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3 years ago

A famous instance of variation is Newton’s Law of Gravity. It states that the magnitude of the Force, F, of gravitational attrac

tion between two masses, m1 and m2, varies directly with the product of the masses and inversely with the square of the distance, r, between them. Write a variation equation relating F, m1, m2, and r.

Mathematics

1 answer:

adelina 88 [10]3 years ago

5 0

$\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ F=\cfrac{k(m_1\cdot m_2)}{r^2}\leftarrow \textit{F varies directly with a product and inversely with }r^2$

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The first term in a geometric series is 64 and the common ratio is 0.75. Find the sum of the first 4 terms in the series.

maks197457 [2]

Answer:

195.25

Step-by-step explanation:

Consider geometric series S(n) where initial term is a

So S(n)=a+ar^1+...ar^n

Factor out a

S(n)=a(1+r+r^2...+r^n)

Multiply by r

S(n)r=a(r+r^2+r^3...+r^n+r^n+1)

Subtract S(n) from S(n)r

Note that only 1 and rn^1 remain.

S(n)r-S(n)=a(r^n+1 -1)

Factor out S(n)

S(n)(r-1)=a(r^n+1 -1)

The formula now shows S(n)=a(r^n+1 -1)/(r-1)

Now use the formula for the problem

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3 years ago

Gabrielle and John each

vivado [14]

Answer:

$64=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2=2^6$

Step-by-step explanation:

Gabrielle and John each

wrote the prime factorization of 64.

64 can be break into 32 times 2

32 can be break into 16 times 2

16 can be break into 8 and 2

8 can be break into 4 times 2

4 can be break into 2 times 2

So 64 is equal to 2 times 2 times 2 times 2 times 2 times 2

$64=2^6$

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3 years ago

A charity is collecting donations as a part of their yearly fundraising event. They are going door-to-door, asking for a donatio

tino4ka555 [31]

Step-by-step explanation:

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3 years ago

Help ASAP show work please thanksss!!!!

Llana [10]

Answer:

$\displaystyle log_\frac{1}{2}(64)=-6$

Step-by-step explanation:

<u>Properties of Logarithms</u>

We'll recall below the basic properties of logarithms:

$log_b(1) = 0$

Logarithm of the base:

$log_b(b) = 1$

Product rule:

$log_b(xy) = log_b(x) + log_b(y)$

Division rule:

$\displaystyle log_b(\frac{x}{y}) = log_b(x) - log_b(y)$

Power rule:

$log_b(x^n) = n\cdot log_b(x)$

Change of base:

$\displaystyle log_b(x) = \frac{ log_a(x)}{log_a(b)}$

Simplifying logarithms often requires the application of one or more of the above properties.

Simplify

$\displaystyle log_\frac{1}{2}(64)$

Factoring $64=2^6$ .

$\displaystyle log_\frac{1}{2}(64)=\displaystyle log_\frac{1}{2}(2^6)$

Applying the power rule:

$\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}(2)$

Since

$\displaystyle 2=(1/2)^{-1}$

$\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}((1/2)^{-1})$

Applying the power rule:

$\displaystyle log_\frac{1}{2}(64)=-6\cdot log_\frac{1}{2}(\frac{1}{2})$

Applying the logarithm of the base:

$\mathbf{\displaystyle log_\frac{1}{2}(64)=-6}$

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2 years ago

How do you simplify (d+5) +(d+5) +(d+5)?

kompoz [17]

Answer:

Step-by-step explanation:

(d + 5) + (d + 5) + (d + 5).....combine like terms

3d + 15 <===

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