write using exponents
(3)(3)(3)(3)(x)(x)(y)

Step-by-step explanation:

f(x) = -3x - 8

f(-3) = -3(-3) - 8

f(-3) = 9 - 8

f(-3) = 1

Answer:

(by using the first principle of differentiation)

We have the "Limit definition of Derivatives":

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

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

[tex]\implies \mathsf{f'(x)= \lim_{h \to 0} \{\frac{sec(x+h)-sec(x)}{h} \} }[/tex]

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

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

[tex]\boxed{\mathsf{cos\:A-cos\:B=-2sin(\frac{A+B}{2} )sin(\frac{A-B}{2} )}}[/tex]

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

[tex]\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} }[/tex]

[tex]\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} }[/tex]

[tex]\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} } }[/tex]

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

Substituting 0 for h and h/ 2

[tex]\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x+0)}{cos(x+0)cos(x)} }[/tex]

[tex]\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x)}{cos(x)cos(x)} }[/tex]

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

[tex]\implies \mathsf{f'(x)= tan(x)\times sec(x) }[/tex]

Hence, we got

[tex]\underline{\mathsf{\overline{\frac{d}{dx} (sec(x))=sec(x)tan(x)}}}[/tex]

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

(by using other standard derivatives)

[tex] \boxed{ \mathsf{ \frac{d}{dx} ( \sec \: x) = \sec x \tan x }}[/tex]

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

[tex] \boxed{ \mathsf{ \frac{d}{dx}(x)^{n} = n(x)^{n - 1} }}[/tex]

Therefore,

[tex] \mathsf{ \frac{d}{dx}( \cos x)^{ - 1} = - 1( \cos \: x) ^{( - 1 - 1} } \\ \implies \mathsf{\ - 1( \cos \: x) ^{- 2 }}[/tex]

[tex] \implies \: \mathsf{ - \frac{1}{ (\cos x) {}^{2} } }[/tex]

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.

[tex] \implies \mathsf{ - \frac{1}{ (\cos x )^{2} } \times ( - \sin x) }[/tex]

[tex] \implies \mathsf{ \frac{ \sin x }{ \cos x } \times ( \frac{1}{cos x} ) }[/tex]

[tex] \implies \mathsf{ \tan x \times \sec x }[/tex]

= sec x. tan x

Answer:

27

Step-by-step explanation:

6/4 = 1.5

1.5 * 18 = 27

Answer:

20400

Step-by-step explanation:

its 2.03x10x10x10x10 so first ten: 20.4 and ten: 204 3rd ten: 2040 last ten :20400

Answer:

She can fit 9 cubic feet of clothing in the two boxes.

Step-by-step explanation:

6 cubic feet + 3 cubic feet = 9 cubic feet.

-Lexi

Answer:

9 ft^3

Step-by-step explanation:

Add together the box capacities:  3 ft^3 + 6 ft^3 = 9 ft^3.

Maddie can pack a total of 9 ft^3 of clothing into these two boxes.

Answer:

2n-3

Step-by-step explanation:

three less so -3

Julie runs three less than 2 times what Hannah ran

Hannah ran n miles

so Julie ran three less than 2n

Answer:

The kinetic energy of the car is 43,200 Joules.

Step-by-step explanation:

KE = (1/2)mv^2

KE = (1/2)(600 kg)(12 m/s)^2

KE = (1/2)(600 kg)(144 m^2/s^2)

KE = 43,200 kg*m^2/s^2 = 43,200 Joules

Answer:

Step-by-step explanation:

KE= 1/2mv^2

KE = 1/2(600) 12^2

KE = 300 * 144 = 43200J

Answer:

x = -.1715 ≈ - .172    or x = -5.83

Step-by-step explanation:

x² + 6x + 1 = 0

x² + 6x = -1

Complete the square   Add to both sides (1/2 of the x-term, then square it.)

x² + 6x + 9  = -1 + 9

(x + 3)(x + 3) = 8

(x + 3)² = 8

[tex]\sqrt{(x + 3)^{2}[/tex]  = [tex]\sqrt{8}[/tex]

 x + 3 = ±  [tex]\sqrt{8}[/tex]

  x = -3 ± [tex]\sqrt{8}[/tex]

   x = -3 + [tex]\sqrt{8}[/tex]   or x = -3 - [tex]\sqrt{8}[/tex]

   x = -.1715 ≈ - .172    or x = -5.83

Answer:

No

Step-by-step explanation:

The answer is to find the sum of each number, because factors are pulling out from total numbers, but when multiplying you don't need to pull out anything so it would be number

Yep!!! Your correct

Answer:

4x - 12 = 84

Step-by-step explanation:

The last answer choice is correct because when you cross-multiply:

you get 4x - 12 = 84.

Therefore, the last option is correct.

Answer:

D would be the answer (4x-12=84)

Step-by-step explanation:

4/7=12/x-3

=>1/7=3/x-3

=>x-3=21

Multiplying both sides by 4

4(x-3)=4x21

=>4x-12=84

Hope this helped :)

Answer:

1.) x = 2

2.) x = 5

3.) x = 9

4.) x = 0

Step-by-step explanation:

1.) -3x - 8 = -14

-3x = -6

x = 2

2.) 4x - 6 = 14

4x = 20

x = 5

3.) -3 - 3x = -30

-3x = -27

x = 9

4.) -5x + 5 = 5

-5x = 0

x = 0

Answer:

i think the answer should be 8

Step-by-step explanation:

Step-by-step explanation:

5x - 6 = 3x + 2

5x - 3x = 2 + 6

2x = 8

x = 8/2

x = 4

Step-by-step explanation:

[tex]f(x) = 7x - 6[/tex]

[tex] \: [/tex]

Inverse

[tex]y = 7x - 6[/tex]

[tex]x = 7y - 6[/tex]

[tex]x + 6 = 7y[/tex]

[tex]y = \frac{x + 6}{7} [/tex]

[tex] {f}^{ - 1} (x) = \frac{x + 6}{7} [/tex]

Answer:

9/4

hope it helps.................

Answer:

1/2 + 1/2 = 1

1/4 + 1/4 = 1/2

So you would walk 1/2 mile in 1 hour

Answer:

1/2

Step-by-step explanation:

1/4*2  multiply 1/4 by 2 because its you walk 1/4 in half a hour so times that by 2 for a full hour.

Answer:

first put 2 in the numerator for the first blank and 2/9 in the second blank

Step-by-step explanation:

1/3 equals 3/9 and 3/9-1/9=2/9

Answer:

[tex]\frac{3}{9}[/tex]

Step-by-step explanation:

Answer:

4 3/4

Step-by-step explanation:

8 1/2=8 2/4

8 2/4-3 3/4= 4 3/4

Answer:

i think it is 49:9

Step-by-step explanation:

because number going in 49:9 by which multiple it is 7x7 is 49 3x3 is 9 so the answer is 49:9

Answer:

28:12

Step-by-step explanation:

Multiply both 7 and 3 by 4 and you get the ratio 28:12.

Answer:

101

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

Suplemetary angles

180-79=101

Answer:

here the answer is 24

Step-by-step explanation:

answerrrrrerrr issss hereeeeeee

Answer:

0

Step-by-step explanation:

4 multiply by x(3) = 12

6 multiply by y(2) = 12

12 -12 =0

Answer:

Step-by-step explanation:

a. [tex]\left(5\times \:10^3\right)\left(9\times \:10^7\right)[/tex]

[tex]5\times 10^3 = 5000\\\\5000\times \:9\times \:10^7[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:5000\times \:9=45000[/tex]

[tex]=45000\times \:10^7[/tex]

b. [tex]\left(7\times 10^5\right)\div \left(2\times 10^2\right)[/tex]

[tex]\left(7\times 10^5\right)\div \left(2\times 10^2\right)=\frac{7\times \:10^5}{2\times \:10^2}[/tex]

[tex]\frac{10^5}{10^2} = 10^3[/tex]

[tex]\frac{7\times \:10^3}{2}[/tex]

[tex]\mathrm{Factor}\:\: 10^3 : 2^3\times5^3[/tex]

[tex]\frac{7\times \:2^3\times \:5^3}{2}[/tex]

[tex]\frac{2^3}{2}=2^2[/tex]

[tex]7\times \:2^2\times \:5^3=3500[/tex]

Answer:

If we divide twice the qualifier of Jose by 4 it results in less than 8. What is Jose's highest grade?

Answer:

Step-by-step explanation:

Here we need to find a 3rd degree polynomial that has only two distinct zeros:  {-3, 8}.  

Focusing on the zero x = 8 and assuming that this 8 has a multiplicity of 2, we come up with the following polynomial in which the factor x - 8 shows up twice:

f(x) = a(x - 8)(x - 8)(x + 3), or f(x) = a(x - 8)^2(x + 3)

One such polynomial is thus

f(x) = a(x - 8)^2(x + 3), where 'a' is a constant coefficient.  This polynomial has a double zero at x = 8 and a third zero at x = -3.

Step-by-step explanation:

The polynomial has degree 3 and two zeros: - 3 and 8.

Since it has degree 3 it should have 3 zero's.

Two possible scenarios

1. -3 has multiplicity of two:

2. 8 has multiplicity of two:

Answer:

3 i belive  100 pecent tho

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

questions which include 'of 'usually means "×" (multiplication sign) so when u multiply them it gives 1/6

Answer:

[tex]\left \{ {{y=x; \ \ x\le 0} \atop {y=4+ \frac12x;\ \ x>0}} \right.[/tex]

Step-by-step explanation:

If you look at the graph you see that:

before 0, the graph has same y as it has x, or y=x.

after 0, the graph starts at 4, and increases by 1 every 2 steps horizontally, or has a slope of 1/2.

Finally, the 0 has to be included in the blue part of the graph based on where the solid dot is.