Answer:
No
Step-by-step explanation:
Hope this helps :))
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Once the numbers have the same base and exponents, we can add or subtract their coefficients.Here are the steps to adding or subtracting numbers in scientific notation:Determine the number by which to increase the smaller exponent by so it is to the equal larger exponent
30 gallons of red paint & 20 gallons of blue paint
Step-by-step explanation:
The ratio of red to blue paint drops to make purple paint is 3 : 2
Therefore the total number of gallon, in this case, fifty (50) is equivalent to the total of two ratios (which is 3 + 2 5)
If 5 in the ratio = 50; what about 2 & 3
5 = 50
2 = x
After cross multiplication;
5x = 50 * 2
X = 100/5
X = 20
The same for ratio 3
5 = 50
3 = y
5y = 50 * 3
y = 150/5
y = 30
The answer is therefore; 30 gallons of red paint to 20 gallons of blue paint
Learn More:
For more on ratios check out;
brainly.com/question/11662922
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This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...
Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.
Let y = (x+8)^(3x)
Take the natural log of both sides:
ln(y) = ln((x+8)^(3x))
By laws of logarithms, this can be rearranged:
ln(y) = 3xln(x+8)
Next, differentiate both sides. By implicit differentiation:
d/dx(ln(y)) = 1/y dy/dx
The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):
d/dx(3xln(x+8)) = d/dx(uv)
du/dx = 3
Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:
v = ln(a)
da/dx = 1
dv/da = 1/a
By chain rule:
dv/dx = dv/da * da/dx = 1/a = 1/(x+8)
Finally, use the product rule:
d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)
This overall produces the equation:
1/y * dy/dx = 3x/(x+8) + 3ln(x+8)
We want to solve for dy/dx, achievable by multiplying both sides by y:
dy/dx = y(3x/(x+8) + 3ln(x+8))
Since we know y = (x+8)^(3x):
dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))
Neatening this up a bit, we factorise out 3/(x+8):
dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))
Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.
I hope this helped you :)
