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
AveGali [126]
1 year ago
6

I needs help with it ​

Mathematics
1 answer:
Slav-nsk [51]1 year ago
6 0

Answer:

a)  initial height = 0 m

b)  8 s

c)  vertex = (4, 32)

    maximum height = 32 m

Step-by-step explanation:

<u>Given equation</u>:

h=-2t^2+16t

where:

  • h is the height of the arrow about the ground (in metres)
  • t is the time (in seconds)

<h3><u>Part (a)</u></h3>

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

\implies h=-2(0)^2+16(0)

\implies h=0

Therefore, the initial height of the arrow is 0 m.

<h3><u>Part (b)</u></h3>

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

\implies -2t^2+16t=0

Factor out -2t:

\implies -2t(t-8)=0

Therefore:

\implies -2t=0 \implies t=0

And:

\implies t-8=0 \implies t=8

Therefore, the arrow will hit the ground at 8 seconds.

<h3><u>Part (c)</u></h3>

The vertex is the <u>turning point</u> of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is <u>negative</u>, the parabola <u>opens downwards</u> and so its <u>vertex</u> is its <u>maximum point</u>.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds.  Therefore, t = 0 and t = 8 are the x-intercepts.  The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

\implies h=-2(4)^2+16(4)

\implies h=-32+64

\implies h=32

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

You might be interested in
Simplify the expression: 3(4d + 1) <br>​
Alexeev081 [22]

Answer:

12d+3

Step-by-step explanation: multiply 3x4d and 3x1 and you get 12d+3

3 0
3 years ago
Read 2 more answers
The graph below represents the price of sending text messages using the services of a phone company. What is the constant of pro
Misha Larkins [42]

Answer:

8

Step-by-step explanation:

The equation is of the form

y = kx ← k is the constant of proportionality

To find k use the slope formula

k = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, 16) ← 2 points on the line

k = \frac{16-0}{2-0} = \frac{16}{2} = 8

4 0
3 years ago
Read 2 more answers
What is the factored form of -7y-y^2=0
Sveta_85 [38]
Factor out like terms
-y(7+y)=0
4 0
3 years ago
When I count as a principal of $1000 and earns 4% simple interest per year and other account as a principal $1000 and earns 4% i
OLga [1]

Answer: the account that earned compound interest has the greater balance at the end of four years.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount invested.

P represents the principal or amount invested.

R represents interest rate

T represents the duration of the investment in years.

From the information given,

P = 1000

R = 4%

T = 4 years

I = (1000 × 4 × 4)/100 = 160

Total amount earned is

1000 + 160 = $1160

The formula for determining compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1000

r = 4% = 4/100 = 0.04

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,.

A = 1000(1+0.04/1)^1 × 4

A = 1000(1.04)^4

A = $1170

3 0
3 years ago
The sum of two numbers is 12. The difference of the two numbers is 22. Find the two numbers
valentina_108 [34]

Answer:

-5 and 17

Step-by-step explanation:

The sum of two numbers (let's just say number a and number b) is 12.

a + b = 12

The difference between the same two numbers (still a and b) is 22.

b - a = 22

(Move variable a to the right side to get the following.)

b = 22 + a

(This way, we can substitute b = 22 + a into the first equation, a + b = 12, and solve.)

a + (22 + a) = 12

a + a + 22 = 12

2a = -10

a = -5

a + b = 12

-5 + b = 12

b = 17

7 0
2 years ago
Other questions:
  • What percent of the DVD's cost between $14.50 and $26.00?​
    13·2 answers
  • Use the point-slope equation to identify the slope and the coordinates of a point
    6·1 answer
  • 1. In Brad's golf bag, he has 4 times more white golf balls than yellow golf balls. He has 20 white golf balls in his bag. Which
    15·2 answers
  • A catering service offers 11 appetizers, 12 main courses, and 8 desserts. A customer is to select 9 appetizers, 2 main courses,
    8·1 answer
  • What is the nth term in 3,9,15,21,27?
    13·1 answer
  • Is the first side “WX and ZX” or “WX and XZ?”<br><br> This is sss congruence
    15·1 answer
  • What 2 figures Will <br><br> have 20 edges?
    9·2 answers
  • Select the equivalent expression.<br><br><br><br><br> Umm so yeah... happy pride month royals!
    14·1 answer
  • F(x) = 3 x e^2x<br>That's the problem​
    8·2 answers
  • When Donetle stands at point R, he is 1000 feet from point S at the base of a cliff.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!