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max2010maxim [7]
3 years ago
6

Help plz geometry !!!!​

Mathematics
1 answer:
VLD [36.1K]3 years ago
5 0

Answer:

<em>27 ) x = 15°,</em>

<em>28 ) x = 18°</em>

Step-by-step explanation:

27 ) We are given angle measures of 85 degrees, consecutively 6x + 5, each forming a linear pair;

85 + ( 6x + 5 ) = 180 ⇒ by definition of linear pair we have two measures of angles that add to 180°,

85 + ( 6x + 5 ) = 180 ⇒ take out ( ),

85 + 6x + 5 = 180 ⇒ combine like terms,

90 + 6x = 180 ⇒ subtract 90 from either side of equation,

6x = 90 ⇒ divide 6 on either side of equation,

<em>Solution; x = 15°</em>

28 ) We are given angle measures of 110 degrees, consecutively 3x + 16, each forming a linear pair;

110 + ( 3x + 16 ) = 180 ⇒ by definition of linear pair we have two measures of angles that add to 180°,

110 + ( 3x + 16 ) = 180 ⇒ take out ( ),

110 + 3x + 16 = 180 ⇒ combine like terms,

126 + 3x = 180 ⇒ subtract 126 from either side of equation,

3x = 54 ⇒ divide 6 on either side of equation,

<em>Solution; x = 18°</em>

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A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on top, where the radius o
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Answer:

  about 10.24 ft

Step-by-step explanation:

The formula for the volume of a cylinder is ...

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The formula for the volume of a sphere is ...

  V = (4/3)πr³ = πr²·(4/3r) . . . . equivalent to a cylinder of height 4/3r

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We have a cylinder of height 3d = 3(2r) = 6r. It has half a sphere on top, so the equivalent height of that is (1/2)·(4/3r) = 2/3r.

Then our total volume is equivalent to a cylinder with radius r and height (6 2/3)r = (20/3)r. That is, ...

  22,500 ft³ = πr²·(20/3)r = (20π/3)r³

Multiplying by the inverse of the coefficient of r³, then taking the cube root, we have ...

  r = ∛(22,500·3/(20π)) ft ≈ 10.24 ft

The radius of the silo should be about 10.24 feet.

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The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the h
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The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively

<h3>Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. </h3>

<u>Juan</u>

Juan's equation is given as:

h = -0.001d^2 + 0.5d + 2.5

h =

Set d to multiples of 50 from 0 to 400.

So, the table of values of Juan's function is:

d (ft)                   h(ft)

0                          2.5

50                        25

100                      42.5

150                        55

200                      62.5

250                        65

300                      62.5

350                        65

400                      42.5

See attachment for the graph of Juan's function

<u>Mark</u>

A quadratic function is represented as:

h = ad^2 + bd + c

Using the values on the table of values, we have:

c = 3 -- the constant value

So, the equation becomes

h = ad^2 + bd + 3

Using the two other values on the table of values, we have:

23 = a(50)^2 + b(50) + 3

38 = a(100)^2 + b(100) + 3

Using a graphing tool, we have:

a = -0.001

b = 0.45

So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3

See attachment for Mark's graph.

<u>Barry</u>

From the graph, we have the table of values of Barry's function to be:

d (ft)                   h(ft)

0                          2.5

50                        21

100                      35

150                       44

200                      48

250                       46

300                      41

350                       30

400                      14

450                      0

Using a graphing tool, we have the quadratic function to be:

y = -0.001x^2 +0.4x +2.5

<h3><u>The shortest and the greatest distance before hitting the ground</u></h3>

From the graphs, equations and tables, the distance travelled by the balls are:

Juan = 505 feet

Mark = 457 feet

Barry = 450 feet

This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.

<h3>The height the balls hit a fence at 350 ft distance</h3>

To do this, we set d = 350

From the graphs, equations and tables, the height at 350 ft by the balls are:

Juan = 65 feet

Mark = 38 feet

Barry = 30 feet

The above represents the height the balls hit the fence

Read more about quadratic functions at:

brainly.com/question/12446886

#SPJ1

4 0
1 year ago
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