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3 years ago

What’s the formula to -1/2,-3/10,-9/50,-27/250,....

Mathematics

1 answer:

laila [671]3 years ago

5 0

Answer:

The formula is ⇒ $\frac{-1}{2}(\frac{3}{5})^{n-1}$

Step-by-step explanation:

∵ The sequence is -1/2 , -3/10 , -9/50 , -27/250

∵ (-3/10) ÷ (-1/2) = 3/5

∵ (-9/50) ÷ (-3/10) = 3/5

∴ It is a geometric sequence

∴ The formula is Tn = ar^(n - 1)

Where a is the first term , r is the constant ratio between each two consecutive terms and n is the position of the number

∴ Tn = -1/2 ( 3/5)^(n - 1)

∴ $Tn= \frac{-1}{2}(\frac{3}{5})^{n-1}$

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In a certain city, the record rainfall during an 24-hour period is 14 and one fourth inches. How much rain fell per hour on a

lubasha [3.4K]

Answer:

the answer us about .53 per hour

Step-by-step explanation:

You just divide 14.25 by 24

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3 years ago

Use the distributive property to remove the parentheses -5(-4y-w+3)

vampirchik [111]

Answer:

Step-by-step explanation:

Original Equation:

-5(-4y - w + 3)

Multiply -5 by -4y

20y

Multiply -5 by -w

Multiply -5 by 3

-15

Plug these values back into the equation

20y + 5w - 15

Hope this helps :)

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3 years ago

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3 years ago

Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

2 years ago

Bess has $2.80 in quarters and dimes. The number of dimes is 7 less than the number of quarters. Find the number of quarters and

Nezavi [6.7K]

Answer:

3 dimes and 10 quarters

Step-by-step explanation:

If you add 7 dimes, then the number of dimes and quarters is the same, and the total increases to $3.50. A dime and a quarter have a value together of $0.35. Since there are equal numbers, the value $3.50 must be made up of some quantity of groups with a value of $0.35. That number of groups must be ...

... $3.50/$0.35 = 10

Thus, there are 10 quarters and 10-7 = 3 dimes.

_____

Using an equation

Let q represent the number of quarters. Then the amount Bess has is ...

... 0.10(q -7) +0.25q = 2.80

... 0.35q - 0.70 = 2.80

... 0.35q = 3.50 . . . . . add 0.70 . . . . . . . this should look familiar

... q = 3.50/0.35 = 10

4 0

3 years ago