<em>Greetings from Brasil...</em>
According to the statement of the question, we can assemble the following system of equation:
X · Y = - 2 i
X + Y = 7 ii
isolating X from i and replacing in ii:
X · Y = - 2
X = - 2/Y
X + Y = 7
(- 2/Y) + Y = 7 <em>multiplying everything by Y</em>
(- 2Y/Y) + Y·Y = 7·Y
- 2 + Y² = 7X <em> rearranging everything</em>
Y² - 7X - 2 = 0 <em>2nd degree equation</em>
Δ = b² - 4·a·c
Δ = (- 7)² - 4·1·(- 2)
Δ = 49 + 8
Δ = 57
X = (- b ± √Δ)/2a
X' = (- (- 7) ± √57)/2·1
X' = (7 + √57)/2
X' = (7 - √57)/2
So, the numbers are:
<h2>
(7 + √57)/2</h2>
and
<h2>
(7 - √57)/2</h2>
The width used for the car spaces are taken as a multiples of the width of
the compact car spaces.
Correct response:
- The store owners are incorrect
<h3 /><h3>Methods used to obtain the above response</h3>
Let <em>x</em><em> </em>represent the width of the cars parked compact, and let a·x represent the width of cars parked in full size spaces.
We have;
Initial space occupied = 10·x + 12·(a·x) = x·(10 + 12·a)
New space design = 16·x + 9×(a·x) = x·(16 + 9·a)
When the dimensions of the initial and new arrangement are equal, we have;
10 + 12·a = 16 + 9·a
12·a - 9·a = 16 - 10 = 6
3·a = 6
a = 6 ÷ 3 = 2
a = 2
Whereby the factor <em>a</em> < 2, such that the width of the full size space is less than twice the width of the compact spaces, by testing, we have;
10 + 12·a < 16 + 9·a
Which gives;
x·(10 + 12·a) < x·(16 + 9·a)
Therefore;
The initial total car park space is less than the space required for 16
compact spaces and 9 full size spaces, therefore; the store owners are
incorrect.
Learn more about writing expressions here:
brainly.com/question/551090
Answer:
628
Step-by-step explanation:
using formula 1/3 x pi x r x r x h
1/3 x 3.14 x 10 x 10 x 6 = 628
The volume of the solid objects are 612π in³ and 1566πcm³
<h3>Volume of solid object</h3>
The given objects are composite figures consisting of two shapes.
The volume of the blue figure is expressed as;
Volume = Volume of cylinder + volume of hemisphere
Volume = πr²h + 2/3πr³
Volume = πr²(h + 2/3r)
Volume = π(6)²(13+2/3(6))
Volume = 36π(13 + 4)
Volume = 612π in³
For the other object
Volume = Volume of cylinder + volume of cone
Volume = πr²h + 1/3πr²h
Volume = π(9)²(15) + 1/3π(9)²(13)
Volume= 81π (15+13/3)
Volume= 1566πcm³
Hence the volume of the solid objects are 612π in³ and 1566πcm³
Learn more on volume of composite figures here: brainly.com/question/1205683
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