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Nezavi [6.7K]
3 years ago
11

Please help! ive been stuck on this for so long and i just keep getting frustrated can someone help walkme through this?

Mathematics
1 answer:
bagirrra123 [75]3 years ago
6 0

For firework launched from height 100ft with initial velocity 150ft/sec, equation made is correct

(a) equation will be h(t) = -16t^2+150t+100

(b) Now we have to see when it will land. At land or ground level height h will be equal to 0. So simply plug 0 in h place in equation made in part (a)

0 = -16t^2 + 150t + 100

Now we have to solve this quadratic. We will use quadratic formula method to solve this equation.

t = \frac{-b \pm  \sqrt{b^2-4ac}}{2a}

a = -16, b = 150, c = 100.

Plugging these values in quadratic formula we get

t = \frac{-150 \pm  \sqrt{150^2-4(-16)(100)}}{2(-16)}

t = \frac{-150 \pm  \sqrt{22500+6400}}{-32}

t = \frac{-150 \pm  \sqrt{28900}}{-32}

t = \frac{-150+170}{-32}  = \frac{20}{-32} = -0.625

time cannot be negative so we will drop this answer

then t = \frac{-150-170}{-32}  = \frac{-320}{-32} = 10

So 10 seconds is the answer for this

(c) To make table simply plug various value for t like t =0, 2, 4, 6, 8 till 10. Plug values in equation mad in part (a) and find h value for each t as shown

For t =0 seconds, h = -16(0)^2+150(0)+100 = 100 feet

For t =2 seconds, h = -16(2)^2+150(2)+100 =336 feet

For t =4 seconds, h = -16(4)^2+150(4)+100 = 444 feet

For t =6 seconds, h = -16(6)^2+150(6)+100 = 424 feet

For t =8 seconds,h = -16(8)^2+150(8)+100 = 276 feet

For t =10 seconds, h = -16(10)^2+150(10)+100 = 0 feet

(d) Axis of symmetry is given by formula

x = \frac{-b}{2a}

t = \frac{-150}{2(-16)} =\frac{-150}{-32} = 4.6875

t = 4.6875 is axis of symmetry line

(e) x-coordinate of vertex is again given by formula

x = \frac{-b}{2a}

so t = 4.6875

then to find y coordinate we will plug this value of t as 4.6875 in equation made in part (a)

For t =4.6875, h = -16(4.6875)^2+150(4.6875)+100 = 451.563

so vertex is at (4.6875, 451.563)

(f) As the firework is launched so in starting time is t=0, we cannot have time before t=0 (negative values) practically. Also we cannnot have firework going down into the ground so we cannot have h value negative physically.

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5 0
1 year ago
1) Relacione o nome dos polígonos de acordo com o total de lados. a) Triângulo ( ) 8 lados. b) Quadrilatero ( ) 6 lados. c) Pent
GuDViN [60]

Answer:

1

O nome de um polígono é um nome que se deve ao número de lados que o polígono possui.

a) Triângulo = 3 lados.

b) Quadrilátero = 4 lados.

c) Pentágono = 5 lados.

d) Hexágono = 6 lados.

e) Heptágono = 7 lados.

f) Octógono = 8 lados.

2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 °

3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a) agudo

4) 2240

5) 5040 sinalizadores

6) Calcule: a) 861 x 27 = 23247

b) 798 x 45 = 35910

Step-by-step explanation:

1) Liste o nome dos polígonos de acordo com o número total de lados.

a) Triângulo = 3 lados.

b) Quadrilátero = 4 lados.

c) Pentágono = 5 lados.

d) Hexágono = 6 lados.

e) Heptágono = 7 lados.

f) Octógono = 8 lados.

2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 ° b) 180 ° c) 270 ° d) 360 °

= a) 90°

Um triângulo ângulo reto pode ser definido como um triângulo onde um de seus 3 ângulos é equivalente a 90 graus (90°).

3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a ) agudo b) raso c) reto d) obtuso.

Um ângulo maior que 0 ° e menor que 90 ° pode ser definido como um ângulo agudo.

= a) agudo

4) Um teatro com 64 filas de assentos e cada fila tem 35 assentos. Qual é a capacidade deste teatro?

No teatro, cada fila tem 35 lugares.

Temos 64 linhas

O número total de licenças que temos é calculado como:

1 fila = 35 assentos

64 linhas =

Multiplicação cruzada

64 filas × 35 assentos

= 2.240 assentos.

Portanto, a capacidade do teatro é de 2240.

5) André e Federico confeccionaram 28 embalagens contendo 180 bandeiras cada embalagem. Quantas bandeiras os meninos fizeram?

O número de bandeiras que os meninos fizeram é calculado como:

28 pacotes × 180 bandeiras

= 5040 sinalizadores

6) Calcule: a) 861 x 27 = 23247

b) 798 x 45 = 35910

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Step-by-step explanation:

3x+2y=-12

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3x=-2y-12

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x= -2/3y-4

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Answer:

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Step-by-step explanation:

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2 years ago
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