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3 years ago

14

Luca has a book collection of 95 books. She has read 3/5 of the books in her collection. If Luca reads 12 more books this summer

, what is the total number of
books she will have read from her collection?

2 answers:

jenyasd209 [6]3 years ago

4 0

Answer:

68

Step-by-step explanation:

snow_lady [41]3 years ago

3 0

Answer:

she will have to read 26 more books

Step-by-step explanation:

3/5 of 95 is 57

57+12=69

95-69=26

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Step-by-step explanation:

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2 years ago

You have 100 cm of string which can be cut in one place (or not cut at all) and then formed into a circle and a square (or just

Ne4ueva [31]

Answer:

44cm for minimum area and 0 for maximum area (circle)

Step-by-step explanation:

Let's C be the circumference of the circle and S be the circumference of the square. If we cut the string into 2 pieces the total circumferences would be the string length 100cm.

S + C = 100 or S = 100 - C

The side of square is S/4 and radius of the circle is $\frac{C}{2\pi}$

So the area of the square is

$A_S = \frac{S^2}{4^2} = \frac{S^2}{16}$

$A_C = \pi\frac{C^2}{(2\pi)^2} = \frac{C^2}{4\pi}$

Therefore the total area is

$A = A_S + A_C = \frac{S^2}{16} + \frac{C^2}{4\pi}$

We can substitute 100 - C for S

$A = \frac{(100 - C)^2}{16} + \frac{C^2}{4\pi}$

$A = \frac{100^2 - 200C + C^2}{16} + \frac{C^2}{4\pi}$

$A = 625 -12.5C + \frac{C^2}{16} + \frac{C^2}{4\pi}$

$A = 625 -12.5C + C^2(\frac{1}{16} + \frac{1}{4\pi})$

To find the maximum and minimum of this, we can take the first derivative and set that to 0

$A^{'} = -12.5 + 2C(\frac{1}{16} + \frac{1}{4\pi}) = 0$

$C(\frac{1}{8} + \frac{1}{2\pi}) = 12.5$

$C \approx 44 cm$

If we take the 2nd derivative:

$A^{''} = \frac{1}{8} + \frac{1}{2\pi} > 0$

We can see that this is positive, so our cut at 44 cm would yield the minimum area.

The maximum area would be where you not cut anything and use the total string length to use for either square or circle

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if S = 100 then $A_S = \frac{S^2}{16} = \frac{100^2}{16} = 625 cm^2$

So to yield maximum area, you should not cut at all and use the whole string to form a circle

4 0

3 years ago

Please solve this for me!

tatuchka [14]

Step-by-step explanation:

To find the slope between two given points you use the equation:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

(8,10) are $(x_{1},y_{1})$

(16,24) are $(x_{2},y_{2})$

After that you just plug in:

$m=\frac{24-10}{16-8}$

$m=\frac{14}{8}$

Simplify:

<h2><u><em></em></u> $m= \frac{7}{4}$ <u><em></em></u></h2>

Answer:

The slope is $\frac{7}{4}$ for #1

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2 years ago