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monitta
3 years ago
10

I don’t know # 6 and #8 plz help

Mathematics
1 answer:
aalyn [17]3 years ago
3 0
#6. the answer is 12 it increases by 4 every time

#8. the answer is every week he runs his miles increase by 5
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17.
Marta_Voda [28]

Answer:

a) 50 meters

b) 2354 meters

c) 12 seconds

d) 24.13 seconds

Step-by-step explanation:

Hello!

<h3>a) How far is Lincoln above the ground when he shoots the gun?</h3>

We need to really understand what the variables represent in this question. Given that t is time, and h is height, the time at which he shoots the bullet will be 0, as the bullet hasn't started traveling yet. This means that we can solve for the original height of the bullet by plugging in 0 for time in the equation.

Equation: h = -16t^2 + 384t + 50

Plug in 0 for t:

  • h = -16t^2 + 384t + 50
  • h = -16(0)^2 + 384(0) + 50
  • h = 50

The height at which Lincoln shot the bullet is 50 meters.

We can also look at this graphically. The height of origin will simply be when the x-value (in this case t-value) is 0. That means it is the point at which the graph intersects the y-axis, known as the y-intercept.

Standard form of a Parabola: y = ax^2 + bx + c

The y-intercept is the "c" value.

Given our equation: h = -16t^2 + 384t + 50

The c-value is 50. This proves that the y-intercept is 50.

<h3 /><h3>b)How high does the bullet travel vertically relative to the ground?</h3>

We want to find the highest point of the graph. To do that, we can find the vertex.

We can utilize the Axis of Symmetry (AOS) to find the Vertex.

First, find the AOS using the formula: AOS = -\frac{b}{2a}

  • a = -16
  • b = 384

Plug it into the formula:

  • AOS = -\frac{b}{2a}
  • AOS = -\frac{384}{2(-16)}
  • AOS = \frac{384}{32}
  • AOS = 12

Plug in 12 for t in the equation:

  • h = -16t^2 + 384t + 50
  • h = -16(12)^2 + 384(12) + 50
  • h = -2304 + 4608 + 50
  • h = 2304+50
  • h = 2354

Therefore, the highest point of the bullet is 2354 meters.

<h3>c)How long does it take the bullet to reach its greatest height?</h3>

We answered this in the last question. The t-value when h is at its highest is 12.

<h3>d)After how many seconds (round to nearest 100th) does the bullet hit the ground?</h3>

We have to solve for the values of t when h is 0 (when it touches the ground).

Set the equation to 0, and solve using the quadratic formula.

Quadratic formula: x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}

  • x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}
  • x = \frac{-384\pm\sqrt{384^2 - 4(-16)(50)}}{2(-16)}
  • x = \frac{-384\pm\sqrt{147456 +3200}}{-32}
  • x = \frac{-384\pm\sqrt{150656}}{-32}
  • x = \frac{-384\pm388.14}{-32}
  • x = -\frac{4.14}{32}, x = \frac{772.14}{32}

We are only going to take the positive solution, as we can't have a negative time. The solution that doesn't work is called an extraneous solution.

  • x = \frac{772.14}{32}
  • x = 24.13

It takes approximately 24.13 seconds for the bullet to hit the ground.

6 0
2 years ago
Find the distance between the 2 points (6, - 4) and (2, - 7). Please show me how you found it.
Serga [27]
\bf \textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%  (a,b)&#10;&({{ 6}}\quad ,&{{ -4}})\quad &#10;%  (c,d)&#10;&({{ 2}}\quad ,&{{ -7}})&#10;\end{array}\qquad &#10;%  distance value&#10;d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}&#10;\\\\\\&#10;d=\sqrt{[2-6]^2+[-7-(-4)]^2}\implies d=\sqrt{(2-6)^2+(-7+4)^2}
5 0
3 years ago
Four points, A(0,0), B(1, 2), C(3, 1), and D(2,-1) lie in a plane. Line AD and Line BC are BEST described as
anygoal [31]

Answer:

Parallel

Step-by-step explanation:

Parallel lines are 2 coplanar lines that dont intersect at any point

4 0
2 years ago
This is a linear equation/ graph quiz ! please help , my teacher makes no sense to me!
JulijaS [17]

Answer:

(8,5)

Step-by-step explanation:

5x - 2y = 30

coordinates are (x,y) so you plug in 8 for x and solve for y

5(8) - 2y = 30

40 - 2y = 30

subtract 40 from both sides to isolate y

-2y = -10

divide both sides by -2 to isolate y

y = 5

6 0
3 years ago
Read 2 more answers
Geometry Question: BK bisects angle ABC and M angle ABK=28.3 degrees. Find M angle KBC and M angle ABC.
Nookie1986 [14]

Answer:

ABK = 28.3

Step-by-step explanation:

Given

ABK = 28.3

Required

Determine KBC

Since BK is a bisector of ABC at B,

this implies that:

ABK = KBC

Substitute 28.3 for ABK

28.3 = ABK

Reorder

ABK = 28.3

7 0
3 years ago
Read 2 more answers
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