Which measure correctly completes the statement?

there are 28 books on the shelf.one-fourth of the books are about animals. two are adventure. the rest are mystery.How many book

yanalaym [24]

Answer:

19

Step-by-step explanation:

1/4 are animal. 28/4 = 7

2 are adventure.

7+2 = 9

9 are not mystery

28-9 = 19

19 are mystery.

4 0

3 years ago

Emily completed reading 24/3 books in 32/4 days. Find the number of books she would have completed in one day.

AlexFokin [52]

The number of books she would have completed in one day will be 2 books.

<h3>What is an expression?</h3>

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

Emily completed reading 24/3 books in 32/4 days

Emily completed 8 books in 4 days. The number of the books will be calculated by using the expression below:-

4 days = 8 books

1 day = 8 / 4 = 2 books

Therefore the number of books she would have completed in one day will be 2 books.

To know more about expression follow

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3 0

2 years ago

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:

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3 0

2 years ago

The temperature in Greenland is -8.3°C. The temperature in Jamaica is 30°C. What is the difference between the temperatures in t

Fantom [35]

Answer:

The difference between the temperatures in the two countries is 38.3°C.

Step-by-step explanation:

Given:

Temperature in Greenland = - 8.3°C

Temperature in Jamaica = 30°C

To find :

The difference between the temperature in the two countries = ?

$\textrm{difference between the temperature in the two countries} =\textrm{temperature in Jamaica} - \textrm{temperature in Greenland}\\= 30 - (-8.3)\\= 30 +8.3\\= 38.3\°C$

Therefore,the difference between the temperatures in the two countries is 38.3°C

6 0

3 years ago

The Fun Guys game rental store charges an annual fee of $10 plus $6.50 per game rented. The Game Bank charges an annual fee of $

Leni [432]

Step-by-step explanation:

solve it through simultaneous equations

for fun guys : 10+6.5x=y

for game bank : 22+3.5x=y

10+6.5x=22+3.5x

3x=12

x=4

cost is same when game rentals =4

that cost= $36

7 0

3 years ago