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liubo4ka [24]
2 years ago
7

Element X is a radioactive isotope such that every 20 years, its mass

Mathematics
1 answer:
faust18 [17]2 years ago
3 0

Answer:

12.1

Step-by-step explanation:

y=a(1/2)^t/h

270=410(1/2)^t/20

Divide both sides by 410

0.6585365854 = (1/2)^t/20

Log Both sides

Log(0.6585365854) / Log(1/2)

.6026645024= t/20

20 x .6026645024 = t

12.05329005 to the nearest tenth is 12.1 = t

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The number of girls in cobbs class is 2 less than 3 times the number of boys. She has 26 students in her class how many are boys
Natalka [10]

Answer:

7 are boys

Step-by-step explanation:

Make a system of equations where g is for girls and b is for boys.

b+g=26

g=3b-2

Substitute "3b-2" in for "g" in the first equation.

b+(3b-2)=26

Rewrite without the parentheses because it's addition and not multiplication.

b+3b-2=26

Combine like terms.

4b-2=26

Add 2 to both sides.

4b=28

Divide by the coefficient of the variable to get it alone.

b=7

3 0
3 years ago
What simple interest rate would allow $6000 to grow to an amount of $14550 in 10 years?
Harman [31]

Answer:

\boxed{ \bold{ \huge{  \boxed{ \sf{ \: 14.25 \: \% \: }}}}}

Step-by-step explanation:

Given,

Principal ( P ) = $ 6000

Amount ( A ) = $ 14550

Time ( T ) = 10 years

Rate ( R ) = ?

<u>Finding </u><u>the </u><u>Interest</u>

The sum of principal and interest is called an amount.

From the definition,

\boxed{ \sf{Amount =  \: Principal + Interest}}

plug the values

⇒\sf{14550 = 6000 + Interest}

Swap the sides of the equation

⇒\sf{6000 + Interest = 14550}

Move 6000 to right hand side and change its sign

⇒\sf{Interest = 14550 - 6000}

Subtract 6000 from 14550

⇒\sf{Interest = \: 8550 \: }

Interest = $ 8550

<u>Finding </u><u>the </u><u>rate </u>

{ \boxed{ \sf{Rate =  \frac{Interest \times 100}{Principal \times Time}}}}

plug the values

⇒\sf{ Rate = \frac{8550  \times 100}{6000 \times 10} }

Calculate

⇒\sf{Rate =  \frac{855000}{60000} }

⇒\sf{Rate = 14.25 \: \% \: }

Hope I helped!

Best regards!!

8 0
3 years ago
Emergency I need help I don't understand this​
lora16 [44]

Answer:

108 is your answer.

Step-by-step explanation:

1 x + 2x + 3x = 180

10 x = 180

x = 180/ 10

x = 18

Then

18 X 6 = 108

I HOPE IT WILL HELP YOU.

Have a great day.

it's me Sopnila.

❤❤❤

8 0
2 years ago
Read 2 more answers
Please and thank you help me
Leona [35]

Answer:

y = 3x - 5

Step-by-step explanation:

y = mx + b

m (slope) = 3/1 or 3

b (y-intercept) = -5

y = 3x - 5

8 0
2 years ago
Evaluate the following integral using trigonometric substitution
serg [7]

Answer:

The result of the integral is:

\arcsin{(\frac{x}{3})} + C

Step-by-step explanation:

We are given the following integral:

\int \frac{dx}{\sqrt{9-x^2}}

Trigonometric substitution:

We have the term in the following format: a^2 - x^2, in which a = 3.

In this case, the substitution is given by:

x = a\sin{\theta}

So

dx = a\cos{\theta}d\theta

In this question:

a = 3

x = 3\sin{\theta}

dx = 3\cos{\theta}d\theta

So

\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}

We have the following trigonometric identity:

\sin^{2}{\theta} + \cos^{2}{\theta} = 1

So

1 - \sin^{2}{\theta} = \cos^{2}{\theta}

Replacing into the integral:

\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C

Coming back to x:

We have that:

x = 3\sin{\theta}

So

\sin{\theta} = \frac{x}{3}

Applying the arcsine(inverse sine) function to both sides, we get that:

\theta = \arcsin{(\frac{x}{3})}

The result of the integral is:

\arcsin{(\frac{x}{3})} + C

8 0
2 years ago
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