The answer should be 0.001703578
to solve for x you take tangent inverse of both sides then you get what x is equal to, it rounds to 30.1
Answer:
4
Step-by-step explanation:
solving equation 1
- log125 base 5√5=x
- [5√5=√(25×5)=√125]
- log125 base 125=x
- [From one of the principles of logarithm " logA base a =1]
- therefore, log125 base 125=1
- x=1
solving equation 2
- log 64 base 2√2=y
- [2√2=√(4×2)=√8]
- log 64 base√8=y
- 64=(√8)^y
- 64=8^(½y)
- 8²=8^(½y)
- (8 cancels in both equations and I evaluate the powers figures)
- 2=½y
- y=2×2=4
the product of x and y=x•y=1×4=4
Answer:
Dimensions of cabinet
x (wide) = 1.93 ft
y (hight) = 2.895 ft
p (depth) =0.43 ft
Step-by-step explanation:
Dimensions of cabinet
y height
x wide
p deph
From problem statement
y = 1.5 x V = y * x * p V = 1.5*x²p but p = V/y*x p = 2.4/1.5 x²
p = 1.6 / x²
Then
Area of top and bottom A₁ = 2*x*p ⇒ 2*x*1.6/x²
A₁ = 3.2 /x
And cost in $ C₁ = 0,9 * 3.2 /x ⇒ C₁ = 2.88/x
Area of sides (front and rear not included)
A₂ = 2*y *p A₂ = 3*x*1.6/x² A₂ = 4.8/x
And cost in $ C₂ = 0.9 * 4.8 /x C₂ = 4.32 /x
Area of front and rear A₃ =2* y*x A₃ = 2*1.5 *x² A₃ = 3x²
And cost C₃ = 0.3 * 3/x² = 0.9/x²
Total cost C(x) = C₁ + C₂ + C₃ C(x) = 2.88/x + 4.32/x + 0.9x²
Taking derivatives
C´(x) = -2.88/x² - 4.32 /x² + 0.9 x
C´(x) = 0 -2.88/x² - 4.32/x² + 0.9 x = 0 -2.88 - 4.32 + 0.9 x³ = 0
-7.2 + x³ = 0 x³ = 7.2
x = 1.93 ft y = 1.5*1.93 = 2.895 ft and p = 0.43 ft
