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2 years ago

20 points!! What are the next three terms of the arithmetic sequence -18, -13, -8, -3,…?

Mathematics

2 answers:

GarryVolchara [31]2 years ago

4 0

Answer:

3, 8, 13, 18

Step-by-step explanation:

Novosadov [1.4K]2 years ago

3 0

I think the pattern goes plus five each time so the next three numbers would be 2, 7, 12

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Solve for the following inequality: -7x - 15 <20

gregori [183]

Answer:

x>-5/7

Step-by-step explanation:

Because our dividing 5 by a negative 7 the symbol flips

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3 years ago

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What is the wave speed of a wave that has a frequency of 25 Hz and a wavelength of 0.80 m?

tatuchka [14]

Answer:

Speed = 20 m/s

Step-by-step explanation:

The formula to find the speed of a wave is found by

Speed = Wavelength x Frequency where the frequency is in HZ and the wavelength is in meters

Speed = .80*25

Speed = 20 m/s

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3 years ago

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Use polar coordinates to find the volume of the given solid. Inside both the cylinder x2 y2 = 1 and the ellipsoid 4x2 4y2 z2 = 6

Anton [14]

The Volume of the given solid using polar coordinate is: $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

V= $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

<h3>What is Volume of Solid in polar coordinates?</h3>

To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.

Consider the cylinder, $x^{2}+y^{2} =1$ and the ellipsoid, $4x^{2}+ 4y^{2} + z^{2} =64$

In polar coordinates, we know that

$x^{2}+y^{2} =r^{2}$

So, the ellipsoid gives

$4{(x^{2}+ y^{2)} + z^{2} =64$

4( $r^{2}$ ) + $z^{2}$ = 64

$z^{2}$ = 64- 4( $r^{2}$ )

z=± $\sqrt{64-4r^{2} }$

So, the volume of the solid is given by:

V= $\int\limits^{2\pi}_ 0 \int\limits^1_0{} \, [\sqrt{64-4r^{2} }- (-\sqrt{64-4r^{2} })] r dr d\theta$

= $2\int\limits^{2\pi}_ 0 \int\limits^1_0 \, r\sqrt{64-4r^{2} } r dr d\theta$

To solve the integral take, $64-4r^{2}$ = t

dt= -8rdr

rdr = $\frac{-1}{8} dt$

So, the integral $\int\ r\sqrt{64-4r^{2} } rdr$ become

= $\int\ \sqrt{t } \frac{-1}{8} dt$

= $\frac{-1}{12} t^{3/2}$

= $\frac{-1}{12} (64-4r^{2}) ^{3/2}$

so on applying the limit, the volume becomes

V= $2\int\limits^{2\pi}_ {0} \int\limits^1_0{} \, \frac{-1}{12} (64-4r^{2}) ^{3/2} d\theta$

= $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(64-4(1)^{2}) ^{3/2} \; -(64-4(2)^{0}) ^{3/2} ] d\theta$

V = $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

Since, further the integral isn't having any term of $\theta$ .

we will end here.

The Volume of the given solid using polar coordinate is: $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

Learn more about Volume in polar coordinate here:

brainly.com/question/25172004

#SPJ4

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1 year ago

2x - 3y = 1 and x + 2y = 18

Yuliya22 [10]

Answer:

x = 8 and y = 5

Step-by-step explanation:

2x - 3y = 1 --(1)

x + 2y = 18

x = 18 - 2y --(2)

sub (2) into (1):

2(18 - 2y) - 3y = 1

36 - 4y - 3y = 1

-7y = 1 -36

7y = 35

y = 5

x = 18 - 2(5) = 8

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2 years ago

What Is a median ,mode,range and IQR ?

Katarina [22]

Median: is the number in the middle when the set data set is in order
mode: it the number that occurs the most in the set
range:difference between the smallest and largest number
IQR: interquartile range is a measure of a data set separated into quartiles

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3 years ago

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