Answer:
x y
-5 1
-5 -2
-5 -5
Step-by-step explanation:
same x value, but different y value
find the value of x. only type the “number”
Step-by-step explanation:
5x - 6 = 3x + 2
5x - 3x = 2 + 6
2x = 8
x = 8/2
x = 4
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Question ~}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Prove that ~
[tex] \dfrac{d}{dx}\sec(x) = \sec(x) \tan(x) [/tex]
by using first principle of differentiation ~
Answer:
METHOD I:(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)
Substituting these in eqn. (i)[tex]\implies \mathsf{f'(x)= \lim_{h \to 0} \{\frac{sec(x+h)-sec(x)}{h} \} }[/tex]
sec x can be written as 1/ cos(x)[tex]\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{1}{h} \{\frac{1}{cos(x+h)} -\frac{1}{cos(x)} \} }[/tex]
Taking LCM[tex]\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{1}{h} \{\frac{cos(x)-cos(x+h)}{cos(x)cos(x+h)} \} }[/tex]
By Cosines sum to product formula, i.e.,[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]
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[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]
2/ h can also be written as 1/(h/ 2)[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]
We have limₓ→₀ (sin x) / x = 1.[tex]\implies \mathsf{f'(x)= \lim_{h \to 0} \frac{sin(x+\frac{h}{2} )}{cos(x+h)cos(x)}\:.\: 1 }[/tex]
h→0 means h/ 2→0Substituting 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]
sin x/ cos x is tan x whereas 1/ cos (x) is sec (x)[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]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
METHOD II:(by using other standard derivatives)
[tex] \boxed{ \mathsf{ \frac{d}{dx} ( \sec \: x) = \sec x \tan x }}[/tex]
sec x can also be written as (cos x)⁻¹We 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]
Any base with negative exponent is equal to its reciprocal with same positive exponent[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.
The inner function that remains is cos x whose derivative is -sin x.[tex] \implies \mathsf{ - \frac{1}{ (\cos x )^{2} } \times ( - \sin x) }[/tex]
cos²x can also be written as (cos x).(cos x)[tex] \implies \mathsf{ \frac{ \sin x }{ \cos x } \times ( \frac{1}{cos x} ) }[/tex]
sin x/ cos x is tan x, while 1/ cos x is sec x[tex] \implies \mathsf{ \tan x \times \sec x }[/tex]
= sec x. tan x
Hence, Proved!The Sydney Harbour Bridge is approximately 1200 metres long. A model of the bridge is built with a scale of 1:6000. What is the length of the model?
Pick one:
5cm
20cm
200cm
720cm
Answer:
20cmStep-by-step explanation:
The Sydney Harbour Bridge is approximately 1200 metres long. A model of the bridge is built with a scale of 1:6000. What is the length of the model?
Pick one:
5cm
20cm
200cm
720cm
--------------------
scale = 1:6000
so
1200 : 6000 = 0.2m
0.2m = 20 cm
Answer:
20cm
Step-by-step explanation:
«A scale of 1:6000» means the model is smaller than the bridge by a factor of 6000. We can also make up a proportion [tex]\dfrac{1}{6000}=\dfrac{x}{1200}[/tex], where the left side is the scale, x is the model length, 1200 is the bridge length (in meters). So, finding x or just dividing 1200 by 6000, we get 0.2 meters. Provided 1 m = 100 cm, 0.2 m is 0.2 × 100 = 20 cm.
What is the 4th equivalent fraction to 1/12?
Answer:
Where's the Answer? There's No
Hello there!
Remember that equivalent fractions have the same value.
[tex]\frac{1}{2} , \frac{2}{24} ,\frac{3}{36}, \frac{4}{48}[/tex]
Therefore, the 4th equivalent fraction to 1/12 is [tex]\frac{4}{48}[/tex]Hope this helps you!
~Just a felicitous girlie
#HaveASplendidDay
[tex]SilentNature :)[/tex]
9. 2 less than 3 times a number is the same as 2114. What is the number?
Enter your answer as a decimal or simplified mixed number in the box. The number is.
Answer:
705.3 repeated I don't know if that's what you want but
3 times of 705.33 and 2 subtracted is equal to 2114.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
Given that,
2 less than 3 times a number equal to 2114.
Let the required number is x.
According to given condition,
3x - 2 = 2114
3x = 2114 + 2
3x = 2116
x = 2116 / 3
x = 705.33
The required number is 705.33.
To know more about Simplification on :
https://brainly.com/question/2804192
#SPJ5
If f(x) = 7x- 6, which of the following is the inverse of kx)?
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]
if y varies inversely as n and m = 8 when n = 3 find m whenn =12
Answer:
24
Step-by-step explanation:
m=8x4 n=3x4 so that is the answer
What is 4 times 3/4 multiples by 3/4
Answer:
9/4
hope it helps.................
Monique wants to check out as many books by her favorite author as possible. She can check out 3 books at a time from her library, where there are 6 books available written by her favorite author. How many different sets of 3 of these books can Monique choose
Monique can choose 20 different sets of 3 of the books
What is a combination?The set of books she can select from the library is an illustration of combination (or selection)
The expression that represents combination is represented as:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
Where:
The total number of books [tex]n = 6[/tex]The set of books to check out [tex]r = 3[/tex]So, we have:
[tex]^6C_3 = \frac{6!}{(6 - 3)!3!}[/tex]
Evaluate the differences
[tex]^6C_3 = \frac{6!}{3!3!}[/tex]
Evaluate the factorials
[tex]^6C_3 = \frac{720}{6 \times 6}[/tex]
Evaluate the products
[tex]^6C_3 = \frac{720}{36}[/tex]
Divide 720 by 36
[tex]^6C_3 = 20[/tex]
Hence, Monique can choose 20 different sets of 3 of the books
Read more about combination at:
https://brainly.com/question/11732255
Answer:
it is in fact 20 (for khan)
Step-by-step explanation:
credit goes to person above
Write 2.04 × 10 ⁴ as an ordinary number
Answer:
20400
Step-by-step explanation:
its 2.03x10x10x10x10 so first ten: 20.4 and ten: 204 3rd ten: 2040 last ten :20400
1. When do we use the method of Difference of two squares?
*
(Factoring polynomials)
Answer:
a
Step-by-step explanation:
on average, 8 potatoes cost $1.50 at a farmers market. fernando needs to buy 22 potatoes
a. estimate the cost of 22 potatoes. explain
b. how much will it cost fernando to buy 22 potatoes? how does this compare to your estimate ?
c. how many potatoes could fenando buy with $7 ?
d. what is the unit cost per potato
Answer: a) it will cost him $4.13 rounded
B)about 36
C)$ 0.19 (rounded) per potato
pls helppppppp ill give brainliest
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
1.) From a group of 8 people, 5 will each win $1,000. How many different winning groups are
possible?
A.) 56
B.) 6720
C.) 168
D.) 336
Anwser 6720 ways different
Step-by-step explanation:
In this case, we must calculate the different ways using the permutation formula:
nPr = n! / (n - r)!
where n is the total number of people and r would come being the group of person that you want to put together the groups, therefore n = 8 and r = 5
replacing:
8P5 = 8! / (8 - 5)!
8P5 = 6720
That is to say that there are 6720 ways different winning groups are possible
Maddie is packing moving boxes. She has one 3 cubic-foot box and one 6 cubic-foot box. How many cubic feet of clothing can she fit in the two boxes?
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.
Which of the following tables does not represent a function?
x y
-1 1
-2 1
-3 1
x y
-5 1
-5 -2
-5 -5
x y
-4 0
2 0
5 7
x y
-5 1
-3 -2
-1 -5
Step-by-step explanation:
the second one (with the -5 as x values) is not a function, because the valid x value -5 has more than one associated different solution value y.
for a function a valid x value can lead only to exactly one result y value.
2x2-5x-2 solve by quadratic formula 9leave answers in simplest radical form)
Answer:
-5x+2
Step-by-step explanation:
1. Multiply number 2 and 2=4 so it is
4-5x-2
2. Combine like terms
-5x+4-2
3. Subtract the numbers
-5x+2
Find the value of x.
Answer:
i think the answer should be 8
Step-by-step explanation:
in your own words explain the phrases "claming first and second place respectively"
Answer:
If we divide twice the qualifier of Jose by 4 it results in less than 8. What is Jose's highest grade?
Write the equation for 5x + 2y = 3 in slope-intercept form..
Answer:
[tex]y=-\frac{5}{2}x+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]5x+2y=3\\\\2y=-5x+3\\\\y=-\frac{5}{2}x+\frac{3}{2}[/tex]
Answer:
Step-by-step explanation:
Slope-intercept from: y = mx + b
5x + 2y = 3
2y = -5x + 3
Divide the whole equation by 2
[tex]\dfrac{2y}{2}=\dfrac{-5x}{2}+\dfrac{3}{2}\\\\y=\dfrac{-5}{2}x +\dfrac{3}{2}[/tex]
Is 126 divisible by 3
Answer:
yes
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
126/3 = 42
write a peacewise function for the graph
please help me
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.
1.) -3x-8=-14
2.) 4x-6=14
3.)-3-3x=-30
4.) -5x+5=5
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
Which ratio is equivalent to 7:3?
217
49:9
12: 8
28:12
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.
Anne goes out to buy lunch every Friday. On average she spends around $18 each time. How much money can she save in one year if she stops going out for lunch each week?
Write in slope-intercept form an equation of the line that passes through the given points. (0,−1),(−8,−2)
Please help xxxxxxxx
Answer:
a. [tex]\bold{45000\times \:10^7}[/tex]b. [tex]\bold{3500}[/tex]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]
2m to 2km converted representative fraction
Answer:
1/1000
Step-by-step explanation:
A car is moving at 12 m/s and has a mass of 600 kg. What is the kinetic energy of the car? (Formula: KE = 1/2mv^2) WILL GIVE BRAINLEST
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
find the slope of the line
Answer:
3 i belive 100 pecent tho
Step-by-step explanation:
