Answer:
x = 13.75
Step-by-step explanation:
a right-angled triangle.
so, we use Pythagoras
c² = a² + b²
where c is the Hypotenuse (the side opposite of the 90 degree angle).
so, in our case
17² = 10² + x²
289 = 100 + x²
189 = x²
x = 13.75
3x+4=10
Subtract 4 from both sides
3x=6
Divide both sides by 3
X=2
Sides = 10,10,5
Problem 5. 4x+1=29
Subtract 1 from both sides
4x=28
X=7
Answer as an inequality:
Answer in interval notation:
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
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Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of is x > 0 which in interval notation would be . This is the interval from 0 to infinity, excluding both endpoints.
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The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
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In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
Only the first one works
y = 3(-1)-2 = -5
y = -(0) -6 = -6 not -2
This is a substitution problem...
Answer:
A. Cylinder + cone
<u>Volume is the sum of volumes:</u>
- V = Vcon + Vcyl = 1/3πr²h₁ + πr²h₂
- V = 1/3π*9²*12 + π*9²*120 = 31554.2 cm³
<u>Surface area of cone:</u>
- A = A=πr(r+√(h₁²+r²)) = π*9(9 + √(9²+12²)) = 678.6 cm²
<u>Surface area of cylinder minus bases:</u>
- A = 2πrh₂ = 2π*9*120 = 6785.8 cm²
<u>Total surface area:</u>
- 678.6 + 6785.8 = 7464.4 cm²
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B. Cube+ pyramid
<u>Volume:</u>
- V = a³ + (1/3)a²h = a³ + (1/3)a²√(l²-(a/2)²)
- V = 8³ + (1/3)8²√(10²-4²) = 707.5 cm³
<u>Surface area of pyramid:</u>
- A = a² + 2al = 8² + 2*8*10 = 224 cm²
<u>Surface area of cube minus bases:</u>
- A = 4a² = 4(8²) = 256 cm²
<u>Total surface area:</u>