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My name is Ann [436]
3 years ago
11

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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PLEASE HELP!!!!!
Katena32 [7]

Answer:6018

Step-by-step explanation:

Given Sequence

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

It represent an A.P. with

first term a=-282

common difference d=16

So sum of 51 term

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

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

S_{51}=\frac{51}{2}\times [-564+800]

S_{51}=\frac{51}{2}\times [236]

S_{51}=51\times 118

S_{51}=6018

7 0
3 years ago
Please help me with my math
Taya2010 [7]
3x + 22 is the equation that represents the perimeter of the triangle.  4x + 10 is the perimeter of the rectangle.  Setting the two equal:

3x + 22 = 4x + 10

and collecting like terms:

x=11

We find that the perimeter of both shapes is equal to 11 units.
8 0
3 years ago
X=y+1400<br> 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 <u>substitution</u>, where you replace a variable in one equation with an equivalent expression.

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

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
Read 2 more answers
Reduce the following expression: (a-b) / (b-a)
Lynna [10]

Answer:

Simplify   —————

           b - a

1.1    Rewrite   (b-a)    as  (-1) •  (a-b)

Canceling Out :

1.2    Cancel out  (a-b)  which now appears on both sides of the fraction line.

Final result :

 -1

Step-by-step explanation:

4 0
2 years ago
What is the mean of this data set? 12, 17, 16, 10, 20, 13, 14, 14, 12, 12, 19, 18 0 13.50 O 14.00 O 14.75 O 15.75​
ra1l [238]
The numbers seem to be going up and down but definitely not by a pattern
8 0
2 years ago
Read 2 more answers
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