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aev [14]
2 years ago
6

Ernest’s favorite lunch is a turkey, lettuce, and tomato sandwich Ernest can make the sandwich using either white bread or wheat

bread Sometimes he adds cheese, pickles, or mayonnaise in any combination, but other times he doesn’t add anything Ernest says that there are 8 different ways to make his favorite sandwich Is he correct? Explain
Mathematics
1 answer:
Novay_Z [31]2 years ago
3 0

Answer:

Ernest is wrong, because the sandwich can be made in 6 different ways (lunch > sandwich: white bread > <em>cheese, pickles, mayonnaise</em> ; wheat bread > <em>cheese, pickles, mayonnaise</em>) and the lunch can be made in 8 different ways.

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A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ
jonny [76]

Let \vec r(t),\vec v(t),\vec a(t) denote the rocket's position, velocity, and acceleration vectors at time t.

We're given its initial position

\vec r(0)=\langle0,0,10\rangle\,\mathrm m

and velocity

\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}

Immediately after launch, the rocket is subject to gravity, so its acceleration is

\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}

where g=9.8\frac{\rm m}{\mathrm s^2}.

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}

\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}

and

\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m

\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m

\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}

b. The rocket stays in the air for as long as it takes until z=0, where z is the z-component of the position vector.

10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}

c. The rocket reaches its maximum height when its vertical velocity (the z-component) is 0, at which point we have

-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)

\implies\boxed{z_{\rm max}=125,010\,\rm m}

7 0
3 years ago
Let f(x) = 5x + 6 and g(x) = -7x - 4. <br> Find f(x) + g(x)
sattari [20]
5x + 6 + (-7x - 4)

5x + 6 - 7x - 4

-2x + 2
4 0
3 years ago
Paula completely covered a square wall using 87.5 ft2 of wallpaper without any overlap. Which measurement is closest to the side
charle [14.2K]

Answer:

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Step-by-step explanation:

6 0
3 years ago
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A manufacturing plant earned 4000 pesos per man-hour of labor when it opened. Each year, the plant earns an additional 6% per ma
Lyrx [107]

Answer:

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Step-by-step explanation:

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3 years ago
When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected
jasenka [17]

Answer:

A. Initially, there were 12 deer.

B. <em>N(10)</em> corresponds to the amount of deer after 10 years since the herd was introducted on the reserve.

C. After 15 years, there will be 410 deer.

D. The deer population incresed by 30 specimens.

Step-by-step explanation:

N=\frac{12.36}{0.03+0.55^t}

The amount of deer that were initally in the reserve corresponds to the value of N when t=0

N=\frac{12.36}{0.33+0.55^0}

N=\frac{12.36}{0.03+1} =\frac{12.36}{1.03} = 12

A. Initially, there were 12 deer.

B. N(10)=\frac{12.36}{0.03 + 0.55^t} =\frac{12.36}{0.03 + 0.0025}=\frac{12.36}{y}=380

B. <em>N(10)</em> corresponds to the amount of deer after 10 years since the herd was introducted on the reserve.

C. N(15)=\frac{12.36}{0.03+0.55^15}=\frac{12.36}{0.03 + 0.00013}=\frac{12.36}{0.03013}= 410

C. After 15 years, there will be 410 deer.

D. The variation on the amount of deer from the 10th year to the 15th year is given by the next expression:

ΔN=N(15)-N(10)

ΔN=410 deer - 380 deer

ΔN= 30 deer.

D. The deer population incresed by 30 specimens.

8 0
3 years ago
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