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3 years ago

Rewrite the following problems using exponent rules. Then, solve using logarithms.

Mathematics

1 answer:

Anna35 [415]3 years ago

3 0

9514 1404 393

Answer:

1. 3(0.96059601^t) = 15; t = -40.03

2. 4.121204(1.01^t) = 8; t = 66.66

Step-by-step explanation:

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

(a^b)(a^c) = a^(b+c)

The solution for an exponential problem using logarithms is ...

a·b^x = c ⇒ log(c/a)/log(b) = x

_____

1. Rewrite: (3)(0.99^4)^t = 15 ⇒ 3(0.96059601^t) = 15

Solution: t = log(15/3)/log(0.96059601) ≈ -40.03

2. Rewrite: 4(1.01^3)(1.01^t) = 8 ⇒ 4.121204(1.01^t) = 8

Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66

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Katena32 [7]

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Step-by-step explanation:

Given Sequence

$-282-266-250-234.....$

It represent an A.P. with

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common difference $d=16$

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$S_n=\frac{n}{2}[2a+(n-1)d]$

$S_{51}=\frac{51}{2}\times [2\times (-282)+(51-1)16]$

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3 years ago

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Taya2010 [7]

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and collecting like terms:

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We find that the perimeter of both shapes is equal to 11 units.

8 0

3 years ago

X=y+1400 0.08x+0.05=840

mezya [45]

Answer:

x = 7000

y = 5600

(7000, 5600)

Step-by-step explanation:

To solve the system of equations means to find the point of intersection (graphically). You are finding what value of 'x' and what value of 'y' fits both equations.

x = y + 1400

0.08x + 0.05y = 840

We can solve using the method substitution, where you replace a variable in one equation with an equivalent expression.

Since "x" is y + 1400, we can replace "x" in the second equation.

0.08x + 0.05y = 840

0.08(y + 1400) + 0.05y = 840

Distribute over brackets by multiplying 0.08 with y, then 0.08 with 1400.

0.08y + 112 + 0.05y = 840 Collect like terms (with "y" variable)

112 + 0.13y = 840

Now isolate "y" in the simplified equation.

112 - 112 + 0.13y = 840 - 112 Subtract 112 from both sides

0.13y = 728

0.13y/0.13 = 728/0.13 Divide both sides by 0.13

y = 5600 Solved for y

We can substitute "y" with 5600 in any other equation that has "x".

x = y + 1400

x = 5600 + 1400 Add

x = 7000 Solved for x

You may express the answer as a coordinate, or an ordered pair (x, y).

The solution is (7000, 5600).

3 0

3 years ago

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Answer:

Simplify —————

b - a

1.1 Rewrite (b-a) as (-1) • (a-b)

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Step-by-step explanation:

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