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1 year ago

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A camp counselor and four campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must

be seated in the fourth and a camper who has a tendency to engage in food fights must sit to the counselor's immediate ?

1 answer:

Lady_Fox [76]1 year ago

4 0

Answer: 6 ways

Step-by-step explanation:

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A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 34.5 ft3. what dimensions

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Answer:

$l \approx 3.3\,ft$ , $x = 3.2\,ft$

Step-by-step explanation:

The equations of volume and surface area are presented below:

$34.5 = l^{2}\cdot x$

$A_{s} = 2\cdot l^{2} + 4\cdot l \cdot x$

The length of the tank is:

$x = \frac{34.5}{l^{2}}$

The expression fo the surface area is therefore simplified into an univariable form:

$A_{s} = 2\cdot l^{2} + 4\cdot \left(\frac{34.5}{l} \right)$

$A_{s} = 2\cdot l^{2} + \frac{138}{l}$

The first and second derivatives of the expression are, respectively:

$A_{s}' = 4\cdot l -\frac{138}{l^{2}}$

$A_{s}'' = 4 +\frac{276}{l^{3}}$

The first derivative is equalized to zero and length of the square side is now found:

$4\cdot l -\frac{138}{l^{2}} = 0$

$4\cdot l^{3}-138 = 0$

$l^{3} = \frac{138}{4}$

$l = \sqrt[3]{\frac{138}{4} }$

$l \approx 3.3\,ft$

Now, the second derivative offers a criteria to determine if solution leads to an absolute minimum:

$A_{s}'' = 4 + \frac{276}{(3.3\,ft)^{3}}$

$A_{s}'' = 11.7$ (Absolute minimum)

The depth of the tank is:

$x = \frac{34.5\,ft^{3}}{(3.3\,ft)^{2}}$

$x = 3.2\,ft$

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3 years ago

The expression 20l + 25g - 10, gives the number of dollars that Josie makes from mowing l lawns and raking g gardens. How many d

tiny-mole [99]

20 • 3=60, 25 • 4=100. 60+100=160. 160-10=150. Josie makes $150.

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2 years ago

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An online music club sells compact discs for $13.95 each plus $1.95 shipping and handling per order. If Maria’s total bill was $

hoa [83]

Answer:

she purchased 6 compact discs

Step-by-step explanation:

13.95 × 6 + 1.95= 85.65

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3 years ago

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Find the area of a parallelogram ABCD with AB =7 m. AD = 20 m and BAD = 62°.

nikklg [1K]

9514 1404 393

Answer:

123.6 m²

Step-by-step explanation:

The area is given by the formula ...

A = (AB)(AD)sin(∠A)

A = (7 m)(20 m)sin(62°) ≈ 123.6 m²

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3 years ago

Write two expressions that are equivalent to the expression below. (9- c) +(9 -c)+(9- c) +(9- c)

GREYUIT [131]

Answer:

${ \tt{4(9 - c)}} \\ and \\ { \tt{36 - 4c}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}$

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