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xxTIMURxx [149]
1 year ago
12

Chegg An evergreen nursery usually sells a certain shrub after 5 years of growth and shaping. The growth rate during those 5 yea

rs is approximated by dh/dt = 1.5t + 4, where t is the time in years and h is the height in centimeters. The seedlings are 12 centimeters tall when planted (t = 0). (a) Find the height after t years.
Mathematics
1 answer:
Alex1 year ago
8 0

Answer:

h(t) = 1.5t²/2 + 4t +12

Step-by-step explanation:

The growth rate is given by

dh/dt = 1.5t + 4

To determine the height of the seedlings we integrate the rate with respect to t.

The integral of dh/dt = integral of 1.5t + integral of 4

The integral of dh/dt = h

The integral of dh/dt = 1.5t²/2 + 4t

So at t = 0

h = 12

That makes the equation

h = 1.5t²/2 + 4t +12

Where 12 is the constant

So h(t) = 1.5t²/2 + 4t +12

Will give us the height after t years

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allochka39001 [22]

Answer:

Slope: 10

y-intercept: (0,0)

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1 year ago
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The Masseys are installing new tiles in their bathroom. Each tile is 1 2 of a foot long, and the bathroom is 6 feet long. How ma
Zielflug [23.3K]

Answer:

12 tiles will fit

Step-by-step explanation:

1/2 foot is 6 inch

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10 months ago
Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of converge
tresset_1 [31]

Answer:

Radius of the convergence is R = \frac{1}{21}

and,

The Interval of convergence is -\frac{1}{21}

Step-by-step explanation:

Given function : Σ(21x)^k

Now,

Using the ratio test, we have

R = \lim_{n \to \infty} |\frac{21x^{k+1}}{21x^{k}}|

or

R = \lim_{n \to \infty} |\frac{21x^{k}\times21x^{1}}{21x^{k}}|

or

R = \lim_{n \to \infty} |21x^{1}|

now,

for convergence R|x| < 1

Therefore,

\lim_{n \to \infty} |21x^{1}| < 1

or

-\frac{1}{21}

and,

Radius of the convergence is R = \frac{1}{21}

and,

The Interval of convergence is -\frac{1}{21}

8 0
1 year ago
an economics professor gives a test to gauge the math preparedness of his students. he believes that the performance on the test
STALIN [3.7K]

Answer:

hello your question is incomplete, the missing part of the question is attached below

answer :

1) β1 = 0.25

  β2 = 4.85

2)  40.55 + 0.25 ( math score ) + 4.85 ( hours )

Step-by-step explanation:

<u>1) The estimate for β1 and β2 </u>

From the attached excel result the estimates are ;

β1 = 0.25 : This shows the change in the mean value of the  final score in relation to the change in math score while the time is kept constant

β2 = 4.85 : This represents the change in the mean value of the final score in relation to the change in time while the math score is held constant

<u>2) sample regression equation</u>

The Final sample regression equation = 40.55 + 0.25 ( math score ) + 4.85 ( hours )

4 0
1 year ago
A game is played using ne die. If the die is rolled and shows 3, the player wins $45. If the die shows any number other than 3,
I am Lyosha [343]

Answer:

-$13.5

Step-by-step explanation:

Let x be a random variable of a count of player gain.

- We are told that if the die shows 3, the player wins $45.

- there is a charge of $9 to play the game

If he wins, he gains; 45 - 9 = $36

If he looses, he has a net gain which is a loss = -$9

Thus, the x-values are; (36, -9)

Probability of getting a 3 which is a win is P(X) = 1/6 since there are 6 numbers on the dice and probability of getting any other number is P(X) = 5/6

Thus;

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E(X) = (1/6)(36 - (5 × 9))

E(X) = (1/6)(36 - 45)

E(X) = -9/6 = -3/2

E(X) = -3/2

This represents -3/2 of $9 = -(3/2) × 9 = - 27/2 = -$13.5

3 0
1 year ago
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