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soldier1979 [14.2K]

2 years ago

14

The function f(t) = 2t2 + 3t - 1 can be used to determine the position of a worm, f(t), in centimeters, after t seconds. Find th

e average rate of change of the function over the interval [3, 6]?

1 answer:

ExtremeBDS [4]2 years ago

7 0

Use (f(6) - f(3))/3 and you'll get your answer :)

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PLEASE someone help its due tonight im almost done

marusya05 [52]

<h3>Answers:</h3>

48 seconds
3624 feet

========================================================

Explanation:

x = number of seconds that elapse

y = altitude (aka height) of the plane

The equation for plane A is

y = 20.25x+2652

because it starts off at 2652 ft in the air, and then adds on 20.25 feet per second which is what the 20.25x describes

The equation for plane B is

y = 75.5x

The y intercept is zero because plane B starts on the ground, aka height 0.

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

The system of equations is

$\begin{cases}y = 20.25x+2652\\y = 75.5x\end{cases}$

If we want to know when they'll reach the same height (y), then we can set the two right hand sides equal to each other and solve for x.

75.5x = 20.25x+2652

75.5x-20.25x = 2652

55.25x = 2652

x = (2652)/(55.25)

x = 48

The two planes reach the same altitude at exactly <u>48 seconds</u>

That altitude is <u>3624 feet</u> because

y = 20.25*x + 2652 = 20.25*48+2652 = 3624
y = 75.5*x = 75.5*48 = 3624

Notice I plugged x = 48 into each equation and I got the same y value of y = 3624. This helps confirm the answers.

7 0

1 year ago

Let v1=(3,5) and v2=(-4,7) Compute the unit vectors in the direction of |v1| and |v2|?

AleksandrR [38]

By definition, the unit vector of v = (a,b) is
$\hat{v} = \frac{\vec{v}}{|v|}$

Therefore,
The unit vector of v₁ = (3,5) in the direction of |v₁| s
(3,5)/√[3² + 5²]
= (3,5)/√34

The unit vector of v₂ in the direction of |v₂| is
(-4,7)/√[(-4)² + 7²]
= (-4,7)/√65

Answer:
The unit vector of v₁ in the direction of |v₁} is $( \frac{3}{\sqrt{34}} , \frac{5}{\sqrt{34}} )$
The unit vector of v₂ in the directin of |v₂| is
$( \frac{-4}{\sqrt{65}} , \frac{7}{\sqrt{65}} )$

6 0

3 years ago

Please help asap!!!! 53 points!

AfilCa [17]

The easiest way is to graph it based upon the slope (m) and y-intercept (b), in the standard slope-intercept form: y = m (x) + b.
The line above intercepts the y-axis at y = -2, which is b. The slope (m) = rise/run = (y2-y1)/(x2-x1 ); so for the point (-4, 2) to (-6, 4) is:
(4-2)/(-6--4) = 2/(-6+4) = 2/-2 = -1.
So one form of the equation would be:
y = -1x - 2
Now the other form of an equation is point-slope: y-k = m (x-h), where the point is at (h, k)
and if we pick -5 for x (bc 5 it listed in 3 of the answers), the y at x=-5 looks like around +3
so we get: y-k = -1 (x--5)...
y-3 = -(x+5)... therefore D) is the correct answer:

8 0

3 years ago

Read 2 more answers

30 boxes of melons and 4 melons in each bag . Each bag holds two melons. How melons are there in the store.

SVEN [57.7K]

The answer is the store has 240 melons.
(30x4)x2=240

8 0

3 years ago

Verify the identity. Show your work. (1 + tan^2u)(1 - sin^2u) = 1

yuradex [85]

$\bf \textit{Pythagorean Identities}
\\\\
sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)
\\\\ 1+tan^2(\theta)=sec^2(\theta)\\\\
-------------------------------\\\\\
[1+tan^2(u)][1-sin^2(u)]=1
\\\\\\\
[sec^2(u)][cos^2(u)]\implies \cfrac{1}{cos^2(u)}\cdot cos^2(u)\implies \cfrac{cos^2(u)}{cos^2(u)}\implies 1$

7 0

3 years ago