Answer:
- as written, c ≈ 0.000979 or c = 4
- alternate interpretation: c = 0
Step-by-step explanation:
<em>As written</em>, you have an equation that cannot be solved algebraically.
(32^2)c = 8^c
1024c = 8^c
1024c -8^c = 0 . . . . . . rewrite as an expression compared to zero
A graphical solution shows two values for c: {0.000978551672551, 4}. We presume you're interested in c = 4.
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If you mean ...
32^(2c) = 8^c
(2^5)^(2c) = (2^3)^c . . . . rewriting as powers of 2
2^(10c) = 2^(3c) . . . . . . . simplify
10c = 3c . . . . . . . . . . . . . .log base 2
7c = 0 . . . . . . . . . . . . . . . subtract 3c
c = 0 . . . . . . . . . . . . . . . . divide by 7
Answer:
The answer is
<h2>
</h2>
Step-by-step explanation:
To find the inverse of f(x) , equate f(x) to y
That's
y = f(x)
We have
Next interchange the terms that's x becomes y and y becomes x
<u>Next solve for y</u>
Move 3 to the other side of the equation
That's
<u>Divide both sides by 25</u>
We have the final answer as
Hope this helps you
It costs $3.63 more for the gold die than the gold plated die.
The volume of each half of the die is given by the formula
V=1/3s³.
This means the total volume is V = 2(1/3s³) = 2(1/3(2³)) = 16/3 = 5.33 mm³.
For the solid gold die, we know that it weighs 0.02g per mm³:
5.33(0.02) = 0.1066g
Gold costs $40.38 per gram:
40.38(0.1066) = $4.30
For the plastic die, plastic weighs 0.01 g per mm³:
0.01(5.33) = 0.0533g
Plastic costs $10 per gram:
0.0533(10) = 0.533 ≈ $0.54.
We also need to find the surface area, as it will be painted. Each face is an equilateral triangle; the area of a triangle is given by the formula
A = 1/2bh
We need to use the Pythagorean theorem to find the height. The height will be one leg and 1/2 of the base will be the other; the slanted side will be the hypotenuse:
h² + (1/2(2))² = 2²
h² + 1² = 2²
h² + 1 = 4
h² = 3
h = √3
The area of the triangle would then be A = 1/2bh = 1/2(2)(√3) = √3. There are 8 such faces on the die, so the total surface area would be 8√3 = 13.86mm².
Paint costs $0.01 per mm²:
13.86(0.01) = 0.1386 ≈ $0.14
Together the cost for the plastic is 0.14+0.53 = $0.67.
The difference between it and the cost for the gold die is 4.30 - 0.67 = $3.63.
The sum that represents the number of tickets sold if 35 tickets were sold Monday, half of the remaining tickets were sold on Tuesday and 14 tickets were sold on Wednesday.
To start solving this, we can assign t as the variable to the total number of tickets that were sold. So, t = 35 (for Monday) + (t - 35)/2 (for Tuesday) + 14 (for Wednesday). To solve this, we can say t = 49 + (t - 35)/2, or 2t = 98 + t - 35, which equals t = 63. Therefore, 63 tickets were sold total.
Answer:
D
Step-by-step explanation:
using the formula y = mx + b we can plug in the m and the b, getting
y = -5x - 9
