7/8)

Answers

Answer:

The difference is 6 3/4

Step-by-step explanation:

Plz give brainliest I am trying to rank up.

if f(x)= 1/x+2, what is f(3+h)?

A. 1/ (x+2)(3+h)
B. (3+h)/(x+2)
C. 1/(3+h)
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Answers

Answer:

D. 1/h+5

Step-by-step explanation:

f(x)=1/3+h+2

F(x)=1/h+5

They who answer first, brainliest is thy prize

Answers

Answer:

Quotient: 3x+3

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Step-by-step explanation:

Use polynomial long division

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Answer:

A=[tex]\pi r^{2}[/tex]

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Answers

Answer:

The solution is:

[tex]\frac{0.5^{10}}{0.5^7}=0.125[/tex]

Step-by-step explanation:

Given the expression

[tex]0.5^{10}\div 0.5^7[/tex]

Solving

[tex]\frac{0.5^{10}}{0.5^7}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]

so

[tex]\frac{0.5^{10}}{0.5^7}=0.5^{10-7}[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:10-7=3[/tex]

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Therefore, the solution is:

[tex]\frac{0.5^{10}}{0.5^7}=0.125[/tex]

6/7 ÷ 1/6



this is for flash cuz hes smart​

Answers

Answer:

5.1

Step-by-step explanation:

Major League Baseball fans eat about 21 million hot dogs every season. There are a total of 2,430 games each season. About how many hot dogs are eaten at each game?

Answers

Answer:

About 8642

Step-by-step explanation:

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3 + 2x -y =0
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Answers

Answer:

(-1, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Solving systems of equations using substitution/eliminationSolving systems of equations by graphing

Step-by-step explanation:

Step 1: Define systems

3 + 2x - y = 0

-3 - 7y = 10x

Step 2: Rewrite systems

3 + 2x - y = 0

Add y to both sides:                    3 + 2x = y

Step 3: Redefine systems

y = 2x + 3

-3 - 7y = 10x

Step 4: Solve for x

Substitution

Substitute in y:                     -3 - 7(2x + 3) = 10xDistribute -7:                        -3 - 14x - 21 = 10xCombine like terms:            -14x - 24 = 10xAdd 14x on both sides:        -24 = 24xDivide 24 on both sides:     -1 = xRewrite:                                 x = -1

Step 5: Solve for y

Define original equation:                    -3 - 7y = 10xSubstitute in x:                                     -3 - 7y = 10(-1)Multiply:                                                -3 - 7y = -10Add 3 to both sides:                            -7y = -7Divide -7 on both sides:                      y = 1

Step 6: Graph

Check the solution set.

Help

The diameter of the circle is 8in

Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Answer:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Which value is a solution of the inequalityx∕5 + 2 ≤ 6?
A) 
x = 49

B) 
x = 15

C) 
x = 37

D) 
x = 21

Answers

Answer:

B

Step-by-step explanation

the answer comes to [tex]x\leq 20[/tex] and 15 is the only answer below 20

Answer:

B. x = 15

Step-by-step explanation:

Firstly we simplify the inequality, so we have x on the left side, and every number on the right side[tex]\frac{x}{5}+2\leq 6\\ \frac{x}{5}+2-(2)\leq 6-(2)[/tex] so we take away 2 on both sides[tex]\frac{x}{5}\leq 4[/tex] now this is the same as [tex]\frac{1}{5}*x\leq 4[/tex] Now we multiply by 5 on both sides [tex]5*\frac{1}{5}*x\leq 5*4[/tex] which is [tex]\frac{5}{5}*x \leq 20[/tex] which is simply [tex]x \leq 20[/tex] since 5 divide by 5 is 1 and 1 times x is xSo the inequality [tex]x \leq 20[/tex] means "every number for x that is less than or equal to 20"Now from the list, the only number that fits is 15. So that's our answer

its a funny shape ;) but if you answer correctly ill give brainliest

Answers

Answer:

Rectangle

Step-by-step explanation:

2 cadenas de operaciones distintas cuyo resultado sea 325 utilizando las 4 operaciones básicas

Answers

Answer:

Dos cadenas de operaciones matemáticas distintas, cuyo resultado sea 325 utilizando las 4 operaciones básicas (suma, resta, multiplicación y división) pueden ser las siguientes:

((2 + 8) / 2) x 65 = 325

10 / 2 x 65 = 325

5 x 65 = 325

325 = 325

((300 / 10) x 15) - 130 + 5 = 325

(30 x 15) - 130 + 5 = 325

450 - 130 + 5 = 325

325 = 325

The 2 different chains of operations resulting in 325 using the 4 basic operations are;

[tex]=[(500 +(450\times2)) - 100]\div4\\=[(500+900)-100]\div4\\=[1400-100]\div4\\=1300\div4\\=325[/tex]

and;

[tex]=[(140 +125)-135)] \div 2]\times5\\=[(265-135)\div2] \times 5\\=(130\div2)\times 5\\=65\times 5\\=325[/tex]

According to the question, we are to find 2 different chains of operations resulting in 325 using the 4 basic operations.

The four basic operations are addition(+), subtraction(-), division(÷) and multiplication (×).

One of the chains of operation will be:

[tex]=[(500 +(450\times2)) - 100]\div4\\=[(500+900)-100]\div4\\=[1400-100]\div4\\=1300\div4\\=325[/tex]

Another chain of reaction will be:

[tex]=[(140 +125)-135)] \div 2]\times5\\=[(265-135)\div2] \times 5\\=(130\div2)\times 5\\=65\times 5\\=325[/tex]

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Solve for X. Send help please!!

Answers

Answer:

x=118

Step-by-step explanation:

180-62=118

hope it helps !

X=118
Straight Line Contains 180°
Subtract 62 from 180 leaves you with 118
Therefore X=118

Y=-x-6 with slope graph Please help me answer this

Answers

Answer: the slope of the graph is -1

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