MATHEMATICS MIDDLE SCHOOL

In 2000 the total amount of gamma ray bursts was recorded at 6.4 million for a city. In 2005, the same survey was made and the total amount of gamma ray bursts was 7.3 million. If the Earth can only withstand 1 billion gamma ray bursts, in what year will this become a problem? (Find the year in which the gamma ray bursts is 1 billion.)

Answers

Answer 1

Answer:

Let's assume

It started in 2000

so, t=0 in 2000

$P_0=6.4million$

we can use formula

$P(t)=P_0 e^(rt)$

we can plug value

$P(t)=6.4 e^(rt)$

In 2005, the same survey was made and the total amount of gamma ray bursts was 7.3 million

so, at t=2005-2000=5

P(t)=7.3 million

we can plug value and then we can solve for r

$7.3=6.4 e^(r*5)$

$r=0.02632$

now, we can plug back

$P(t)=6.4 e^(0.02632t)$

now, we have

P(t)=1 billion =1000 million

so, we can set it and then we can solve for t

$1000=6.4 e^(0.02632t)$

$t=191.924$

approximately

$t=192$

Year is 2000+192

year is 2192................Answer

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Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.f(x)= 5x²-3.
g(x)= 5x²+3

Answers

Answer:

see the explanation

The graph in the attached figure

Step-by-step explanation:

we have

Function f(x)

$f(x)=5x^(2)-3$ ----> equation A

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

The vertex is the point (0,-3)

The y-intercept is the point (0,-3) [value of y when the value of x is equal to zero]

The x-intercepts are the points

$(-\sqrt{(3)/(5)},0)$ and $(\sqrt{(3)/(5)},0)$

Function g(x)

$g(x)=5x^(2)+3$ ----> equation B

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

The vertex is the point (0,3)

The y-intercept is the point (0,3) [value of y when the value of x is equal to zero]

The function don't have x-intercepts (the roots are complex numbers)

We can say that the function g(x) is the translation of the function f(x) 6 units up

using a graphing tool

The graph in the attached figure

The graphs of these quadratic functions are similar in shape, with the main differences being vertical shifts and y-intercepts. The graph of g(x)=5x^2 +3 is obtained by shifting the graph of f(x)=5x^2 −3 upward by 6 units.

The graphs of the quadratic functions f(x)=5x^2 −3 and g(x)=5x^2 +3

Both functions are quadratic, which means they have a graph in the shape of a parabola. The coefficient of the x^2 term in both functions is 5, indicating that the parabolas open upwards.

Now, let's analyze the differences:

Vertical Shift:

For f(x)=5x^2 −3, there is a vertical shift downward by 3 units due to the constant term -3.

For g(x)=5x^2 +3, there is a vertical shift upward by 3 units due to the constant term +3.

Y-Intercept:

The y-intercept of f(x) occurs when x=0, and f(0)=−3, so the y-intercept is (0, -3).

The y-intercept of g(x) occurs when x=0, and g(0)=3, so the y-intercept is (0, 3).

Overall Shape:

Both graphs have the same overall shape since the coefficient of the

x^2 term is the same in both functions.

Symmetry:

The parabolas are symmetric with respect to the y-axis, as changing

x to −x in the quadratic term does not affect the overall value of the function.

Simplify (2x+y^2) (2y-4x-3y^2)

Answers

explaining

Algebra

Simplify (2x^2)(4x^3y^2)

(2x2)(4x3y2)(2x2)(4x3y2)

Multiply x2x2 by x3x3 by adding the exponents.

Tap for more steps...

2x5(4y2)2x5(4y2)

Rewrite using the commutative property of multiplication.

2⋅4(x5y2)2⋅4(x5y2)

Multiply 22 by 44.

8x5y2

Can someone help me with this page?

Answers

B is the first one
D
C
And finally (most likely) A

sure
i will help with the page if i can do it…

I need help can someone help me please

Answers

Answer:

Step-by-step explanation:

"Congruent" here means that if you place a drawing of one angle on top of another and the two drawings match perfectly, you've got congruence.

Is 1/81 = to 81 ? I think it is but I'm just making sure :)

Answers

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you are correct it is 81

Mumbi is approximately 845 kilometers away from Bangalore, and Mumbai is approximately 1160 km away from Delhi. The distances, measured in centimeters between cities on Allyson’s map are proportional to the real distances.Which of the following could be the the distances on Allyson’s map?

Choose 3 answers

Bangalore to Mumbai: 116.5 cm
Mumbai to Delhi: 174 cm

Bangalore to Mumbai: 42.25
Mumbai to Delhi: 58 cm

Bangalore to Mumbai: 23.4 cm
Mumbai to Delhi: 29 cm

Bangalore to Mumbai: 16.9 cm
Mumbai to Delhi: 23.2 cm

Bangalore to Mumbai: 25.35 cm
Mumbai to Delhi: 34.8cm

Answers

Mumbi is approximately 845 kilometers away from Bangalore, and Mumbai is approximately 1160 km away from Delhi, then the ratio between these distances is

$(845)/(1160)=(169)/(232).$

A. Bangalore to Mumbai: 116.5 cm;

Mumbai to Delhi: 174 cm

The ratio:

$(116.5)/(174)=(233)/(348)\neq (169)/(232)$

This option is false.

B. Bangalore to Mumbai: 42.25

Mumbai to Delhi: 58 cm

The ratio is

$(42.25)/(58)=(845)/(1160)=(169)/(232)$

This option is true.

C. Bangalore to Mumbai: 23.4 cm

Mumbai to Delhi: 29 cm

The ratio is

$(23.4)/(29)=(117)/(145)\neq (169)/(232)$

This option is false.

D. Bangalore to Mumbai: 16.9 cm

Mumbai to Delhi: 23.2 cm

The ratio is

$(16.9)/(23.2)=(169)/(232)$

This option is true.

E. Bangalore to Mumbai: 25.35 cm

Mumbai to Delhi: 34.8cm

The ratio is

$(25.35)/(34.8)=(507)/(696)=(169)/(232)$

This option is true.

Answer: correct options are B, D and E

Answer:

Step-by-step explanation:

Mumbi is approximately 845 kilometers away from Bangalore, and Mumbai is approximately 1160 km away from Delhi, then the ratio between these distances is

A. Bangalore to Mumbai: 116.5 cm;

Mumbai to Delhi: 174 cm

The ratio:

This option is false.

B. Bangalore to Mumbai: 42.25

Mumbai to Delhi: 58 cm

The ratio is

This option is true.

C. Bangalore to Mumbai: 23.4 cm

Mumbai to Delhi: 29 cm

The ratio is

This option is false.

D. Bangalore to Mumbai: 16.9 cm

Mumbai to Delhi: 23.2 cm

The ratio is

This option is true.

E. Bangalore to Mumbai: 25.35 cm

Mumbai to Delhi: 34.8cm

The ratio is

This option is true.

Answer: correct options are B, D and E

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