Let smaller number be x.
Larger number is : 5x-6
5x - 6 - x = 6
4x = 12
x = 3
Smaller number is 3 and larger number is (5x-6) = 9
Answer:
<h3>METHOD I:</h3>
(by using the first principle of differentiation)
We have the <u>"Limit definition of Derivatives"</u>:
<em>Here, f(x) = sec x, f(x+h) = sec (x+h)</em>
- <em>Substituting these in eqn. (i)</em>
<em />
- <em>sec x can be written as 1/ cos(x)</em>
<em /><em />
<em /><em />
- <em>By Cosines sum to product formula, i.e.,</em>
<em>=> cos(x) - cos(x+h) = -2sin{(x+x+h)/2}sin{(x-x-h)/2}</em>
- <em>I shifted a 2 from the first limit to the second limit, since the limits ar ein multiplication this transmission doesn't affect the result</em>
- <em>2/ h can also be written as 1/(h/ 2)</em>
- <em>We have limₓ→₀ (sin x) / x = 1. </em>
<em /><em />
- <em>h→0 means h/ 2→0</em>
<em>Substituting 0 for h and h/ 2</em>
<em /><em />
- <em>sin x/ cos x is tan x whereas 1/ cos (x) is sec (x)</em>
Hence, we got
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
<h3>METHOD II:</h3>
(by using other standard derivatives)
- sec x can also be written as (cos x)⁻¹
We have a standard derivative for variables in x raised to an exponent:
Therefore,
- Any base with negative exponent is equal to its reciprocal with same positive exponent
The process of differentiating doesn't just end here. It follows chain mechanism, I.e.,
<em>while calculating the derivative of a function that itself contains a function, the derivatives of all the inner functions are multiplied to that of the exterior to get to the final result</em>.
- The inner function that remains is cos x whose derivative is -sin x.
- cos²x can also be written as (cos x).(cos x)
- <u>sin x/ cos x</u> is tan x, while <u>1/ cos x</u> is sec x
= sec x. tan x
<h3>Hence, Proved!</h3>
Answer:
42.43 ft
Step-by-step explanation:
Please find attached an image of the softball pitch
h² = p² + f² -2x p×f×cos45
h² = 43² + 60² - 2x (43)(60) x 0.7071
h² = 1849 + 3600 - 3648.636
h² = 1800.364
h = √1800.364
h = 42.43 feet
Answer:
170
Step-by-step explanation:
20 + (26 - 1)6
= 20 + (25)6
= 20 + 150
= 170
Answer:
4 questions left
Step-by-step explanation:
32 × 87.5% = 28
32 -28= 4