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lidiya [134]
2 years ago
13

When a stone is dropped from a height, the time taken to fall, t, is proportional to the square root of the distance fallen, d.

Mathematics
1 answer:
DanielleElmas [232]2 years ago
5 0

Step-by-step explanation:

We know that in kinematics we can write the formula for uniformly accelerated bodies:

s = 1/2 a t^2 + v0 t + s0

In our case s0 (initial deployment)  = 0m and v0 (initial velocity) = 0

So:

s = 1/2 a t^2

Now we isolate t:

t = \sqrt[2]{\frac{2s}{a} }

All proportionalities are obvious.

Note: I forgot to say that a, the acceleration, is the gravitational acceleration. It can be g or -g depending on how you'll choose the reference system.

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Pls help i am on a timer
stich3 [128]

Answer:

x = 1 + \sqrt{2} \ \ or \ 1- \sqrt{2}

Step-by-step explanation:

Given;

x² - 2x - 1 = 0

Solve by completing the square method;

⇒ take the constant to the right hand side of the equation.

x² - 2x = 1

⇒ take half of coefficient of x = ¹/₂ x -2 = -1

⇒ square half of coefficient of x and add it to the both sides of the equation

x^2 +  (-1)^2 = 1 + (-1)^2

(x-1)^2 = 1 + 1\\\\(x-1)^2 = 2\\\\

⇒ take the square root of both sides;

x-1 = +/- \ \ \sqrt{2} \\\\x = 1 + \sqrt{2} \ \ or \ 1- \sqrt{2}

Therefore, option B is the right solution.

3 0
2 years ago
Can someone help me solve this?
Dovator [93]

Answer:

5 felt pads.

7 cards.

Step-by-step explanation:

Remark

  • The total number of items is 12
  • So let the felt sheets be x
  • Let the cards = y

Equations and Solution

x + y = 12

Now the price is 7.75 that she has to pay for the 12 items. She wants to come back with 0 dollars.

0.5x + 0.75y = 7.75             Multiply this equation by 2

x + 1.5y = 15.50                    write the first equation underneath and subtract.

<u>x +    y =   12</u>

      .5y =  3                          Divide by 0.5

y = 3/0.5

y = 7

So she can get 7 cards.

x + y = 12

x + 7 = 12

x = 12 - 7

x = 5

So she can buy 5 felt pads.

8 0
2 years ago
1-25. Given f(x) =- 2/3x +3 and g(x) = 2x2 - 5, complete parts (a) through (f).
Korolek [52]

Answer:

When f or g are equivalent to a number you are solving for x. For example b, d, e, f. In the equation g(x) =2x2-5 I assumed 2 was a typo. So, if it's incorrect, please use same steps and just adjust the solution.

Step-by-step explanation:

f(x)=-\frac{2}{3x}+3

a) f(3)=-\frac{2}{2(3)} +3

           =-\frac{1}{3}+3 =\frac{-1+6}{3} =\frac{5}{3}

b) f(x)=-5

      -5=-\frac{2}{3x}+3

      -8=-\frac{2}{3x}

  -24x=-2

        x=\frac{1}{12}

g(x)=2x-5

c) g(-3)=2(-3)-5

               =-6-5

               =-11

d) g(x)=-7

      -7=2x-5

      -2=2x

        x=-1

e) g(x)=8

        8=2x-5

       12=2x

        x=6

f)  g(x)=9

         9=2x-5

        11=2x

         x=\frac{11}{2}

3 0
3 years ago
Reggie earns $12.65 per hour and works 38 hours per week. How much does he warm in a week before taxes are taken out?
nexus9112 [7]
Reggie earns $480.70 a week before taxes are taken out.
6 0
3 years ago
0.5x -2 = 1.5x + 0.15
frutty [35]

Answer: x=−2.15

Step-by-step explanation : Alright Let's solve your equation step-by-step.

0.5x−2=1.5x+0.15

Step 1: Subtract 1.5x from both sides.

0.5x−2−1.5x=1.5x+0.15−1.5x

−x−2=0.15

Step 2: Add 2 to both sides.

−x−2+2=0.15+2

−x=2.15

Step 3: Divide both sides by -1.

−x

−1

=

2.15

−1

x=−2.15<em>        hope this helped!- Alex</em><u> </u>

8 0
3 years ago
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