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4 years ago

Question 9

Mathematics

1 answer:

vagabundo [1.1K]4 years ago

5 0

Answer:

6.9 miles.

Step-by-step explanation:

2.3mph x 3h=6.9m

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You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

1 year ago

Jing is helping the kindergarten teacher put together bags of crayons. Each bag has 4 crayons, and 1/4 of the crayons in each ba

wariber [46]

Answer:

A) $\frac{3}{12}$

Step-by-step explanation:

Given:

Jing is helping the kindergarten teacher put together bags of crayons.

Each bag has 4 crayons, and 1/4 of the crayons in each bag are green.

What fraction of the crayons in 3 bags are green?

<u>Solution:</u>

1 bag contains number of crayons = 4

1 bag contains number of green crayons = $\frac{1}{4} \ of\ 4 = \frac{1}{4}\times4=1$

Total number of bags = 3

Total number of crayons in 3 bags = 4 $\times$ 3 = 12

1 bag contains number of green crayons = 1

Total number of green crayons in 3 bags = 1 $\times$ 3 = 3

Fraction of the green crayons out of total = 3 out of 12 = $\frac{3}{12}$

Therefore, fraction of the crayons in 3 bags are green are $\frac{3}{12}$

7 0

4 years ago

If I have 87 points and I want to get to 700, how many more points do I need?

garri49 [273]

Subtract 87 from 700
700 - 87 = 613
You need 613 more points

4 0

3 years ago

Read 2 more answers

Is the difference of a rational number and an irrational number always irrational? Explain.

ladessa [460]

Answer:

Yes, because a rational, for example, 1, minus tt (that is supposed to be Pi Lol)

is approximately -2.14.

7 0

3 years ago

A company is packing cartons of candles. Each carton can hold 72 candles. So far, 48 cartons have been packed, but only 30 carto

Lelu [443]

Answer: 1,296 candles

Step-by-step explanation:

48 cartons have been packed yet only 30 have been loaded. The cartons still left are;

= 48 - 30

= 18 cartons

Each carton holds 72 candles so the candles that have not yet been loaded are:

= 18 * 72

= 1,296 candles

7 0

3 years ago