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2 years ago

A race car accelerates at 2 m/s2 from 12 m/s to 18 m/s. Find distance and time

Mathematics

1 answer:

Marizza181 [45]2 years ago

6 0

Answer:

Distance = 45 meters

Time = 3 seconds

Step-by-step explanation:

Here, we want to calculate distance and time

To find the time, we can use one of the Newtons law of motion

V = U + at

In this question

V = final velocity = 18 m/s

U = initial velocity = 12 m/s

a = acceleration

Thus;

18 = 12 + 2(t)

18-12 = 2t

2t = 6

t = 6/2

t = 3 seconds

Mathematically we can also find the distance using one of the equation of motion;

D = ut + 1/2 at^2

D = 12(3) + 1/2 * (2) * 3^2

D = 36 + 9

D = 45 m

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Jamie is riding a Ferris wheel that takes fifteen seconds for each complete revolution. The diameter of the wheel is 10 meters a

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Answer:

The answers to the question is

(a) Jamie is gaining altitude at 1.676 m/s

(b) Jamie rising most rapidly at t = 15 s

At a rate of 2.094 m/s.

Step-by-step explanation:

(a) The time to make one complete revolution = period T = 15 seconds

Here will be required to develop the periodic motion equation thus

One complete revolution = 2π,

therefore the we have T = 2π/k = 15

Therefore k = 2π/15

The diameter = radius of the wheel = (diameter of wheel)/2 = 5

also we note that the center of the wheel is 6 m above ground

We write our equation in the form

y = $5*sin(\frac{2*\pi*t}{15} )+6$

When Jamie is 9 meters above the ground and rising we have

9 = $5*sin(\frac{2*\pi*t}{15} )+6$ or 3/5 = $sin(\frac{2*\pi*t}{15} )$ = 0.6

which gives sin⁻¹(0.6) = 0.643 = $\frac{2*\pi*t}{15}$

from where t = 1.536 s

Therefore Jamie is gaining altitude at

$\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =$ 1.676 m/s.

(b) Jamie is rising most rapidly when the velocity curve is at the highest point, that is where the slope is zero

Therefore we differentiate the equation for the velocity again to get

$\frac{d^2y}{dx^2} = -5*(\frac{\pi *2}{15} )^2*sin(\frac{2\pi t}{15})$ =0, π, 2π

Therefore $-sin(\frac{2\pi t}{15} )$ = 0 whereby t = 0 or

$\frac{2\pi t}{15}$ = π and t = 7.5 s, at 2·π t = 15 s

Plugging the value of t into the velocity equation we have

$\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =$ - 2/3π m/s which is decreasing

so we try at t = 15 s and we have $\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi *15}{15}) = \frac{2}{3} \pi$ m/s

Hence Jamie is rising most rapidly at t = 15 s

The maximum rate of Jamie's rise is 2/3π m/s or 2.094 m/s.

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3 years ago

Will mark brainliest

Lerok [7]

Answer:

Step-by-step explanation:

We know she gets 4 more quarters so: q+4

She gives away 3 dime so: d-3

And the nickels stay the same: n

In total the expression would be: q+4+d-3+n

Hope this helps :D

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3 years ago

3 determine the highest real root of f (x) = x3− 6x2 + 11x − 6.1: (a) graphically. (b) using the newton-raphson method (three it

Juliette [100K]

(a) See the first attachment for a graph. This graphing calculator displays roots to 3 decimal places. (The third attachment shows a different graphing calculator and 10 significant digits.)

(b) In the table of the first attachment, the column headed by g(x) gives iterations of Newton's Method. (For Newton's method, it is convenient to let the calculator's derivative function compute the derivative f'(x) of the function f(x). We have defined g(x) = x - f(x)/f'(x).) The result of the 3rd iteration is ...

... x ≈ 3.0473167

(c) The function h(x₁, x₂) computes iterations using the secant method. The results for three iterations of that method are shown below the table in the attachment. The result of the 3rd iteration is ...

... x ≈ 3.2291234

(d) The function h(x, x+0.01) computes the modified secant method as required by the problem statement. The result of the 3rd iteration is ...

... x ≈ 3.0477377

(e) Using Mathematica, the roots are found to be as shown in the second attachment. The highest root is about ...

... x ≈ 3.0466805180

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Comment on these methods

Newton's method can have convergence problems if the starting point is not sufficiently close to the root. A graphing calculator that gives a 3-digit approximation (or better) can help avoid this issue. For the calculator used here, the output of "g(x)" is computed even as the input is typed, so one can simply copy the function output to the input to get a 12-significant digit approximation of the root as fast as you can type it.

The "modified" secant method is a variation of the secant method that does not require two values of the function to start with. Instead, it uses a value of x that is "close" to the one given. For our purpose here, we can use the same h(x1, x2) for both methods, with a different x2 for the modified method.

We have defined h(x1, x2) = x1 - f(x1)(f(x1)-f(x2))/(x1 -x2).

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2 years ago

The temperature of a city at sunset was -1 overnight,the temperature decreased by 11 what was the lowest temperature overnight i

docker41 [41]

Answer:

-12

Step-by-step explanation:

-1 - 11 = -12

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3 years ago

James invested $300 in a bank account that earns simple interest. He earns $24 at the end of 12 months. James invests $500 at th

NARA [144]

Answer: $40

Step-by-step explanation:

The key formula to use for this problem is the simple interest formula, which is $I=prt$ ; where I is the interest earned, p is the principal (initial) amount, r is the interest rate, and t is the amount of time that passes.

Since we know that both investments have the same interest rate, we can use the information from the first part of the problem to solve for the interest rate. Using algebra, we can rearrange the simple interest formula to solve for the interest rate: $r=I/pt$ . We know that our interest earned is $24 and our principal amount is $300. To make things easier, we'll also convert months to years, which is easy to do since we know that 12 months = 1 year. This gives us our value for the amount of time that passes. Now, all we have to do is plug in our values into the rearranged equation above.

We should now have: $r=\frac{24}{300*1}=0.08$

Now, to find the interest earned from the $500 investment, we just need to plug in our values from the second part of the problem, along with our calculated interest rate of 0.08, into the original formula of $I=prt$

This should result in $I=500*0.08*1=40$

Therefore, James will receive $40 on his $500 investment after 12 months.

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3 years ago