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3 years ago

a rectangular patio is 9 yards 2 ft long and 5 yards 2 feet wide what is the perimeter of the patio in yards

Mathematics

1 answer:

qaws [65]3 years ago

7 0

Answer:36 yards and 2 feet

Step-by-step explanation:

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You have 8,640 grams of a radioactive kind of cesium. If its half-life is 30 years, how much

Vikki [24]

The mass of cesium left afer 120 years if the original mass of cesium is 8640 with an half-life of 30 years, is 540 grams.

This can be defined as the time taken for half the amount of a radioactive substance to decay.

To calculate the amount of cesium left after 120 years, we use the formua below.

Formula:

R' = R/( $2^{T/t}$ )............. Equation 1

Where:

R = Original amount of Cesium
R' = New amount of cesium
T = Total time
t = Half-life

From the question,

Given:

R = 8640
T = 120 years
t = 30 years

Substitute these values into equation 1

R' = 8640/( $2^{120/30}$ )
R' = 8640/ $2^{4}$
R' = 8640/16
R' = 540 grams.

Hence, The mass of cesium left afer 120 years is 540 grams.

Learn more about half-life here: brainly.com/question/25750315

4 0

2 years ago

How many different squares appear in this picture?

ArbitrLikvidat [17]

Answer:

Step-by-step explanation:

4 times 4 is 16

2 boxes in the middle

4 tiny boxes in each one in the middle

1 entire one on the outside

1+4+4+2+16= 27

7 0

3 years ago

Find each percent increase round to the nearest percent from $5 to $8

asambeis [7]

First subtract the two numbers:

8 - 5 = 3

Now divide this to the original:

3 / 5 = 0.6

Multiply by 100:

0.6 * 100 = 60%

7 0

3 years ago

Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 an

Leya [2.2K]

Parameterize the lateral face $T_1$ of the cylinder by

$\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v$

where $0\le u\le2\pi$ and $0\le v\le3$ , and parameterize the disks $T_2,T_3$ as

$\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)$
$\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)$

where $0\le r\le2$ and $0\le\theta\le2\pi$ .

The integral along the surface of the cylinder (with outward/positive orientation) is then

$\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}((2\cos u)^2+(2\sin u)^2+v^2)\left\|{{\mathbf r}_1}_u\times{{\mathbf r}_2}_v\right\|\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+0^2)\left\|{{\mathbf r}_2}_r\times{{\mathbf r}_2}_\theta\right\|\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+3^2)\left\|{{\mathbf r}_3}_r\times{{\mathbf r}_3}_\theta\right\|\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r^3\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r(r^2+9)\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr$
$=136\pi$