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3 years ago

X=3m/2-m make m the subject of the formulahelp me plss

Mathematics

1 answer:

wel3 years ago

8 0

Answer:

2X/(3+X)

Step-by-step explanation:

X = 3m/2-m

Cross multiply both sides

X × (2-m)= 3m

2X-Xm= 3m

2X= 3m+Xm

2X= m(3+X)

Divide both sides by the coefficient of m which is (3+X)

m= 2X/(3+X)

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Which term of the Ap: 3,8,13,18.......is 78?

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Answer:

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Step-by-step explanation:

$a_1=3,\ a_2=3+5=8,\ a_3=8+5=13,\ a_4=13+5=18\ \implies\ d=5\\\\a_n=a_1+(n-1)d\\\\a_n=3+(n-1)(5)\\\\a_n=3+5n-5\\\\a_n=5n-2\\\\ a_n=78\quad\implies\quad n=\,??\\\\78=5n-2\\\\78+2=5n\\\\5n=80\\\\n=16$

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3 years ago

Prove divisibility 45^45·15^15 by 75^30

Anuta_ua [19.1K]

Answer:

$3^{75}$

Step-by-step explanation:

We are asked to divide our given fraction: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(3*15)^{45}=3^{45}*15^{45}$

$75^{30}=(5*15)^{30}=5^{30}*15^{30}$

Substituting these values in our division problem we will get,

$\frac{3^{45}*15^{45}*15^{15}}{5^{30}*15^{30}}$

Using power rule of exponents $a^m*a^n=a^{m+n}$ we will get,

$\frac{3^{45}*15^{45+15}}{5^{30}*15^{30}}$

$\frac{3^{45}*15^{60}}{5^{30}*15^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{45}*15^{60-30}}{5^{30}}$

$\frac{3^{45}*15^{30}}{5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{3^{45}*(3*5)^{30}}{5^{30}}$

$\frac{3^{45}*3^{30}*5^{30}}{5^{30}}$

Upon canceling out $5^{30}$ we will get,

$3^{45}*3^{30}$

Using power rule of exponents $a^m*a^n=a^{m+n}$ we will get,

$3^{45+30}$

$3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

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3 years ago