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3 years ago

What is the next term of the geometric sequence?375,75,15

Mathematics

2 answers:

ANTONII [103]3 years ago

5 0

Answer:

Step-by-step explanation:

375/5 = 75

75/5 = 15

15/5 = 3

.... Basically you are dividing each term by 5 until you reach 3.... the most simplified version of this equation.

Damm [24]3 years ago

3 0

Answer:

Step-by-step explanation:

ΔΔπФ⇵β³Δ⊄⊇≡⊕⊕π⇆ω∩∨

You might be interested in

A circle has a circumference of 28π centimeters. In terms of π, what is the area of the circle to the nearest square centimeter?

Vadim26 [7]

Hi there!

The formula to find the are of a circle is :

a = $\pi$ r²

The formula to find the circumference of a circle is :

c = 2 $\pi$ r

In order to use the area formula, you need to figure out what the radius (r) is.

If we solve for "r" in the circumference equation, we have :

r = c ÷ (2 $\pi$ )

Now we use this to replace "r" in the area formula :

a = $\pi$ ( c ÷ (2 $\pi$ ))²

When we simplify this we get :

a = c² ÷ 4 $\pi$

Now you can put your value of "c" into this equation and find "a".

*Remember, $\pi$ is about 3.1416.

Solving for "a" :

a = c² ÷ 4 $\pi$

a = 28² ÷ 4 $\pi$

28² = 28 × 28 = 784

a = 784 ÷ 4 $\pi$

4 $\pi$ = 4 × $\pi$ = 12.56637061435917

a = 784 ÷ 12.56637061435917

a = 62.38873769202297cm²

You need to round to the nearest square centimeter, which means that you need to round to the nearest whole number :

a = 62cm²

There you go! I really hope this helped, if there's anything just let me know! :)

8 0

3 years ago

Please help, I am not able to find the answer

Anton [14]

Answer:

Assuming you are asked for the equation of the graph, the answer would be y=|x+2|-1.

Step-by-step explanation:

The parent function for the "V-shape" is y=|x|. This particular function is translated to the left two units and down one. This is shown by adding two to x within the absolute value and subtracting one from the absolute value of x+2, leaving you with y=|x+2|-1. If you plug this equation into desmos online graphing calculator, you will see that the graph is identical to the one given.

6 0

2 years ago

What is the weight of a square if a triangle weighs 4 grams? Explain your reasoning

stellarik [79]

Answer:

8 grams

Step-by-step explanation:

The balance is in equilibrium, so the weights of the two sides are equal.

Let the weight of a square be s.

Left side: 2s + 4

Right side: s + 3(4) = s + 12

The weights are equal, so we set the two expressions equal.

2s + 4 = s + 12

s = 8

Answer: The weight of a square is 8 grams.

8 0

3 years ago

how much wrapping paper would you need to cover a rectangular that is 18.25 inches by 12inches by 3 inches if you need 10% more

natita [175]

Answer: 681 square inch

Step-by-step explanation:

Hi, we have to apply the formula for the surface area:

A = 2wl + 2lh + 2hw

Where:

w: width

l: length

h: height

Replacing with the values given:

A = (2x12x18.25) + (2x12x3)+(2x18.25x3)

A= 438+72+109.25

A=619.5 in2

Since it has to be 10% more than the surface.

619.5 x (10/100) = 61.95 in2

Adding that value to the surface area

619.5+61.95 = 681.45in2 = 681 in2

4 0

2 years ago

Solve the following differential equation using using characteristic equation using Laplace Transform i. ii y" +y sin 2t, y(0) 2

kifflom [539]

Answer:

The solution of the differential equation is $y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)$

Step-by-step explanation:

The differential equation is given by: y" + y = Sin(2t)

<u>i) Using characteristic equation:</u>

The characteristic equation method assumes that y(t)= $e^{rt}$ , where "r" is a constant.

We find the solution of the homogeneus differential equation:

y" + y = 0

$y'=re^{rt}$

$y"=r^{2}e^{rt}$

$r^{2}e^{rt}+e^{rt}=0$

$(r^{2}+1)e^{rt}=0$

As $e^{rt}$ could never be zero, the term (r²+1) must be zero:

(r²+1)=0

r=±i

The solution of the homogeneus differential equation is:

$y(t)_{h}=c_{1}e^{it}+c_{2}e^{-it}$

Using Euler's formula:

$y(t)_{h}=c_{1}[Sin(t)+iCos(t)]+c_{2}[Sin(t)-iCos(t)]$

$y(t)_{h}=(c_{1}+c_{2})Sin(t)+(c_{1}-c_{2})iCos(t)$

$y(t)_{h}=C_{1}Sin(t)+C_{2}Cos(t)$

The particular solution of the differential equation is given by:

$y(t)_{p}=ASin(2t)+BCos(2t)$

$y'(t)_{p}=2ACos(2t)-2BSin(2t)$

$y''(t)_{p}=-4ASin(2t)-4BCos(2t)$

So we use these derivatives in the differential equation:

$-4ASin(2t)-4BCos(2t)+ASin(2t)+BCos(2t)=Sin(2t)$

$-3ASin(2t)-3BCos(2t)=Sin(2t)$

As there is not a term for Cos(2t), B is equal to 0.

So the value A=-1/3

The solution is the sum of the particular function and the homogeneous function:

$y(t)= - \frac{1}{3} Sin(2t) + C_{1} Sin(t) + C_{2} Cos(t)$

Using the initial conditions we can check that C1=5/3 and C2=2

<u>ii) Using Laplace Transform:</u>

To solve the differential equation we use the Laplace transformation in both members:

ℒ[y" + y]=ℒ[Sin(2t)]

ℒ[y"]+ℒ[y]=ℒ[Sin(2t)]

By using the Table of Laplace Transform we get:

ℒ[y"]=s²·ℒ[y]-s·y(0)-y'(0)=s²·Y(s) -2s-1

ℒ[y]=Y(s)

ℒ[Sin(2t)]= $\frac{2}{(s^{2}+4)}$

We replace the previous data in the equation:

s²·Y(s) -2s-1+Y(s) = $\frac{2}{(s^{2}+4)}$

(s²+1)·Y(s)-2s-1= $\frac{2}{(s^{2}+4)}$

(s²+1)·Y(s)= $\frac{2}{(s^{2}+4)}+2s+1=\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)}$

Y(s)= $\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)(s^{2}+1)}$

Y(s)= $\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}$

Using partial franction method:

$\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}=\frac{As+B}{s^{2}+4} +\frac{Cs+D}{s^{2}+1}$

2s^{3}+s^{2}+8s+6=(As+B)(s²+1)+(Cs+D)(s²+4)

2s^{3}+s^{2}+8s+6=s³(A+C)+s²(B+D)+s(A+4C)+(B+4D)

We solve the equation system:

A+C=2

B+D=1

A+4C=8

B+4D=6

The solutions are:

A=0 ; B= -2/3 ; C=2 ; D=5/3

So,

Y(s)= $\frac{-\frac{2}{3} }{s^{2}+4} +\frac{2s+\frac{5}{3} }{s^{2}+1}$

Y(s)= $-\frac{1}{3} \frac{2}{s^{2}+4} +2\frac{s }{s^{2}+1}+\frac{5}{3}\frac{1}{s^{2}+1}$

By using the inverse of the Laplace transform:

ℒ⁻¹[Y(s)]=ℒ⁻¹[ $-\frac{1}{3} \frac{2}{s^{2}+4}$ ]-ℒ⁻¹[ $2\frac{s }{s^{2}+1}$ ]+ℒ⁻¹[ $\frac{5}{3}\frac{1}{s^{2}+1}$ ]

$y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)$

3 0

3 years ago

What is the next term of the geometric sequence?375,75,15​

What is the next term of the geometric sequence?375,75,15