Log base b=logb
4 log₂ 2x+ 2logb x=4
log₂(2x)⁴+logb x²=log₂16
log₂ 16x⁴+ logb x²=log₂ 16
logb x²=log₂ 16 - log₂ 16x⁴
logb x²=log₂ (16/16x⁴)
logb x²= log₂ x⁻⁴
logb x²=log₂ x² / log₂ b
log₂ x² / log₂ b=-log x⁴
log₂ b=log₂ x² /- log₂ x⁴
log₂ b=2 log x / -4 log₂ x
log₂ b=-1/2 ⇔ b=2⁻¹/² =1/√2=(√2)/2≈ 0.707106781....
Answer: b=(√2)/2
To chek
if x=10
log base √2/2= log√2/2
4 log₂ 20 + 2log√2/2 10=4(4.321928095...)+2 (-6.64385619=
= 17.28771238-13.28771238=4
Questions:
A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?
Answer:
32 units of fabrics
Step-by-step explanation:
Given
![a = \sqrt{f + 4} - \sqrt{36 - f}](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7Bf%20%2B%204%7D%20-%20%5Csqrt%7B36%20-%20f%7D)
Required
Find f when a = 4
Substitute 4 for a
![4 = \sqrt{f + 4} - \sqrt{36 - f}](https://tex.z-dn.net/?f=4%20%3D%20%5Csqrt%7Bf%20%2B%204%7D%20-%20%5Csqrt%7B36%20-%20f%7D)
Rewrite as:
![\sqrt{36 - f} + 4 = \sqrt{f + 4}](https://tex.z-dn.net/?f=%5Csqrt%7B36%20-%20f%7D%20%2B%204%20%3D%20%5Csqrt%7Bf%20%2B%204%7D)
Square both sides
![(\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7B36%20-%20f%7D%20%2B%204%29%5E2%20%3D%20%28%5Csqrt%7Bf%20%2B%204%7D%29%5E2)
![(\sqrt{36 - f} + 4)^2 = f + 4](https://tex.z-dn.net/?f=%28%5Csqrt%7B36%20-%20f%7D%20%2B%204%29%5E2%20%3D%20f%20%2B%204)
![36 - f + 8\sqrt{36 - f} + 16 = f + 4](https://tex.z-dn.net/?f=36%20-%20f%20%2B%208%5Csqrt%7B36%20-%20f%7D%20%2B%2016%20%3D%20f%20%2B%204)
Collect Like Terms
![8\sqrt{36 - f}= f +f+ 4 - 36 -16](https://tex.z-dn.net/?f=8%5Csqrt%7B36%20-%20f%7D%3D%20f%20%2Bf%2B%204%20-%2036%20-16)
![8\sqrt{36 - f}= 2f -48](https://tex.z-dn.net/?f=8%5Csqrt%7B36%20-%20f%7D%3D%202f%20-48)
Divide through by 2
![4\sqrt{36 - f}= f -24](https://tex.z-dn.net/?f=4%5Csqrt%7B36%20-%20f%7D%3D%20f%20-24)
Square both sides
![16(36-f) = (f - 24)^2](https://tex.z-dn.net/?f=16%2836-f%29%20%3D%20%28f%20-%2024%29%5E2)
![16(36-f) = f^2 - 48f + 576](https://tex.z-dn.net/?f=16%2836-f%29%20%3D%20f%5E2%20-%2048f%20%2B%20576)
![576-16f = f^2 - 48f + 576](https://tex.z-dn.net/?f=576-16f%20%3D%20f%5E2%20-%2048f%20%2B%20576)
![-16f = f^2 - 48f](https://tex.z-dn.net/?f=-16f%20%3D%20f%5E2%20-%2048f)
Collect like terms
![f^2 - 48f + 16f = 0](https://tex.z-dn.net/?f=f%5E2%20-%2048f%20%2B%2016f%20%3D%200)
![f^2 -32f = 0](https://tex.z-dn.net/?f=f%5E2%20-32f%20%3D%200)
Factorize
![f(f - 32) = 0](https://tex.z-dn.net/?f=f%28f%20-%2032%29%20%3D%200)
or ![f = 32](https://tex.z-dn.net/?f=f%20%3D%2032)
f can not be 0 because some units must be ordered.
So, f = 32
Answer:
190π (not part of the answer choices)
Step-by-step explanation:
The surface area of a cylinder can be found using the formula below:
where
is the radius of the base,
is the diameter of the base and
is the height of the cylinder.
Plug in the given values
![SA=2\pi (\frac{10}{2}) ^2+\pi (10)(14)\\SA=2\pi (\frac{100}{4})+140\pi\\SA=2\pi (25)+140\pi\\SA=50\pi+140\pi\\SA=190\pi](https://tex.z-dn.net/?f=SA%3D2%5Cpi%20%28%5Cfrac%7B10%7D%7B2%7D%29%20%5E2%2B%5Cpi%20%2810%29%2814%29%5C%5CSA%3D2%5Cpi%20%28%5Cfrac%7B100%7D%7B4%7D%29%2B140%5Cpi%5C%5CSA%3D2%5Cpi%20%2825%29%2B140%5Cpi%5C%5CSA%3D50%5Cpi%2B140%5Cpi%5C%5CSA%3D190%5Cpi)
Therefore, although this answer isn't one of the choices, the surface area of the cylinder is 190π.
I hope this helps!
Answer:
2 to the power of 7
Step-by-step explanation:
7 to the power of 2 is 49
2 to the power of 7 is 128
Answer:
4 seconds.
Step-by-step explanation:
The given equation is
where, h is height in feet of a golf ball above the ground after being hit into the air and t is the number of seconds elapsed since the ball was hit.
We need to find the time for the ball to hit the ground.
At ground level the height of ball is 0, i.e., h=0.
Using zero product property, we get
Therefore, it will take 4 seconds for the ball to hit the ground.