A particle moves along the x-axis so that time t>0 the position is given by x(t)=0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1. What is the velocity of the particle at the first instance the particle is at the origin?

Answers

Answer 1

The velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0.

Since the particle is at the origin when x(t) = 0, we have:

[tex]0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1 = 0[/tex]

Using numerical methods or graphing the equation, we find that the roots are approximately t ≈ -0.618, t ≈ 1.532, t ≈ 3.143, and t ≈ 2.944.

Since t > 0, the first instance the particle is at the origin corresponds to t ≈ 2.944 (the smallest positive real root).

Now, to find the velocity of the particle at this instance, we need to find the derivative of the position function x(t) with respect to time t, which gives us the velocity function v(t):

v(t) = dx/dt

[tex]v(t) = d/dt (0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1)\\v(t) = 2t^3 - 4.5t^2 - 4t + 6[/tex]

Now, we can find the velocity at t ≈ 2.944:

[tex]v(t = 2.944) = 2(2.944)^3 - 4.5(2.944)^2 - 4(2.944) + 6[/tex]

v(t ≈ 2.944) ≈ 16.885

So, the velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

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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:

2/3 ÷ 1/3 =

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Answer:

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Answer:

It's kind-of blurry, can you copy-paste the questions?

Step-by-step explanation:

The lengths of the sides of a triangle are square root 139, square root 73, and 6. Classify the trianglo as “acute", "right", or "obtuso".
Choose the correct type of triangle below.
O acute
obtuse
Oright

Answers

Answer:

It's obtuse.

Step-by-step explanation:

Mumble. Smells al-kashi laws of cosine to me.

[tex]a^2-b^2-c^2 = -2bc cos\alpha\\b^2-c^2-a^2=-2ca cos \beta\\c^2-a^2-b^2=-ab cos \gamma[/tex]

Now, we don't need to calculate the RHSs, and then:

If at least one of the three LHSs is greater than zero, the triangle is obtuse

If at least one is zero, it's a right triangle (pythagorean theorem anyone?)

if all three numbers are less than zero, the triangle is acute

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Rachel has a $23,000 six year loan with APR of 7.25%

Answers

Answer:6,000 is the answer

Step-by-step explanation:

What percent of the bottle of apple juice is water?

Answers

percent of water is: 32/80*100= 40%

I want you to set a goal of signing up 25% of your new customers for our new service feature." Representative: "If I get 96 new customers that means I have to get

Answers

If he get 96 new customers that means he will have to sign 24 customers

for the new service features.

The deal is to get 25% of your new customer to sign the new service features.

When the new customers are 96 in numbers, the number of individuals(25%

of the new customers) to be signed for the new features can be calculated as

follows:

New customer to sign for the new features = 25% of 96

New customer to sign for the new features = 25 / 100 × 96

New customer to sign for the new features = 2400 / 100

New customer to sign for the new features = 24

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This means that if I get 96 new customers that means I have to get 24 new customers

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Since we have 96 new customers, hence the total amount of new customers needed will be expressed as:

= 25% of 96

= 0.25 * 96

= 24 new customers

This means that if I get 96 new customers that means I have to get 24 new customers

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Find each missing measure in the diagram below.
EF=(
m2F=d
3.
232
18 in
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E
E

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Answer:

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Step-by-step explanation:

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Answers

Answer:

147 seconds to get to the shore(after the 49 seconds)

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

to find how many mousetraps per person, we need to divide 48 by 6, which gives us 8.

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Answers

∆HFE is similar to ∆HFG and ∆ HEG (they all are right triangles and have the same, shape.)

The given triangle ΔHFE is similar to triangle GFH and triangle GHE.

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Similar triangles are two triangles that have the same shape but may differ in size. They have corresponding angles that are congruent and corresponding sides that are proportional.

Here,

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Answers

Answer:

Slope = -2

Step-by-step explanation:

Given the two points, (-4, 10) and (0, 2), the error in the given problem is the incorrect substitution of values into the formula. It should have been formatted as follows:

Let (x₁, y₁) = (-4, 10)

    (x₂, y₂) = (0, 2)

The formula for solving for the slope of the line is:

m = (y₂ - y₁)/(x₂ - x₁)

where m represents the slope of the line.

Substitute the given values into the formula to solve for the slope:

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Answers

Answer:

18.4 cm

Step-by-step explanation:

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8th Grade Math
Janelle is saving $6 per week to buy a new bike. she has $85 on week five. How do you write this in slope intercept form?

Answers

Let y-axis saving
X-axis weeks
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If at week 5 she has 85
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Wjejjejjsnsbbnxkskakksnsnsnznsmsnndndd

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Answer:

whats

Step-by-step explanation:

[tex]\orange{\rule{40pt}{555555pt}} \green{\rule{40pt}{555555pt}} \blue{\rule{40pt}{555555pt}} \red{\rule{40pt}{555555pt}}\pink{\rule{40pt}{555555pt}}\yellow{\rule{40pt}{555555pt}}[/tex]

1.
What is the sum of
4 |
22 (1 point)
+
+
3
011
o

IN IN NII am |
0
0 0

Answers

Answer:

B. One whole number one over two. 1½

The perimeter of a rectangle is 78 units. The length is 5 units more than the width. Find the length.

Answers

Answer:

W = 8.5 units; L = 30.5 units

Step-by-step explanation:

The formula for the perimeter of a rectangle is P = 2L and 2W, where L and W represent the length and the width respectively.  Here, L = 3W + 5.  Adapting the formula P = 2L and 2W, we get: 78 = 2L + 2W  =  2(3W + 5) + 2W, or 6W + 10 + 2W = 78, or 8W = 68, or W = 68/8 = 8.5 units If W = 8.5 units, then L = 3(8.5 units) + 5 units = 30.5 units  

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Answers

Answer:

I think that you should take your time and answer, every one can help you

Step-by-step explanation:

Step-by-step explanation:

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6. Five more than eight times a number is greater than four less than
seven times the number. Write an inequality to represent this relationship.
Then solve the inequality. *

Answers

8x+5 > 7x -4

X+5> -4

X> -9

Answer:

8x + 5 > 7x - 4

x > -9

Step-by-step explanation:

Five more than eight times a number

8x + 5

is greater than

>

four less than seven times the number

7x - 4

All together:

8x + 5 > 7x - 4

-------------------------------

Solve:

Subtract 7x from both sides

x + 5 > -4

Subtract 5 from both sides

x > -9

What is the range of the graphed function?
O [x1-2 O [yI-2 O {x | x is a real number}
O [vl y is a real number}

Answers

Answer:

first one my sister tried it

Step-by-step explanation:

Rewrite the equation below so that it does not have fractions.

3/4x-5=3/8

Do not use decimals in your answer.

Answers

Answer:

x=  

6

43

 

Step-by-step explanation:

pasos  

4

3

x−5=  

8

3

Agrega 5 a ambos lados.

4

3

x=  

8

3

+5

Convertir 5 a la fracción  

8

40

.

4

3

x=  

8

3

+  

8

40

 

Como  

8

3

 y  

8

40

 tienen el mismo denominador, sume sus numeradores para sumarlos.

4

3

x=  

8

3+40

 

Suma 3 y 40 para obtener 43.

4

3

x=  

8

43

 

Multiplica los dos lados por  

3

4

, el recíproco de  

4

3

.

x=  

8

43

×(  

3

4

)

Multiplica  

8

43

 por  

3

4

 (para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).

x=  

8×3

43×4

 

Realiza las multiplicaciones en la fracción  

8×3

43×4

.

x=  

24

172

 

Reduzca la fracción  

24

172

 a su mínima expresión extrayendo y anulando 4.

x=  

6

43

 

6x=43 should be the answer

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Answers

to get m in an equation u find it in y=mx+b

Liam invests $3,670 in a savings account at his local bank which gives 1.9% simple annual interest. He also invests $2,040 in an online savings account which gives 5.5% simple annual interest. After five years, which one will have earned more interest, and how much more interest will it have earned, to the nearest dollar?

Answers

Step-by-step explanation:

Given:

Investment P₁ = $3670Investment P₂ = $2040Rate of interest r₁ = 1.9% SIRate of interest r₂ = 5.5% SITime t = 5 years

Find amount of interest in both investments:

I₁ = P₁r₁t = $3670*(1.9/100)*5 = $348.65I₂ = P₂r₂t = $2040*(5.5/100)*5 = $561.00

As we see the online savings account earns more interest and the difference is:

$561.00 - $348.65 = $212.35 ≈ $212

Wendy was riding her bike along a trail and travelled 63 miles in 6 hours. When Iman was riding on the same trail she travelled 10.1 miles per hour. What was Wendy's unit rate for her bike ride? (Miles per Hour) Who was riding faster?

Answers

Wendy was going faster at 10.5 mph.

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Answers

For number 13, there is no change. It is 0. The equation is x=7 since the line is on x and not y. The y intercept is 0.
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