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2 years ago

I need to find the volume for number 10

Mathematics

1 answer:

notsponge [240]2 years ago

8 0

Use Pythagorean theorem, and calculate the diameter of the base.

d- diameter

$d^2+9.5^2=19.3^2\\\\d^2+90.25=372.49\qquad\text{subtract 90.25 from both sides}\\\\d^2=282.24\to d=\sqrt{282.24}\\\\d=16.8\ m$

r - radius

d = 2r → 2r = 16.8 → r = 8.4 m

The fromula of a volume of a cylinder:

$V=\pi r^2h$

Substitute r = 8.4 m and h = 9.5 m:

$V=\pi\cdot8.4^2\cdot9.5=670.32\pi\ m^3$

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2 years ago

The produce manager at a market orders 10 lb of tomatoes, 20 lb of zucchini, and 40 lb of onions from a local farmer one week.

rewona [7]

Answer:

(A) $A=\left[\begin{array}{ccc}10&20&40\end{array}\right]$

(B) $B=\left[\begin{array}{ccc}11&22&44\end{array}\right]$

Step-by-step explanation:

The manager ordered 10 lb of tomatoes, 20 lb of zucchini, and 40 lb of onions from a local farmer one week.

(A)

Matrix A represents the amount of each item ordered. It is 1 × 3 matrix.

Then matrix A is:

$A=\left[\begin{array}{ccc}10&20&40\end{array}\right]$

(B)

Next week the manager increases the order of all the products by 10%.

Then the amount of new orders are:

Tomatoes $=10\times [1+\frac{10}{100}]=10\times1.10=11$

Zucchini $=20\times [1+\frac{10}{100}]=20\times1.10=22$

Onions $=40\times [1+\frac{10}{100}]=40\times1.10=44$

Th matrix B represents the amount of each order for the next week. Then matrix B is:

$B=\left[\begin{array}{ccc}11&22&44\end{array}\right]$

(C)

Add the two matrix A and B as follows:

$A+B=\left[\begin{array}{ccc}10&20&40\end{array}\right]+\left[\begin{array}{ccc}11&22&44\end{array}\right]\\=\left[\begin{array}{ccc}(10+11)&(20+22)&(40+44)\end{array}\right]\\=\left[\begin{array}{ccc}21&42&84\end{array}\right]$

The entries of the matrix (A + B) represent the amount of tomatoes, zucchini and onions ordered for two weeks.

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2 years ago

how to integrate <img src="https://tex.z-dn.net/?f=e%5E%7B2s%7D%20%2ACos%20%5Cfrac%7Bs%7D%7B4%7D" id="TexFormula1" title="e^{2s}

icang [17]

Answer:

$\int\limits {e^{2s} cos\frac{s}{4} ds$ = $\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))$

Step-by-step explanation:

Step(i):-

Given that $f(s) = e^{2s} cos\frac{s}{4}$

Now integrating

$\int\limits {f(s)} \, ds = \int\limits {e^{2s} cos\frac{s}{4} ds$

By using integration formula

$\int\limits { e^{ax} cos b x dx = \frac{e^{ax} }{a^{2}+b^{2} } ( a cos b x + b sin b x )$

Step(ii):-

$\int\limits {e^{2s} cos\frac{s}{4} ds$ = $\frac{e^{2s} }{(2)^{2}+(\frac{1}{4}) ^{2} } ( 2 cos (\frac{1}{4} ) s + \frac{1}{4} sin \frac{1}{4} s ))$

= $\frac{e^{2s} }{(4+\frac{1}{16})} ( 2 cos (\frac{1}{4} ) s + \frac{1}{4} sin \frac{1}{4} s ))$

= $\frac{e^{2s} }{(\frac{65}{16} } ( \frac{8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s}{4} ))$

= $16 X\frac{e^{2s} }{65 } ( \frac{8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s}{4} ))$

= $\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))$

Final answer:-

$\int\limits {e^{2s} cos\frac{s}{4} ds$ = $\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))$

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2 years ago