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2 years ago

Are the ratios 9:3 and 6:2 equivalent?

Mathematics

2 answers:

RoseWind [281]2 years ago

5 0

Answer:

yes

Step-by-step explanation:

they both simplify to 3:1

KATRIN_1 [288]2 years ago

5 0

Answer:

Yes

Step-by-step explanation:

To see whether two fractions are equivalent or not we need to simplify them

9:3 can be simplified to 3:1 as the biggest common divisor of 9 and 3 is 3

6:2 can be simplified to 3:1 since the biggest common divisor of this set is 2

as seen we can simplify both to 3:1 so yes, they are equivalent

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IF YOU ARE GOOD AT MATH PLZZ HELPPP!!! Algebra II

dybincka [34]

(a)first term=2

(n)no of term=10

(r)common ratio=8/2=4

sn={a(r^n-1)}÷(r-1)

s1o={2(4^10-1)}÷(4-1)

s10={2(1048576-1)}÷3

s10=2097150÷3

s1o=699050

7 0

3 years ago

Find the inverse Laplace transforms, as a function of x, of the following functions:

inn [45]

Answer: The required answer is

$f(x)=e^x+\cos x+\sin x.$

Step-by-step explanation: We are given to find the inverse Laplace transform of the following function as a function of x :

$F(s)=\dfrac{2s^2}{(s-1)(s^2+1)}.$

We will be using the following formulas of inverse Laplace transform :

$(i)~L^{-1}\{\dfrac{1}{s-a}\}=e^{ax},\\\\\\(ii)~L^{-1}\{\dfrac{s}{s^2+a^2}\}=\cos ax,\\\\\\(iii)~L^{-1}\{\dfrac{1}{s^2+a^2}\}=\dfrac{1}{a}\sin ax.$

By partial fractions, we have

$\dfrac{s^2}{(s-1)(s^2+1)}=\dfrac{A}{s-1}+\dfrac{Bs+C}{s^2+1},$

where A, B and C are constants.

Multiplying both sides of the above equation by the denominator of the left hand side, we get

$2s^2=A(s^2+1)+(Bs+C)(s-1).$

If s = 1, we get

$2\times 1=A(1+1)\\\\\Rightarrow A=1.$

Also,

$2s^2=A(s^2+1)+(Bs^2-Bs+Cs-C)\\\\\Rightarrow 2s^2=(A+B)s^2+(-B+C)s+(A-C).$

Comparing the coefficients of x² and 1, we get

$A+B=2\\\\\Rightarrow B=2-1=1,\\\\\\A-C=0\\\\\Rightarrow C=A=1.$

So, we can write

$\dfrac{2s^2}{(s-1)(s^2+1)}=\dfrac{1}{s-1}+\dfrac{s+1}{s^2+1}\\\\\\\Rightarrow \dfrac{2s^2}{(s-1)(s^2+1)}=\dfrac{1}{s-1}+\dfrac{s}{s^2+1}+\dfrac{1}{s^2+1}.$

Taking inverse Laplace transform on both sides of the above, we get

$L^{-1}\{\dfrac{2s^2}{(s-1)(s^2+1)}\}=L^{-1}\{\dfrac{1}{s-1}\}+L^{-1}\{\dfrac{s}{s^2+1}+\dfrac{1}{s^2+1}\}\\\\\\\Rightarrow f(x)=e^{1\times x}+\cos (1\times x)+\dfrac{1}{1}\sin(1\times x)\\\\\\\Rightarrow f(x)=e^x+\cos x+\sin x.$

Thus, the required answer is

$f(x)=e^x+\cos x+\sin x.$

4 0

4 years ago

The distance Din miles from an observer to the horizon over flat land or water can be estimated using the formula D-123/

sertanlavr [38]

B.) about 2.73 mi is how far the horizon is from a person

3 0

3 years ago

C. If 48 increases by 130%

alexandr402 [8]

Answer:

69%

Step-by-step explanation:

5 0

3 years ago

What is the simplified form of the expression?

SIZIF [17.4K]

Remember
(x^m)/(x^n)=x^(m-n)

(q^(33/4))/(q^8)=q^((33/4)-8)
what is 33/4-8?
33/4-8=33/4-32/4=1/4

result is
q^1/4 or $\sqrt[4]{q}$

answer is $q^{ \frac{1}{4} }$

8 0

3 years ago

Read 2 more answers