How many solutions are there in the equation 2x - 5 = 2x

I needs help with it

Slav-nsk [51]

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)

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.

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.

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

6 0

2 years ago

50 POINTSSS

leonid [27]

Answer:

After 2 minutes the temperature of the hot chocolate will be 149.46 degrees Fahrenheit.

Step-by-step explanation:

We are going to use the Newton's law of cooling to solve this exercise. The Newton's law of cooling states that the amount of heat lost by a body is proportional to the difference of temperature between the body and the enviroment. We are going to use the following function :

T(t)=T_{0}+(T_{i}-T_{0}).e^{-kt}T(t)=T

0

+(T

i

−T

0

).e

−kt

Where ''T(t)'' is the temperature of the body that depends of the variable ''t'' which is time.

Where T_{0}T

0

is the temperature of the surroundings

In this case T_{0}T

0

is the temperature of the freezer

Where T_{i}T

i

is the initial temperature of the body which is cooling. In this case, T_{i}T

i

is the temperature of the hot chocolate

And where ''k'' is a constant. In this case, k=0.12k=0.12 is a data of the exercise

If we replace all the values in the equation and replacing t=2minutest=2minutes

⇒

T(2minutes)=0+(190-0).e^{-(0.12).(2)}T(2minutes)=0+(190−0).e

−(0.12).(2)

T(2minutes)=(190).(e^{-0.24})=149.46T(2minutes)=(190).(e

−0.24

)=149.46

We find that the temperature of the hot chocolate after 2 minutes is 149.46 degrees Fahrenheit

8 0

3 years ago

Sophia's parents spent $100 for

Stolb23 [73]

Uh... this question is quite hard... i can’t solve it...!

OKAY fine whatever

100 - 75 = $25

7 0

3 years ago

Read 2 more answers

PLZ HELP ME WITH THIS I'LL REWARD YOU 30 POINTS!!!

zhannawk [14.2K]

C = 2πr
C ≈ 2 * 22/7 * 7
C ≈ 44 cm

In short, Your Answer would be 44 cm

Hope this helps!

6 0

3 years ago

Read 2 more answers

PLS HELP I DONT UNDERSTAND

suter [353]

Answer:

A

Step-by-step explanation:

4(0.5x+2.5y-0.7x-1.3y+4)

=2x+10y-2.8x-5.2y+16

=-0.8x+4.8y+16

hope this helps :)

6 0

3 years ago

How many solutions are there in the equation 2x - 5 = 2x - 5?