Answer: 17/34 so its 17
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34
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The answer would be 7
2(2)^2+3(2)-7=7
2(4)+3(2)-7=7
8+6-7=7
Answer:
The sound intensity of a whisper is 333.3 times the reference intensity
Step-by-step explanation:
Given : The function
gives the intensity of a sound in decibels, where x is the ratio of the intensity of the sound to a reference intensity.
A whisper has a sound intensity of 30 decibels.
To find : Use your graph to help you complete the following statement. The sound intensity of a whisper is times the reference intensity.
Solution :
Graph is attached which shows their intersection at (1000,30).
We can also verify by substituting value.
We have given that a whisper has a sound intensity of 30 decibels.
Therefore, y=30 , Let log base 10
![3=logx](https://tex.z-dn.net/?f=3%3Dlogx)
Logarithmic property ![log_{x}b=a \Rightarrow b=x^a](https://tex.z-dn.net/?f=log_%7Bx%7Db%3Da%20%5CRightarrow%20b%3Dx%5Ea)
![x=1000](https://tex.z-dn.net/?f=x%3D1000)
The ratio of the intensity of the sound to a reference intensity is 1000 decibels
The sound intensity of a whisper is times the reference intensity is
![\frac{1000}{3}=333.33](https://tex.z-dn.net/?f=%5Cfrac%7B1000%7D%7B3%7D%3D333.33)
The sound intensity of a whisper is 333.3 times the reference intensity.
Answer:
- 20. The vertex is (2/3, 14/3) | p = 3, q = -2/3 and r = 14/3
- 21. 20x² + 2x - 3 = 0
Step-by-step explanation:
20.
<h3>Given</h3>
<h3>To find</h3>
- The least value of the y and the corresponding value of x
- Constants p, q and r such that 3x² - 4x + 6 = p(x + q)² + r
<h3>Solution</h3>
The given is the parabola with positive a coefficient, so it opens up and the minimum point its vertex.
<u>The vertex has x = -b/2a and corresponding y- coordinate is found below: </u>
- x = - (- 4)/2*3 = 2/3, and
- y = 3(2/3)² - 4(2/3) + 6 = 4/3 - 8/3 + 6 = 14/3
- So the vertex is (2/3, 14/3)
<u>The vertex form of the line has the equation:</u>
- y = a(x - h)² + k, where (h, k) is the vertex
<u>Plugging in the values:</u>
<u>Comparing with p(x + q)² + r, to find out that:</u>
- p = 3, q = -2/3 and r = 14/3
=====================================
21.
(i) α and β are the roots of: ax² + bx + c = 0
<u>Show that:</u>
- α + β = -b/a and αβ = c/a
<h3>Solution</h3>
<u>Knowing the roots, put the equation as:</u>
- (x - α)(x - β) = 0
- x² - αx - βx + αβ = 0
- x² - (α+β)x + αβ = 0
<u>Comparing this with the standard form:</u>
<u>Divide by </u><u>a</u><u> to make the constants of x² same:</u>
<u>Now comparing the constants:</u>
- - (α+β) = b/a ⇒ α+β = - b/a
- αβ = c/a
--------------------------------------------
(ii)
<h3>Given</h3>
- α and β are the roots of: 3x² - x - 5 = 0
<h3>To Find </h3>
- The equation with roots 1/2α and 1/2β
<h3>Solution</h3>
<u>The sum and the product of the roots:</u>
- α + β = -b/a = 1/3
- αβ = c/a = -5/3
<u>The equation is:</u>
- (x - 1/2α)(x - 1/2β) = 0
- x² - (1/2α + 1/2β)x + 1/(2α)(2β) = 0
- x² - (α + β)/(2αβ)x + 1/4αβ = 0
- x² - (1/3)/(2(-5/3))x + 1/(4(-5/3)) = 0
- x² + 1/10x - 3/20 = 0
- 20x² + 2x - 3 = 0
Answer:
Step-by-step explanation:
a-b=2
![\frac{27^{\frac{1}{3} b} }{9^{\frac{1}{2}a } } \\=\frac{(3^{3}) ^{\frac{1}{3} b} }{(3^{2} )^{\frac{1}{2} a} } \\=\frac{3^b}{3^a} \\=3^{b-a} \\=3^{-(-b+a)} \\=3^{-2}\\=\frac{1}{3^2} \\=\frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B27%5E%7B%5Cfrac%7B1%7D%7B3%7D%20b%7D%20%7D%7B9%5E%7B%5Cfrac%7B1%7D%7B2%7Da%20%7D%20%7D%20%5C%5C%3D%5Cfrac%7B%283%5E%7B3%7D%29%20%5E%7B%5Cfrac%7B1%7D%7B3%7D%20b%7D%20%7D%7B%283%5E%7B2%7D%20%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20a%7D%20%7D%20%5C%5C%3D%5Cfrac%7B3%5Eb%7D%7B3%5Ea%7D%20%5C%5C%3D3%5E%7Bb-a%7D%20%5C%5C%3D3%5E%7B-%28-b%2Ba%29%7D%20%5C%5C%3D3%5E%7B-2%7D%5C%5C%3D%5Cfrac%7B1%7D%7B3%5E2%7D%20%5C%5C%3D%5Cfrac%7B1%7D%7B9%7D)