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2 years ago

What is the rate of decay in the following function? f(x)=3(67)^x

Mathematics

1 answer:

tigry1 [53]2 years ago

5 0

Answer:

Suppose N is the size of a population of radioactive atoms at a given time t, and dN is the amount by which the population decreases in time dt; then the rate of change is given by the equation dN/dt = −λN, where λ is the decay constant.

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Find a polynomial of degree 3 with a real coefficient that satisfies the given condition. Zeros: -2, 1, 0; f(2)=32

xz_007 [3.2K]

Its factors would be
(x+2)*(x-1)*(x+0)

x^2 +x -2

x^3 + 0 + x^2 + 0 -2x +0

Equation: x^3 + x^2 -2x
f(2) = 8 + 4 -4

2x^3 + 2x^2 -4x +0
f(2) = 16 + 8 -8

3x^3 + 3x^2 -6x +0
f(2) = 24 +12 -12

4x^3 + 4x^2 -8x +0
f(2) = 32 +16 -16

So, the equation is:
4x^3 + 4x^2 -8x = 0

8 0

3 years ago

Find the Quotient and Remainder. 5x^3 - 6x^2 + x + 7 divided by x^2

12345 [234]

Step-by-step explanation:

Solution

According to remainder theorem, when f(x) is divided by (x+2), Remainder =f(−2)

f(x)=5x3+2x2−6x+12

f(−2)=5(−2)3+2(−2)2−6(−2)+12

=5×−8+2×4+12+12

=−40+32=−8

∴ Remainder=−8

5 0

2 years ago

WILL GIVE BRAINLIEST IF CORRECT, IF WRONG NO BRAINLIEST Which statement accurately explains whether a reflection over the x-axis

Paladinen [302]

9514 1404 393

Answer:

No, A″C″B″ is located at A″(1, 1), C″(4, 3), and B″(1, 5)

Step-by-step explanation:

Line AB is horizontal, so reflection across the x-axis maps it to a horizontal line. Then rotation CCW by 90° maps it to a vertical line. The composition of transformations cannot map the figure to itself.

A reasonable explanation is the last one:

No, A″C″B″ is located at A″(1, 1), C″(4, 3), and B″(1, 5)

5 0

3 years ago

How can an expression using the distributive property can be simplified to 12a + 18b - 6c

elena-s [515]

Look for a common number in all the terms

6(2a+3b-c)

3 0

3 years ago

Two planes are the same altitude. From the airport , one plane is 50 km away in the direction of N°60 E and another is 80 km awa

djverab [1.8K]

9514 1404 393

Answer:

78.5 km

Step-by-step explanation:

Measured at the airport, the angle between the two planes is ...

180° -60° -50° = 70°

The law of cosines tells us the distance between the planes is ...

d = √(50² +80² -2·50·80·cos(70°)) ≈ √6163.84 ≈ 78.5 . . . km

The planes are about 78.5 km apart.

6 0

2 years ago