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lys-0071 [83]
3 years ago
13

Simplify: –3(y 2)2 – 5 6y

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
8 0
The answer is -3y^4+6y-5
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Convert the integral below to polar coordinates and evaluate the integral.
White raven [17]

I suppose the integral is

\displaystyle\int_0^5\int_y^{\sqrt{25-y^2}} xy\,\mathrm dx\,\mathrm dy

The integration region corresponds to a sector of a cirlce with radius 5 subtended by a central angle of π/4 rad. We can capture this region in polar coordinates by the set

R=\left\{(r,\theta)\mid0\le r\le5,0\le\theta\le\dfrac\pi4\right\}

Then x=r\cos\theta, y=r\sin\theta, and \mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta. So the integral becomes

\displaystyle\iint_Rxy\,\mathrm dx\,\mathrm dy=\int_0^{\pi/4}\int_0^5r^3\sin\theta\cos\theta\,\mathrm dr\,\mathrm d\theta=\frac{625}{16}

7 0
3 years ago
A line with a slope of 1/2 passes through
Anna [14]
The equation for the line would be Y=1/2x -2
7 0
3 years ago
How to use Pythagorean theorem to find the right triangle side length
MrRissso [65]

Answer:

You would use a^2 + b^2 = c^2

Step-by-step explanation:

a and b are the shorter side of the triangle whereas c is the hypotenuse or longest side of the triangle

5 0
3 years ago
Elsa's magic wand can cast 53 spells. Her wand can cast 17fewer spells than her sister Anna's wand, which is a little bigger and
Mademuasel [1]

Answer:

<em> Anna's wand can cast 70 spells</em>

<em></em>

Step-by-step explanation:

Elsa's wand can cast 53 spells

her wand casts 17 fewer cells than her sister Anna's

Amount of spells cast by Anna's wand = ?

We write the question down in the form of an equation

x - 17 = 53

where x is the amount of spells Anna's wand can cast.

we then proceed to solve by collecting like terms to different sides of the equation. We'll have

x = 53 + 17

which leaves us with

x = 70

This means that<em> Anna's wand can cast 70 spells.</em>

4 0
3 years ago
The length of human pregnancies from conception to birth varies according to an approximately normal distribution with a mean of
Varvara68 [4.7K]

Answer:

A) 68.33%

B) (234, 298)

Step-by-step explanation:

We have that the mean is 266 days (m) and the standard deviation is 16 days (sd), so we are asked:

A. P (250 x < 282)

P ((x1 - m) / sd < x < (x2 - m) / sd)

P ((250 - 266) / 16 < x < (282 - 266) / 16)

P (- 1 < z < 1)

P (z < 1) - P (-1 < z)

If we look in the normal distribution table we have to:

P (-1 < z) = 0.1587

P (z < 1) = 0.8413

replacing

0.8413 - 0.1587 = 0.6833

The percentage of pregnancies last between 250 and 282 days is 68.33%

B. We apply the experimental formula of 68-95-99.7

For middle 95% it is:

(m - 2 * sd, m + 2 * sd)

Thus,

m - 2 * sd <x <m + 2 * sd

we replace

266 - 2 * 16 <x <266 + 2 * 16

234 <x <298

That is, the interval would be (234, 298)

6 0
3 years ago
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