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anyanavicka [17]

3 years ago

10

Coz and Amelia each make a tile design with 24 tiles. Coz puts his in rows of 2.Amelia puts hers in rows of 3.How many more tile

s are in each of Coz's rows than Amelia's?

1 answer:

Ivahew [28]3 years ago

4 0

Answer:

4 tiles

Step-by-step explanation:

Divide 24 by 2 (Coz): 12 tiles

Divide 24 by 3 (Amelia): 8 tiles

Subtract 8 from 12.

12 - 8 = 4

There are 4 more tiles in each of Coz's rows than Amelia's.

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Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =

sashaice [31]

Let $R$ be the solid. Then the volume is

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
(by computing the Jacobian)

and

$z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8$
(we take the positive solution, since it's clear that $R$ lies above the $x$ - $y$ plane)
$r^2+z^2=72\implies z=\pm\sqrt{72-r^2}$
(again, taking the positive root for the same reason)
$z=r^2\implies 8=r^2\implies r=\sqrt8$

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr$
$=\dfrac{32(27\sqrt2-35)\pi}3$

7 0

2 years ago

In order to prove that traingle ADC is congruent to triangle ABC by SAS, we would need to show that

IRISSAK [1]

Answer:

D) Angle DAC is congruent to Angle BAC

Step-by-step explanation:

Given:

The triangles ABC and ADC are congruent by SAS postulate.

SAS postulate means two corresponding sides are congruent to each other and the included pair of angles are also congruent to each other.

From the figure, consider the triangles ABC and ADC.

AB = AD (Given)

AC = AC ( Reflexive property. Side AC is a common side to both triangles)

Now, the pair of angles included between these two pair of sides are angle BAC and angle DAC.

So, in order to prove the two triangles congruent by SAS postulate, we need to prove angle DAC congruent to angle BAC. Therefore, the correct option is option D.

8 0

3 years ago

What is the area, in square units, of the parallelogram?<br><br>12<br>18<br>24<br>36

uysha [10]

24, because area means to multipy and it gives 6 ins. and 4 ins. so 6x4 is 24. Hope I was helpful.

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3 years ago

La ecuación h(x) =23 es lineal?

NARA [144]

Si! H(x)=23 es lineal

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1 year ago

Find the area of the polygon.

svetlana [45]

This is a trapezoid and the trapezoid formula is b1 plus b2/ 2 times height.

17 plus 5 is 22. Divided by 2 is 11.

Now, we have to multiply 11 by the height : 5.

11 times 5 is 55 and that is your area. 55 units squared.

7 0

2 years ago