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Stolb23 [73]
3 years ago
15

The distance that a jogger travels at a constant speed of 6.5 miles per hour can be modeled by the linear function f(x)=6.5x, wh

ere x is the time in hours the jogger runs. What is the domain of this function? How would a graph of this function show it?

Mathematics
1 answer:
Sophie [7]3 years ago
7 0
Domain : [ -infinite , infinite [
graph should be going up diagonally .

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Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of t
MariettaO [177]

Answer:

The width of the box is 6.7 cm

The maximum volume is 148.1 cm³

Step-by-step explanation:

The given parameters of the box Jorge is asked to build are;

The maximum girth of the box = 20 cm

The nature of the sides of the box = 2 square sides and 4 rectangular sides

The side length of square side of the box = w

The length of the rectangular side of the box = l

Therefore, we have;

The girth = 2·w + 2·l = 20 cm

∴ w + l = 20/2 = 10

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l = 10 - w

The volume of the box, V = Area of square side × Length of rectangular side

∴ V = w × w × l = w × w × (10 - w)

V = 10·w² - w³

At the maximum volume, we have;

dV/dw = d(10·w² - w³)/dw = 0

∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0

2×10·w - 3·w² = 20·w - 3·w² = 0

20·w - 3·w² = 0 at the maximum volume

w·(20 - 3·w) = 0

∴ w = 0 or w = 20/3 = 6.\overline 6

Given that 6.\overline 6 > 0, we have;

At the maximum volume, the width of the block, w = 6.\overline 6 cm ≈ 6.7 cm

The maximum volume, V_{max}, is therefore given when w = 6.\overline 6 cm = 20/3 cm  as follows;

V = 10·w² - w³

V_{max} = 10·(20/3)² - (20/3)³ = 4000/27 = 148.\overline {148}

The maximum volume, V_{max} = 148.\overline {148} cm³ ≈ 148.1 cm³

Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)

The width of the box is;

6.7 cm

The maximum volume is;

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5 0
3 years ago
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Fofino [41]

★To Solve :

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⠀⠀⠀⠀⠀

★SOLUTION :

\rm\red\leadsto{13(y+7) = 3(y-1)}

\rm\red\leadsto{13\times{y}+13\times7= 3\times{y}-3\times1}

\rm\red\leadsto{13y+91=3y-3}

\rm\red\leadsto{13y-3y=-3-91}

\rm\red\leadsto{10y=-94}

\rm\red\leadsto{} y =\dfrac{   { \cancel{-94}}^{ \:-45 } }{   { \cancel{10}}^{ \: 5} }

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5 0
3 years ago
Read 2 more answers
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Answer:

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Step-by-step explanation:

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Korvikt [17]

Answer:

y-intercept: (0, -1.2)

Step-by-step explanation:

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