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Sever21 [200]
3 years ago
10

What math operation determines the pattern? 48, 3, 45, -42?

Mathematics
1 answer:
34kurt3 years ago
8 0
Just subtract the following number from the preceding one.
48- 3= 45
3- 45= -42.
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Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is
Mamont248 [21]

Answer:

1)The rocket hit the ground at     x = \frac{5}{4}

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation  

                y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

             \frac{dy}{dx} = -2( 2x) +5(1) =  -4x +5

Equating zero

            \frac{dy}{dx} = 0

⇒      -4 x +5 =0

⇒      -4 x = -5

⇒          x = \frac{5}{4}

<em> The rocket hit the ground at     </em>x = \frac{5}{4}<em></em>

<u><em>Step(ii):</em></u>-

    \frac{dy}{dx}  =  -4x +5  ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

 \frac{d^{2} y}{dx^{2} }  = - 4(1)

The maximum height at x = \frac{-5}{4}

  y = -2 x² + 5 x + 7

 y = -2 (\frac{5}{4})^{2}  + 5 (\frac{5}{4} )  + 7

y = \frac{-2(25)+ 25 (16)+7(64)}{64}

y = \frac{798}{64} = 12.468 feet

<em>The maximum height of the rocket = 12.468 feet</em>

       

4 0
3 years ago
Reduce a ratio 3/4in: 3/16 ft
Dmitrij [34]

Answer:

4in : 1ft

Step-by-step explanation:

We start with:

3/4 in = 3/16 ft

This means that the length of 3/4 inches is the same as the length of 3/16 feet.

To reduce this, we can start by dividing by 3 in both sides of the equation:

(3/4)/3 in = (3/16)/3 ft

1/4 in = 1/16 ft

Now we can multiply both sides by 16:

16/4 in = 16/16ft

4 in = 1ft

now we reduced the ratio to:

4in : 1ft

5 0
3 years ago
Cheese sticks that were previously priced at "10 for $1" are now "4 for $1". Find each percent change.
statuscvo [17]

original quantity : 10 for $1

new quantity: 4 for $1

now we have to find each percent change

10-4=6

6÷100=0.06

0.06=6%

the quantity went down 6%

6 0
3 years ago
What is the approximate diameter of a sphere with a volume of 268cm3
kogti [31]

Answer:

diameter ≈15.6

Step-by-step explanation:

To solve this;

volume of a sphere = 4/3 πr³

From the question given;

volume of the sphere = 268    

lets substitute   and solve for r

volume of sphere = 4/3 πr³

268 = 4/3 × 3.14 × r³

268 =4.19 × r³

Divide both-side of the equation by 4.19

268/4.19 = r³

63.96 = r³

Take the cube root of both-side

∛63.96 = r

7.8 ≈ r

but diameter = 2r = 2×7.8 =15.6

8 0
3 years ago
What is the value of z in the equation 2(4z − 5 − 3) = 166 − 46?
Vera_Pavlovna [14]
Z = 17.
2(4z -8) = 120
8z -16 = 120
z -2 = 15
z = 17
3 0
3 years ago
Read 2 more answers
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