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Andrews [41]
3 years ago
10

All equilateral triangles are _____ triangles. scalene right obtuse acute

Mathematics
2 answers:
Aleksandr [31]3 years ago
8 0
A equilateral triangle has equal sides and it is diagonal, so this means it is: Acute
drek231 [11]3 years ago
6 0
The equailateral triangle are all equally name: scalene, isoscalene
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Rewrite the following integral in spherical coordinates.​
lora16 [44]

In cylindrical coordinates, we have r^2=x^2+y^2, so that

z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}

correspond to the upper and lower halves of a sphere with radius \sqrt2. In spherical coordinates, this sphere is \rho=\sqrt2.

1 \le r \le \sqrt2 means our region is between two cylinders with radius 1 and \sqrt2. In spherical coordinates, the inner cylinder has equation

x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)

This cylinder meets the sphere when

x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)

which occurs at

\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi

where n\in\Bbb Z. Then \frac\pi4\le\phi\le\frac{3\pi}4.

The volume element transforms to

dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi

Putting everything together, we have

\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3

4 0
2 years ago
A local gym offers a trial membership for 3 months. It discounts the regular monthly fee x by $25. If the total cost of the tria
kati45 [8]
3(x - 25) < $100.  We're not req'd to solve this.


8 0
3 years ago
Use the table to write a proportion.
umka21 [38]

Answer:

it's probably ours it's just a lucky guess

Step-by-step explanation:

7 0
3 years ago
Solve the system of equations.
Sauron [17]

Answer: A. X= -5, Y= 3, Z= 4

Step-by-step explanation:

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3 years ago
Vail Resorts pays part-time seasonal employees at ski resorts on an hourly basis. At a certain mountain, the hourly rates have a
notsponge [240]

Answer:

z=0.842

And if we solve for a we got

\mu=13.16 +0.842*3=15.69

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the hourly rates of a population, and for this case we know the distribution for X is given by:

X \sim N(\mu,3)  

For this part we want to find a value a, such that we satisfy this condition:

P(X>13.16)=0.20   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.842

And if we solve for a we got

\mu=13.16 +0.842*3=15.69

3 0
2 years ago
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