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vivado [14]
3 years ago
13

THIS IS THE SECOND TIME IM PUTTING THIS HERE PLS ITS URGENT I STRUGGLE WITH CALCULUS THANK YOU

Mathematics
1 answer:
kiruha [24]3 years ago
3 0
v(t)=t^2-9t+18

1. The velocity is the rate of change of the particle's position over time. The average velocity is then the average rate of change of the particle's position. If s(t) denotes the particle's position at time t, then its velocity at time t satisfies s'(t)=v(t). So to get the average velocity, we need to integrate:

\text{average vel.}=\dfrac{s(8)-s(0)}{8-0}=\displaystyle\frac18\int_0^8v(t)\,\mathrm dt

which follows from the fundamental theorem of calculus. If s'(t)=v(t), then

\displaystyle\int_a^bv(t)\,\mathrm dt=s(b)-s(a)

We get an average velocity of

\displaystyle\frac18\left(\frac{t^3}3-\frac{9t^2}2+18t\right)\bigg|_{t=0}^{t=8}=\frac{10}3

(in meters/second).

2. The instantaneous velocity can be found by simply evaluating the velocity function at the given time. We get v(5)=-2 m/s. Speed is the same as velocity, but we don't account for direction, meaning we just take the magnitude, given by the absolute value of the velocity. So the particle's speed is |v(5)|=2[tex] m/s.\\3. We're using the convention that moving "to the right of zero" corresponds to having a positive velocity. This happens with\\[tex]v(t)=t^2-9t+18=(t-3)(t-6)>0

which is satisfied when both t-3 and t-6 are positive, or both are negative. This occurs when t or when t>6.

4. The particle is moving faster or slower when the rate of change of its velocity is positive or negative, respectively. So we have to check the derivative of v(t) (the acceleration), find its critical points, then examine where the derivative changes sign.

v'(t)=2t-9=0\implies t=\dfrac92

a. When t>\dfrac92, we have v'(t)>0, so the particle is speeding up.

b. When t, we have v'(t), so the particle is slowing down.

5. The total distance traveled can be determined integrating the particle's speed function. When we do so, we're essentially chunking the total time interval into smaller subintervals, checking how much distance is traveled over each subinterval by multiplying the average speed over each subinterval by the length (duration) of each subinterval, and adding all these subdistances together.

So we compute:

\displaystyle\int_0^8|v(t)|\,\mathrm dt=\int_0^8|t^2-9t+18|\,\mathrm dt

In the analysis from part (3), we know v(t) when 3, so it must be non-negative elsewhere. What this means is we have

\displaystyle\int_0^8|v(t)|\,\mathrm dt=\int_0^3v(t)\,\mathrm dt+\int_3^6(-v(t))\,\mathrm dt+\int_6^8v(t)\,\mathrm dt

because |v(t)|=-v(t) whenever v(t), and |v(t)|=v(t) whenever v(t)>0. (This is just the definition of the absolute value function.)

Computing each integral, we get a total distance traveled of \dfrac{107}3 meters.
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Cuál sería la respuesta a esto? La señora María obtuvo un préstamo de 5 millones otorgado por un banco, para devolver el préstam
Lubov Fominskaja [6]

Answer:

La señora María debe pagar 463.635 guaraníes por concepto de intereses,

Step-by-step explanation:

Se recomienda utilizar el modelo de interés compuesto puesto que la tasa de interés es constante y periódico, dado que se conoce el monto a pedir prestado, la tasa de interés y el número de anualidades, se obtiene el monto final. La cantidad de dinero a pagar es la diferencia entre ese resultado y el monto a ser prestado.

El modelo de interés compuesto es representado por la siguiente fórmula:

C(t) =C_{o}\cdot (1+r)^{t} (1)

Donde:

C_{o} - Cantidad de dinero a prestar, medida en guaraníes.

r - Razón de interés interanual, adimensional.

t - Anualidad, medida en años.

C(t) - Cantidad de dinero asociada a la anualidad actual, medida en guaraníes.

Si sabemos que C_{o} = 5.000.000, r = 0.03 y t = 3, entonces la cantidad de dinero asociada al término del período de préstamo es:

C(3) = 5.000.000\cdot (1+0.03)^{3}

C(3) = 5.463.635

Finalmente, la cantidad de dinero a pagar por concepto de intereses es:

\Delta C = 5.463.635-5.000.000

\Delta C = 463.635

La señora María debe pagar 463.635 guaraníes por concepto de intereses,

3 0
2 years ago
James estimated the total cost of groceries to be $50. The actual cost of the groceries is $65. What is the percent error? Round
Yuki888 [10]

The percentage error is 23%

Explanation:

The estimated total cost of the groceries = $50

The actual cost of the groceries = $65

To find the error value, we need to subtract the value of actual cost and total cost of the groceries.

Thus,

error value = actual cost - total cost

error value = 65-50=15

Hence, error value = $15

The formula to determine the percent error is given by

Percent error $=\left(\frac{\text { error value}}{\text {actual value}}\right) \times 100$

Substituting the values in the formula, we get,

$\begin{aligned} \text { Percent error } &=\left(\frac{15}{65}\right) \times 100 \\ &=0.231 \times 100 \\ &=23.1 \end{aligned}$

Rounding off the value, we have, 23%

Thus, the percentage error is 23%

6 0
3 years ago
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
timama [110]
The Mean Value Theorem:
If a function is continuous on [ a, b ] and differentiable on ( a , b ) than there is a point c in ( a, b ) such that:
f ` ( c )=  ( f ( b ) - f ( a ) ) / ( b - a )
f ` ( c ) = ( f ( 2 ) - f ( 0 ) ) / ( 2 - 0 )
f `( x ) = 10 x - 3
f ` ( c ) = 10 c - 3 
2 f ` ( c ) = 16 - 2
f ` ( c ) = 7
7 = 10 c - 3
c = 1
Answer:
          Yes, the function is continuous on [ 0, 2 ] and differentiable on ( 0, 2 ).
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3 years ago
1 unit by 2 units by<br> units
Julli [10]

Answer:

2

Step-by-step explanation:

1 unit by 2 unit means area.

So, know that in area you multiply length times width, you multiply 2 and 1.

1·2

Which is 2

8 0
3 years ago
Which expression is equivalent to 7z + 7z?
Ierofanga [76]

Answer:

14z

Step-by-step explanation:

Since these are like-terms, they can be added together.

7z + 7z = 14z

6 0
2 years ago
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