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2 years ago

Element X is a radioactive isotope such that every 12 years, its mass decreases by half.

Mathematics

1 answer:

morpeh [17]2 years ago

6 0

Answer:636

Step-by-step explanation: I just kno

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Find the equation of the sphere in standard form centered at (−6,10,5) with radius 5.

Dovator [93]

Answer:

The equation of the sphere in standard form is

$x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0$

Step-by-step explanation:

<u>Step 1</u>:-

The equation of the sphere having center and radius is

$(x-h)^{2} +(y-k)^{2} +(z-l)^{2} = r^{2}$

Given centered of the sphere is (-6,10,5) and radius r=5

$(x-(-6))^{2} +(y-10)^{2} +(z-5)^{2} = 5^{2}$

on simplification,we get

$using (a+b)^{2} =a^{2} +2 a b+b^{2}$

$using (a-b)^{2} =a^{2} -2 a b+b^{2}$

simplify , we get

$x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0$

8 0

3 years ago

Drag each expression to show whether it can be used to find the volume, surface area, or neither.

Mumz [18]

Answer:

Volume = 12 *6 *8 , Surface area = 2 ( 12 *6 + 8 *12 + 6* 8 )

Step-by-step explanation:

Given : Cuboid with length 12 , width 6 and height 8 units.

To find : Drag each expression to show whether it can be used to find the volume, surface area, or neither.

Solution : We have given Cuboid with

Length = 12 units ,

Width = 6 units

Height = 8 units.

Volume of cuboid = length * width * height .

Volume = 12 *6 *8.

Surface area = 2 ( l *w + h *+w *h)

Surface area = 2 ( 12 *6 + 8 *12 + 6* 8 ).

None = 12 +6 +8.

Therefore, Volume = 12 *6 *8 , Surface area = 2 ( 12 *6 + 8 *12 + 6* 8 ) .

7 0

3 years ago

Read 2 more answers

Last year Mr. Christian‘s class had 30 students .this year the number of students in his class is 150% of the number of students

kow [346]

Answer:

He has 45 kids now.

Step-by-step explanation:

3 0

2 years ago

Find the area of the region that lies inside the first curve and outside the second curve.

marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = $\dfrac{1}{2}$

$\theta = -\dfrac{\pi}{3}, \ \ \dfrac{\pi}{3}$

Now, the area of the region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \ \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ 5^2 d \theta$

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \ \theta d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ d \theta$

$A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} \dfrac{cos \ 2 \theta +1}{2} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}$

$A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} {cos \ 2 \theta +1} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}} \ \ - \dfrac{25}{2} \begin {bmatrix} \dfrac{2 \pi}{3} \end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3}) \end {bmatrix} - \dfrac{25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} + \dfrac{\pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}$

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx

7 0

3 years ago

If N/8+6=58, then N equals?

GaryK [48]

N equals <em>416</em>

Hope this helps!

8 0

3 years ago

Read 2 more answers