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svp [43]
3 years ago
13

Landon is building new bookshelves for his bookstore's new mystery section. Each shelf can hold 33 books. There are 1,221 myster

y books. How many shelves will he need to build?
Mathematics
1 answer:
kvasek [131]3 years ago
6 0

Answer:

37

Step-by-step explanation:

Landon is building new bookshelves for his book store

Each shelf can hold 33 books

There are 1221 mystery books

Therefore the number of shelves he will need to build can be calculated as follows

= 1221/33

= 37

Hence Landon will need to build 37 shelves

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Find the volume of the solid under the plane 5x + 9y − z = 0 and above the region bounded by y = x and y = x4.
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<span>For the plane, we have z = 5x + 9y

For the region, we first find its boundary curves' points of intersection.
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Since x > x^4 for y in [0, 1],

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\int\limits^1_0 { \int\limits_{x^4}^x {(5x+9y)} \, dy } \, dx = \int\limits^1_0 {\left[5xy+ \frac{9}{2} y^2\right]_{x^4}^{x}} \, dx  \\  \\ =\int\limits^1_0 {\left[\left(5x(x)+ \frac{9}{2} (x)^2\right)-\left(5x(x^4)+ \frac{9}{2} (x^4)^2\right)\right]} \, dx  \\  \\ =\int\limits^1_0 {\left(5x^2+ \frac{9}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx =\int\limits^1_0 {\left( \frac{19}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx \\  \\ =\left[ \frac{19}{6} x^3- \frac{5}{6} x^6- \frac{1}{2} x^9\right]^1_0

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