Answer:
Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude; in terms of energy, each whole number increase corresponds to an increase of about 31.6 times the amount of energy released, and each increase of 0.2 corresponds to approximately a doubling of the energy released.
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
List out factors of 60 =
1 x 60 = 60
2 x 30 = 60
3 x 20 = 60
4 x 15 = 60
5 x 12 = 60
6 x 10 = 60
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 are factors of 60.
List out multiples of 6 from 10 to 20.
12 and 18.
Since 12 is seen on one of the factors of 60 and a multiple of 6 between 10 and 20, the answer is 12.
Answer:
Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]
Step-by-step explanation:
We are given that a function
Interval [1,5]
The given function is defined on this interval.
Hypothesis of Mean Value Theorem:
(1) Function is continuous on interval [a,b]
(2)Function is defined on interval (a,b)
From the graph we can see that
The function is continuous on [1,5] and differentiable at(1,5).
Hence, the function satisfies the hypothesis of the Mean Value Theorem.
Answer:
Style A sold 15 pairs while Style B sold 13 pairs
Step-by-step explanation:
Let the number of Style A pairs be A.
Let the number of Style B pairs be B.
The store sold 28 pairs of cross-trainer shoes for a total of $2,220 and Style A sold for $70 per pair while Style B sold for $90 per pair.
This implies 2 things:
A + B = 28 ________________ (1)
and
(70*A) + (90*B) = 2220
=> 70A + 90B = 2220 ________(2)
We now have two simultaneous equations:
A + B = 28 ________________ (1)
70A + 90B = 2220 __________(2)
From (1):
A = 28 - B ________________ (3)
Put (3) in (2):
70(28 - B) + 90B = 2220
1960 - 70B + 90B = 2220
1960 + 20B = 2220
Collecting like terms:
20B = 2220 - 1960
20B = 260
B = 260 / 20
B = 13
Therefore:
A = 28 - 13 = 15
Style A sold 15 pairs while Style B sold 13 pairs.
Answer:
The equation of the tangent line passing through the point (-2,3) is
4 x + y +5 =0
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given that the slope of the tangent</em>
<em> </em>
<em></em>
<em> m = -2( 3-1) = -4</em>
<em>Given point x = -2</em>
<em> y = f(-2) =3</em>
<em>∴The given point ( x₁ , y₁) = ( -2 ,3)</em>
<u><em>Step(ii):-</em></u>
The equation of the tangent line passing through the point (-2,3)
y -3 = -4( x+2)
y-3 = -4x -8
4x + y -3+8=0
4x +y +5=0
<u><em>Step(iii):-</em></u>
<em>The equation of the tangent line passing through the point (-2,3) is</em>
<em> 4 x + y +5 =0</em>
<em></em>
