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
scZoUnD [109]
3 years ago
8

A ball is thrown from the top of a hill. The graph shows the relationship between the height h, in meters, of the ball above the

ground at the base of the hill and the time t, in seconds, after the ball is thrown. The function h(t) = -4.9t2 + 9.8t + 15 models h as a function of t. What is the significance of the vertex of the parabola in terms of height and/or time?
Mathematics
2 answers:
Nataliya [291]3 years ago
5 0

Answer:

The maximum height of the ball is 19.9 meters after 1 second.

Step-by-step explanation:

The height of a ball represents by the function

h(t) = -4.9t2 + 9.8t + 15

where, h(t) is the height in meters, of the ball above the ground at the base of the hill and the time t, in seconds, after the ball is thrown.

In the given equation leading coefficient is -4.9 which is a negative number. So, it is a downward parabola and vertex of a downward parabola represents the maximum value of the function.

It means vertex of the given function represents the maximum height of the ball.

If a quadratic function is defined as

f(x)=ax^2+bx+c

then vertex of the function is

Vertex=(-\frac{b}{2a},f(-\frac{b}{2a}))

In the given function, a=-4.9,b=9.8,c=15.

-\frac{b}{2a}=-\frac{9.8}{2(-4.9)}=1

Substitute t=1 in the given function.

h(1) = -4.9(1)2 + 9.8(1) + 15=19.9

The vertex of the function is (1,19.9).

Therefore, the maximum height of the ball is 19.9 meters after 1 second.

Nezavi [6.7K]3 years ago
4 0
D. the h coordinate of the vertex is the balls maximum height
You might be interested in
Look at the graph
Ira Lisetskai [31]

y increases as x increases

3 0
3 years ago
Read 2 more answers
Help I’ll give 50 points<br> 12) 4x- y=8<br> 5x+y=1
Luba_88 [7]

12) 4x- y=8

5x+y=1

Correct.

4 0
3 years ago
I need to pass so yk help​
Airida [17]

Answer:

(2)

Step-by-step explanation:

-3,2

-1,-1

y = ax + b \\ 2 =  - 3a + b \\  - 1 =  - a + b \\ 3 =  - 2a \\ a =  - 1.5

slope is -1.5

3 0
3 years ago
2log(base 5)^(x-3)-log(base 5)^8= log(base 5)^2
Alja [10]

Answer:

x = 7

Step-by-step explanation:

2log_5(x-3)-log_58= log_52\\\\2log_5(x-3) =log_52+log_58\\\\2log_5(x-3) =log_5(2\times 8) \\\\2log_5(x-3) =log_516\\\\2log_5(x-3) =log_54^2 \\\\2log_5(x-3) =2 log_54 \\\\log_5(x-3) =log_54 \\\\x - 3 = 4\\\\x = 4+3\\\\\huge \orange { \boxed{x = 7}}

7 0
2 years ago
Rewrite the expression 4+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B16-%284%29%285%29%7D" id="TexFormula1" title="\sqrt{16-(4)(
Inessa05 [86]

Answer:

2+i

Step-by-step explanation:

Given the expression:

\dfrac{4+\sqrt{16-(4)(5)}}{2}

To find:

The expression of above complex number in standard form a+bi.

Solution:

First of all, learn the concept of i (pronounced as <em>iota</em>) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by i.

Value of i =\sqrt{-1}.

Now, let us consider the given expression:

\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i

So, the given expression in standard form is 2+i.

Let us compare with standard form a+bi so we get a =2, b =1.

\therefore The standard form of

\dfrac{4+\sqrt{16-(4)(5)}}{2}

is: \bold{2+i}

8 0
2 years ago
Other questions:
  • A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refe
    7·1 answer
  • What does it mean if your final exam grade is modeled by the function f(x) = 100 - 3.3x?
    10·2 answers
  • 6(x-4)+x=5(x-2) PLEASE HELP
    5·2 answers
  • Eli runs 2 miles on his first day of training for a road race. The next day, he increases his distance run by 0.25 miles. The da
    9·2 answers
  • A square tile has a side of 12 cm. What is the area of the tile?
    15·1 answer
  • Duane can do 46 pullups in two minutes. Find the rate.​
    12·1 answer
  • Please help me, i really need help
    12·2 answers
  • Ava is going to the county fair. The cost of admission is $5.50 and it is $1.50 for each ride. If Ava has $19.00, Write and solv
    15·1 answer
  • A family of 3 got 3 entrees, and 2 desserts, what is the probability that they might get the cake, and chicken dumplings?​
    14·1 answer
  • I need help (;´༎ຶٹ༎ຶ`)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!