1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lana [24]
2 years ago
6

Anne fires a toy rocket into the air from the top of a barn. The height of the rocket above the ground in feet after t seconds i

s given by
the function h(t) = -5t^2 + 20t -15. After completing the trajectory, Anne finds that the maximum height the toy rocket reached in the
air is represented by the expression -5(t-__)^2+5 Write the missing piece of the expression
Mathematics
1 answer:
astra-53 [7]2 years ago
5 0

The missing piece of the expression is 2

<h3>Maximum height of the rocket</h3>

From the question, the height of the rocket above the ground in feet after t seconds is given by the function h(t) = -5t^2 + 20t -15

At maximum height, the velocity of the function is zero. Hence;

dh/dt - -5(2)t + 20
dh/dt = -10t + 20

Write the expression in vertex form as shown:

h(t) = -5t^2 + 20t -15

h(t) = -5(t^2 - 4t +3)

h(t) = -5(t^2 - 4t + 2^2 + 3 - 2^2)

h(t) = -5((t+2)^2 +5
h(t) = -5((t+2)^2 + 11

Hence the missing piece of the expression is 2

Learn more on vertex form here: brainly.com/question/525947

You might be interested in
Estimate the sum or difference <br> 6/10 + 7/12
Marat540 [252]
6/10 + 7/12 = 142/120 = 71/60 = 1.18 (One whole number, and 11/60)
6 0
3 years ago
Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.
Aleks [24]

Answer:

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

Step-by-step explanation:

The actual Series is::

\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}

The method we are going to use is comparison method:

According to comparison method, we have:

\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}

Now:

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty}  \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

\sum_{n=1}^{inf}\frac{1}{n^p}

if p>1 then series converges. In oue case we have:

\sum_{n=1}^{inf}b_n=\frac{1}{n^4}

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

5 0
3 years ago
Please help with 14-17!!
rodikova [14]
14 is always 15 is sometimes 16 is sometimes
4 0
3 years ago
As an estimation we are told 5 miles is 8 km. <br> Convert 32.5 miles to km.
elixir [45]

Answer:

52 km

Step-by-step explanation:

Given, 5 miles is 8km.

So, 1 mile will be (8/5) km.

Now, 32.5 miles will be (8/5) x 32.5 = 52 km

5 0
3 years ago
georges playground is shown in the diagram he wants to buy timber to put all around it so that mulch does not spread how much ti
Xelga [282]
He needs 84 ft.
Step by step explanation:
(24*2)+(18*2)
48+36
84
7 0
3 years ago
Other questions:
  • What is 15.062 in word form
    7·1 answer
  • What is the center? <br><br> (x + 1)2 + (y - 3)2 = 36
    9·1 answer
  • Write 850 as the product of its prime factors. A. 17 × 50 B. 5 × 10 × 17 C. 10 × 85 D. 2 × 5 × 5 × 17
    10·2 answers
  • 1) Considered x + y - 1 and x²y - 8x - 8y = 17 Factor the first member of this equation and the x² value (with resolution)
    11·1 answer
  • If you multiply me by 7 and then add 7 to the product, you get 6x7.
    12·1 answer
  • What is the product of 5.9 x 103 and 5.9 x 104 expressed in scientific notation?
    5·1 answer
  • Which equation represents a line that is parallel to the line y = - 4x +5?
    13·2 answers
  • A bag of apples weighs 8 4 10 pounds. A crate of bananas is 5 times as heavy as the apples. How much heavier are the bananas tha
    10·1 answer
  • 14) Write the equation of the line that is represented by this graph.
    11·2 answers
  • Sam is saving money to buy himself a new phone. He currently has $95. He is able to save about $20 a week. Let represent how muc
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!