The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative. plz show work

Answers

Answer 1

Answer:

The instantaneous velocity at t = 1 will be:

[tex]\frac{d}{dt}\left(-8-9t\right)=-9[/tex]

Step-by-step explanation:

Given the position of an object at a time [tex]t[/tex]

[tex]s\left(t\right)=-8-9t[/tex]

As we know that determining the derivative of the position function with respect to time t would give us the instantaneous velocity, so

[tex]\frac{ds}{dt}=\frac{d}{dt}\left(-8-9t\right)[/tex]

Applying the sum/difference rule:

[tex]\left(f\pm g\right)'=f\:'\pm g'[/tex]

[tex]\frac{ds}{dt}=-\frac{d}{dt}\left(8\right)-\frac{d}{dt}\left(9t\right)[/tex]

as

[tex]\frac{d}{dt}\left(8\right)=0[/tex]    ∵ [tex]\frac{d}{dx}\left(a\right)=0[/tex]

and

[tex]\frac{d}{dt}\left(9t\right)=9[/tex]   ∵ [tex]\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'[/tex]  and [tex]\frac{d}{dt}\left(t\right)=1[/tex]

so the expression becomes

[tex]\frac{ds}{dt}=-\frac{d}{dt}\left(8\right)-\frac{d}{dt}\left(9t\right)[/tex]

   [tex]=-0-9[/tex]

   [tex]=-9[/tex]

As the derivative is constant.

Therefore, the instantaneous velocity at t = 1 will be:

[tex]\frac{d}{dt}\left(-8-9t\right)=-9[/tex]

     


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Answer: 2 bags of soil

Step-by-step explanation:

A circle has radius 40 cm. Which of these is closest to its area, in square centimeters?

Answers

Answer:

251 cm2

Step-by-step explanation:

The area of the circle whose radius is 40 cm is 5026 cm².

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given that the radius of the circle is 40cm. Therefore, the area of the circle will be,

Area of the circle = π × Radius²

                             = π× (40cm)²

                             = 1600π cm²

                             = 5026.54 cm²≈ 5026 cm²

Hence, the area of the circle is 5026 cm².

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if it takes 50 cubes to fill up a rectangular prism, what would be the volume of the rectangular prism?

PLEASE HELP !

Answers

Answer:

50 unit^3

Step-by-step explanation:

you didnt give a unit, and i assumed the cubes are equal to one cubic of that unit, so cant really help

Answer:

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Step-by-step explanation:

82+9/3? find the answe using pemdas

Answers

Answer:

82+(9/3)

Division comes first.

9/3=3

82+3=85

85

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

PEMDAS

P - Parenthases

E - Exponents

M - Multiply

D - Divide

A - Add

S - Subtract

Using the order of opperations above, division comes before addition, so:

9 / 3 = 3.

Then you move on to the left:

3 + 82 = 85.

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Answers

Answer:

0.62, 0.60, Store B

Step-by-step explanation:

Store A is 0.62 per can

Store B is 0.60 per can.

The better deal is B

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Answers

Answer:

71 degrees

Step-by-step explanation:

Sum of three angles of triangle=180

Let's find the third angle

73+36=109

180-109=71

Vertical angles are congruent so x= angle 3

So x is 71 degrees

Answer:

79 degrees

Step-by-step explanation:

Remember: Triangles always add up to 180 degrees.

x is vertical to the missing angle in the triangle, which means x and the missing angle are equal.

to find the missing angle in the triangle, you add up the other angle measurements and subtract from 180.

36+73=109

180-109=71

The third mising angle is 71 degrees.

this means x is also 71.

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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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A building with a height of 6 m casts a shadow that is 8 m long while a taller building casts a 24 m long shadow. What is the height of the taller building?

Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

p : r = 5 : 2

Step-by-step explanation:

Expressing the ratios in fractional form, then

[tex]\frac{p}{r}[/tex] = [tex]\frac{p}{a}[/tex] × [tex]\frac{a}{b}[/tex] × [tex]\frac{b}{c}[/tex] × [tex]\frac{c}{r}[/tex]

  = [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{5}{1}[/tex] × [tex]\frac{3}{2}[/tex]

   = [tex]\frac{30}{12}[/tex]

  = [tex]\frac{5}{2}[/tex]

Thus ratio p : r = 5 : 2

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Answers

Answer:

sorry what do you write for B???

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Answers

Answer:

49Pi

Step-by-step explanation:

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A cyclist starts a journey from town A. He rides 10km north then 5km east and finally 10 km on a bearing of M45°E​

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Answer:

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Step-by-step explanation:

Which of the following expressions is equivalent to –6?

A.

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B.

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C.

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D.

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Answers

Answer:

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Step-by-step explanation:

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I'm not sure if it is A or B

Answer:

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Step-by-step explanation:

The graph below represents the price of sending picture messages using the services of a phone company. What is the constant of proportionality?

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Answers

Answer:

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Step-by-step explanation:

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Answer:

22

Step-by-step explanation:

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Answers

Answer:

1/2 pound brand has a lower price

Step-by-step explanation:

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The price of pears at a farm is $1.41 per pound. Which equation can be used to determine c, the total price of n pounds of pears? (1 point)

a
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c
c = 1.41 − n

d
c = 1.41n

Answers

Answer:

d

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Step-by-step explanation:

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Answers

Answer:

7

Step-by-step explanation:

we need to first find the area

4.5 x 4 = 18

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6+1 = 7

Answer:

7

Step-by-step explanation:

we need to first find the area

4.5 x 4 = 18

1.5 x 2 = 3

18 - 3 = 15

15/2.25 = 20/3

20/3 is 6.666666666666666666666666666666.....

6+1 = 7

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Step-by-step explanation:

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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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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Answer:

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Answers

Answer:

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Step-by-step explanation:

to solve for PQ, use the distance formula

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Paula has $54. She bought some pencils, each costing $0.75, and a paper ream for $2.50. She is left with $42.50 after buying pencils and the ream of paper. She uses the equation Syntax error from line 1 column 49 to line 1 column 73. Unexpected 'mathsize'. to find the number of pencils she bought. How many pencils did Paula buy?

Answers

Answer:

12 pencils

Step-by-step explanation:

let no. of pencils bought be x.

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Topic: algebraic equations

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

x = 17 and y = 8

Step-by-step explanation:

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8x - 31 = 6x + 3

Combine like terms

2x = 34

Divide both sides by two

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Answers

Answer:

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Step-by-step explanation:

Theres a website called triangle calculator and you put in three things wether its SSA or ASA or whatever and it gives you all the measurements. Good luck on your quizzes and tests :)

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Answer:

Step-by-step explanation:

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1.= 1
2.= -15
3.= -18
4.= -1
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6. = 22
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