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3 years ago

A 33 gram sample of a substance that's

Mathematics

1 answer:

Mazyrski [523]3 years ago

6 0

9514 1404 393

Answer:

6.2

Step-by-step explanation:

We presume your "k-value" is the k in the exponential decay term ...

e^(-kt) . . . where t is the number of time units

This is 1/2 when ...

ln(1/2) = -kt

t = ln(1/2)/(-k) = ln(2)/k

t = 0.69315/0.1124 ≈ 6.2

The half life is about 6.2 time units.

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When you graph the exact same equation twice ?

Helen [10]

You will have infinite solutions

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3 years ago

Solving Rational equations. LCD method. Show work. Image attached.

Dmitry [639]

Answer:

$b=1$

Step-by-step explanation:

The given rational equation is

$\frac{2b-5}{b-2} -2=\frac{3}{b+2}$

The Least Common Denominator is $(b+2)(b-2)$ .

Multiply each term in the equation by the LCD.

$(b+2)(b-2)\times \frac{2b-5}{b-2} -(b+2)(b-2)\times2=(b+2)(b-2)\times\frac{3}{b+2}$

Simplify;

$(b+2)\times \frac{2b-5}{1} -2(b+2)(b-2)=(b-2)\times\frac{3}{1}$

$(b+2)(2b-5) -2(b+2)(b-2)=3(b-2)$

Expand and group similar terms

$2b^2-5b+4b-10 -2(b^2-4)=3b-6$

$2b^2-5b+4b-10 -2b^2+8=3b-6$

$-b-2=3b-6$

$3b+b=-2+6$

$4b=4$

$b=1$

3 0

3 years ago

Where does the square root of 40 go on a 1-10 number line?

kaheart [24]

Answer:

Step-by-step explanation:

$36 < 40 < 49\\\\6 < \sqrt{40} < 7\\$

Here is the exact construction of √40 using Pythagorean 's theorem

8 0

2 years ago

Which relationship describes angles 1 and 2?

malfutka [58]

Answer:

vertical angles

Step-by-step explanation:

When two lines intersect at a single point, they form 4 angles. Two angles that are not adjacent are vertical angles. With an intersection of two lines art a single point, there are two pairs of vertical angles. Angles 1 and 2 are vertical angles.

5 0

3 years ago

Read 2 more answers

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.