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3 years ago

Solve for x... please help ASAP

Mathematics

2 answers:

Svetach [21]3 years ago

8 0

Answer:

The answer would be -11

Step-by-step explanation:

The 2 angles in this problem are vertical angles. This means the angles and congruent(=). so 6x+185=8x+207 ----- 2x=-22---------- x=-11

Hope this helps!

SSSSS [86.1K]3 years ago

6 0

-11

8x+207=6x+185
2x=-22
X=-11

Mark brainliest please

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garri49 [273]

Answer:

<h3>METHOD I:</h3>

(by using the first principle of differentiation)

We have the "Limit definition of Derivatives":

$\boxed{\mathsf{f'(x)= \lim_{h \to 0} \{\frac{f(x+h)-f(x)}{h} \} ....(i)}}$

Here, f(x) = sec x, f(x+h) = sec (x+h)

Substituting these in eqn. (i)

$\implies \mathsf{f'(x)= \lim_{h \to 0} \{\frac{sec(x+h)-sec(x)}{h} \} }$

sec x can be written as 1/ cos(x)

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{1}{h} \{\frac{1}{cos(x+h)} -\frac{1}{cos(x)} \} }$

Taking LCM

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{1}{h} \{\frac{cos(x)-cos(x+h)}{cos(x)cos(x+h)} \} }$

By Cosines sum to product formula, i.e.,

$\boxed{\mathsf{cos\:A-cos\:B=-2sin(\frac{A+B}{2} )sin(\frac{A-B}{2} )}}$

=> cos(x) - cos(x+h) = -2sin{(x+x+h)/2}sin{(x-x-h)/2}

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{2sin(x+\frac{h}{2} )}{cos(x+h)cos(x)}\:.\: \lim_{h \to 0} \frac{sin(\frac{h}{2} )}{h} }$

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

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x+\frac{h}{2} )}{cos(x+h)cos(x)}\:.\: \lim_{h \to 0} \frac{2sin(\frac{h}{2} )}{h} }$

2/ h can also be written as 1/(h/ 2)

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x+\frac{h}{2} )}{cos(x+h)cos(x)}\:.\: \lim_{h \to 0} \frac{1\times sin(\frac{h}{2} )}{\frac{h}{2} } }$

We have limₓ→₀ (sin x) / x = 1.

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x+\frac{h}{2} )}{cos(x+h)cos(x)}\:.\: 1 }$

h→0 means h/ 2→0

Substituting 0 for h and h/ 2

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x+0)}{cos(x+0)cos(x)} }$

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x)}{cos(x)cos(x)} }$

$\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x)}{cos(x)}\times \frac{1}{cos x} }$

sin x/ cos x is tan x whereas 1/ cos (x) is sec (x)

$\implies \mathsf{f'(x)= tan(x)\times sec(x) }$

Hence, we got

$\underline{\mathsf{\overline{\frac{d}{dx} (sec(x))=sec(x)tan(x)}}}$

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

<h3>METHOD II:</h3>

(by using other standard derivatives)

$\boxed{ \mathsf{ \frac{d}{dx} ( \sec \: x) = \sec x \tan x }}$

sec x can also be written as (cos x)⁻¹

We have a standard derivative for variables in x raised to an exponent:

$\boxed{ \mathsf{ \frac{d}{dx}(x)^{n} = n(x)^{n - 1} }}$

Therefore,

$\mathsf{ \frac{d}{dx}( \cos x)^{ - 1} = - 1( \cos \: x) ^{( - 1 - 1} } \\ \implies \mathsf{\ - 1( \cos \: x) ^{- 2 }}$

Any base with negative exponent is equal to its reciprocal with same positive exponent

$\implies \: \mathsf{ - \frac{1}{ (\cos x) {}^{2} } }$

The process of differentiating doesn't just end here. It follows chain mechanism, I.e.,

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.

The inner function that remains is cos x whose derivative is -sin x.

$\implies \mathsf{ - \frac{1}{ (\cos x )^{2} } \times ( - \sin x) }$

cos²x can also be written as (cos x).(cos x)

$\implies \mathsf{ \frac{ \sin x }{ \cos x } \times ( \frac{1}{cos x} ) }$

sin x/ cos x is tan x, while 1/ cos x is sec x

$\implies \mathsf{ \tan x \times \sec x }$

= sec x. tan x

<h3>Hence, Proved!</h3>

7 0

3 years ago

What is root 36/49? A 18/25 B 20/27 C 6/7 D 8/9

saveliy_v [14]

Answer:

6/7

Step-by-step explanation:

You need to find what number times itself gets you those two numbers. 6*6=36, 7*7=49.

6 0

3 years ago

All the yellow surfaces on this ferris wheel pod

Ierofanga [76]

20 in because it will over everything

6 0

3 years ago

Find the value of x. Leave your answer in simplest radical form. The chord measures 14, the diameter measures 18. Hint: use pyth

ehidna [41]

Answer:

x = 4√2

Step-by-step explanation:

Find the value of x. Leave your answer in simplest radical form. The chord measures 14, the diameter measures 18. Hint: use pythagorean theorem

To solve, we will follow the steps below:

using Pythagoras theorem

opposite² + adjacent² = hypotenuse²

14² + y² = 18²

196 + y² = 324

subtract 196 from both-side of the equation

196 -196 + y² = 324-196

y² =128

Take the square root of both-side

√y² = √128

y =√128

y = √64×2

y =√64×√2

y = 8√2

x = half of y

x = y/2

x = 8√2 ÷ 2

x = 4√2

8 0

3 years ago

How many solutions in 3(6x-2) = 2(9x-3)

Andreyy89

Answer:

Infinite solutions

Step-by-step explanation:

Distribute the numbers

3(6x-2) = 18x - 6

2(9x-3) = 18x - 6

18x - 6 = 18 - 6

Since both sides of the equal sign are the same, that means you can plug any number into x, and it will always be a valid answer.

7 0

3 years ago