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harina [27]
3 years ago
6

Help for 26!!!!!!!!!!!!!!

Mathematics
1 answer:
qwelly [4]3 years ago
5 0
Total material/materialneededfor1project=number of projects that you can make

4 and 2/3 is the number of bows that can be made

D is the answer
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Find the volume of the solid.
dmitriy555 [2]

In Cartesian coordinates, the region (call it R) is the set

R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}

In the plane z=2, we have

2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2

which is a circle with radius \sqrt2. Then we can better describe the solid by

R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}

so that the volume is

\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx

While doable, it's easier to compute the volume in cylindrical coordinates.

\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}

Then we can describe R in cylindrical coordinates by

R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}

so that the volume is

\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}

3 0
1 year ago
Which statement describes a key feature of function g if g(x) = f(x + 4)?
11111nata11111 [884]

The statement that describes a key feature of function g if g(x) = f(x + 4) is C. horizontal asymptote of y = 0.

<h3>What is a function?</h3>

It should be noted that a function is an expression that shows the relationship between the variables.

In this case, the statement that describes a key feature of function g if g(x) = f(x + 4) is that the horizontal asymptote of y = 0.

The horizontal asymptote is vital for guiding the variables

Learn more about functions on:

brainly.com/question/6561461

#SPJ1

5 0
2 years ago
Hello there
Dafna1 [17]

Answer:

20

Step-by-step explanation:

2/3 want to go

If there are 30 people, we can find our answer pretty easily as 30 is 10 times more than 3.

2/3 = 20/30

So 20 people would like to go :O

Hope this helps, have a nice day :))

6 0
2 years ago
Read 2 more answers
What is the denominator of the fraction 2over3
Nataly [62]
<span>The number below the line in a common fraction

The answer is 3</span>
7 0
2 years ago
Read 2 more answers
Did I do anything wrong? <br>how would I solve it if I did do something wrong??​
s344n2d4d5 [400]
Thats right!well done
5 0
3 years ago
Read 2 more answers
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