Answer:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ 2\sqrt{x } } [/tex]
Step-by-step explanation:
we want to differentiate the following by using limit:
[tex] \displaystyle \frac{d}{dx} \sqrt{x} [/tex]
derivative definition by limit given by
[tex] \rm \displaystyle \frac{d}{dx} = \lim _{\Delta x \to 0} \left( \frac{f(x + \Delta x) - f(x)}{ \Delta x} \right) [/tex]
given that,
f(x)=√x
so,
f(x+∆x)=√(x+∆x)
thus substitute:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \sqrt{x + \Delta x}- \sqrt{x} }{ \Delta x} \right) [/tex]
multiply both the numerator and denominator by the conjugate of the numerator:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \sqrt{x + \Delta x}- \sqrt{x} }{ \Delta x} \times \frac{ \sqrt{x + \Delta x} + \sqrt{x} }{\sqrt{x + \Delta x} + \sqrt{x}} \right) [/tex]
simplify which yields:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ (\sqrt{x + \Delta x}) ^{2} - x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right) [/tex]
simplify square:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{ \Delta x \to 0} \left( \frac{ x + \Delta x - x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right) [/tex]
collect like terms:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ \Delta x }{ \Delta x(\sqrt{x + \Delta x} + \sqrt{x})} \right) [/tex]
reduce fraction:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \lim _{\Delta x \to 0} \left( \frac{ 1 }{ (\sqrt{x + \Delta x} + \sqrt{x})} \right) [/tex]
get rid of ∆x as we are approaching its to 0
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ \sqrt{x } + \sqrt{x}} [/tex]
simplify addition:
[tex] \rm \displaystyle \frac{d }{dx} \sqrt{x} = \frac{ 1 }{ 2\sqrt{x } } [/tex]
and we are done!
How much was your loan
through capital One if you
paid $1200 in interest at a
rate of 1.5% for 5 years?
Answer:
Your loan was for $16,000.
Step-by-step explanation:
The formula for simple interest is i = prt, where p is the principal, r is the interest rate as a decimal fraction, and t is the time in years.
If i = prt, then p = i / (rt)
Here, p = ($1200) / 0.075 = $16,000
Your loan was for $16,000.
Quadrilateral R S T Q is shown. Angle R is 132 degrees, angle Q is 56 degrees, and angle T is 79 degrees.
What is the measure of angle S?
48o
56o
93o
101o
Answer:
C) 93o
Step-by-step explanation:
Trust the process
edge 2021
Answer:
Got a 100% on the Unit Test on Edge and 93 is the correct answer like the person above added! :D
please help!! i will help you back!!
Answer:
c = 50
Step-by-step explanation:
Using the Pythagorean Theorem:
Plug in the values of a = 14, and b = 48
[tex]a^{2} +b^{2} =c^{2}\\14^{2} +48^{2} =c^{2} \\c^{2} = 2500\\c = \sqrt{2500} \\c = 50[/tex]
Which graphs present functions?
A. graph B and D
B. graph A only
C. graph D only
D. graph C and graph D
Find the area of an equilateral triangle (regular 3 Gon) with the given measurement 9 in perimeter a=SQ.in
Answer:
3.897 [tex]in^{2}[/tex]
Step-by-step explanation:
equilateral triangles are also equiangular, meaning the have equal angles.
Triangle sum theory says that angles of a triangle add up to 180.
That means each angle is 60.
A = bh/2
You need the (h). The base of is 3. Perimeter = 9, so each side is 3
Draw a perpendicular line for the height. The line cuts the base in half (1.5)
Using trigonometry you can find the height.
tan 60° = h/1.5
h = height, 1.5 is half of 3, 60° is the base angle.
multiply each side by 1.5
1.5(tan 60°) = h
h=2.598
then substitute h into formula
A= (2.598)(3)
2
A = 3.897 rounded
i need help please. and explanation will help for tomorrow in a test:)
Please help ASAP!!
I'll mark brainliest!
Answer:
729 x [tex]\frac{1}{3}[/tex]^x
Step-by-step explanation:
the third option
- trial and error
Find the value of x.
X
100°
Y
130°
Z
66°
W
x°
Answer:
We are losing Earth's greatest biological treasures just as we are beginning to appreciate their true value. Rainforests once covered 14% of the earth's land surface; now they cover a mere 6% and experts estimate that the last remaining rainforests could be consumed in less than 40 years.
One and one-half acres of rainforest are lost every second with tragic consequences for both developing and industrial countries.
Rainforests are being destroyed because the value of rainforest land is perceived as only the value of its timber by short-sighted governments, multi-national logging companies, and land owners.
Nearly half of the world's species of plants, animals and microorganisms will be destroyed or severely threatened over the next quarter century due to rainforest deforestation.
Experts estimates that we are losing 137 plant, animal and insect species every single day due to rainforest deforestation. That equates to 50,000 species a year. As the rainforest species disappear, so do many possible cures for life-threatening diseases. Currently, 121 prescription drugs sold worldwide come from plant-derived sources. While 25% of Western pharmaceuticals are derived from rainforest ingredients, less that 1% of these tropical trees and plants have been tested by scientists.
Most rainforests are cleared by chainsaws, bulldozers and fires for its timber value and then are followed by farming and ranching operations, even by world giants like Mitsubishi Corporation, Georgia Pacific, Texaco and Unocal.
There were an estimated ten million Indians living in the Amazonian Rainforest five centuries ago. Today there are less than 200,000.
InIIIIII AMMMM ABBBOOuUUTT TOO PI$$$$$$ MINE SELLFF Brazil alone, European colonists have destrotheir homelands continue to be destroyed by deforestation, rainforest peoples are also disappearing.
, it is as if a library has burned down.
When a medicine man dies without passing his arts on to the next generation, the tribe and the world loses thousands of years of irreplaceable knowledge about medicinal plants.
Step-by-step explanation:
Which of the following is acceptable justifications to use in geometry when justifying statements about segments and
angles?
A Theorems, Defintions, Postulates, Conjectures
B. Patterns, Defintions, Conjectures, Assumptions
C. Theorems, Defintions, Assumptions, Properties
D. Theorems, Defintions, Postulates, Properties
Please select the best answer from the choices provided
ОВ
оооо
ОС
Answer:
D.
Theorems, Defintions, Postulates, Properties
Step-by-step explanation:
HELP FAST LOL HAHAHAH
Answer:
184
Step-by-step explanation:
First, note that the sides that are opposite to each other are congruent (this will come into play in a second). We can find the area of each triangle by doing 0.5(b)(h) (aka half * base* height). Since we've established tha opposite sides are congruent and the triangles are opposite to each other, they must be congruent. That means that the area is going to be the exact same for both triangles. So, we get the expression (0.5)(6)(4)(2), which comes out to 6*4 = 24. Then, to find the area of the 2 rectangles that are the sides, just do 5*10*2 = 100 square meters for both rectangles combines. Lastly, we need to find the area of the floor. The dimensions of the floor are 6 and 10, so we just do 6*10 = 60. Now, add all those numbers together. We get 100+60+24 = 184. Hope this helps! Let me know if anything is still confusing.
Solve the following for y: 4x + 2y = −2 (5 points)
y = −2x + 1
y = 2x + 1
y = −2x − 1
y = 2x − 1
Answer:
Step-by-step explanation:
4x + 2y = −2
Divide by two on both sides
2x+y = -1
subtract 2x from both sides
y = -1 -2x = -2x -1
Answer:
y = -2x - 1
Step-by-step explanation:
4x + 2y = -2
→ Minus 4x from both sides
2y = -4x - 2
→ Divide both sides by 2
y = -2x - 1
Use the function below to find F(3).
F(x) = 4•C**
O A.
H im
O B.
O c.
4
27
O D.
81
Answer:
4-3
Step-by-step explanation:
solve for x
Value of function f(x) = 4(1/3)ˣ when x = 3, f(3) = 4/27
Correct option is C.
What is exponential function?As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:
Definition of exponential function
In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.
Given, exponential function
f(x) = 4(1/3)ˣ
exponential function is defined for x∈R
Putting x = 3
f(3) = 4(1/3)³
f(3) = 4/27
Hence, 4/27 is value of function f(x) = 4(1/3)ˣ when x = 3
Learn more about exponential function here:
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A school survey asked students which candidate they supported for class president. the survey data are shown in the relative frequency table.
Answer:
C. 24%
Step-by-step explanation:
hope it works
Answer:
39%
Step-by-step explanation:
Help answer pleaseeeeeee
Answer:
Your answer is C.
Step-by-step explanation:
I answered it on paper. When it comes to explaining I have to be person to person. But I hope this helps. :)
A rectangle has a length of 2x+7 and a width of 3x+8.
Write and simplify an expression for the perimeter of that rectangle
Answer:
2(2x+7)=4x+14
2(3x+8)=6x+16
4x+14+6x+16
4x+6x+14+16
The answer is:
10x+30
what percent of 80 is 42
Answer:
52.5 percent of 80 is 42.
Which is the best description for the graph below?
A graph decreases from (0, 3) to (9, 0).
Answer:
Step-by-step explanation:
As we move from (0, 3) to (9, 0), we see x increasing by 9. This is the 'run.'
At the same time, we see y decreasing by 3. This is the 'rise.'
The slope of this line (graph) is m = rise / run = -3/9, or m = -1/3
Since we witness a decrease in y as we move from the first point to the second, we immediately suspect that the slope is negative.
dilation of ?? about the origin
Help Please... 15 points :)
Answer:
√100 = 10, √36 = 6, √225 = 15
Step-by-step explanation:
100 can be made by 10^2 (10 x 10), 36 has factors of 6 and can be made by 6^2, and 225 can be made by 15^2.
[tex] \sqrt{100} = \sqrt{10 \times 10} [/tex] = [tex]\boxed{10}[/tex]
[tex] \sqrt{36} = \sqrt{6 \times 6} [/tex] = [tex]\boxed{6}[/tex]
[tex] \sqrt{225} = \sqrt{15 \times 15} [/tex] = [tex]\boxed{15}[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
The vertex form of the equation of a parabola is y = 2(x + 4)2 - 7.
What is the standard form of the equation?
Find the 15th term in the following arithmetic sequence : 1, 6, 11, 16, ...
Hint: Write a formula to help you. 1st term + common difference(desired term - 1)
Answer:
a₁₅ = 71
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 1 and d = 6 - 1 = 5 , then
a₁₅ = 1 + (14 × 5) = 1 + 70 = 71
Step-by-step explanation:
hear is your answer in attachment
which following algebraic statements are true
Answer:
All of them are true.
Step-by-step explanation:
x^2 y - z / x^2 is true. x^2, when divided by itself, cancels itself out, so the equation that is left is y - z.
For the second one, a/c + b/c is true because when you add a + b = it will change; it will be added together. the remaining c will stay the same, as it is the denominator/the same, so you keep it as it is.
For the final one, you distribute ^2 to (a+b), so they become a^2 + b^2.
This means that all of the statements are true.
What is the measure of Rsl?
Answer:
x = 13
Step-by-step explanation:
[tex](9x + 27) = (6x + 66) \\ 9x - 6x = 66 - 27 \\ 3x = 39 \\ x = \frac{39}{3} \\ x= 13 [/tex]
The Jaxson Company offers a 6% coupon bond with semi-annual payments and a yield to maturity of 7.27%. The bonds mature in 6 years. What is the market price of a $1,000 face value bond?
Describe the transformation of f(x) to g(x).
(answers and graph in picture) PLSSSS HELP
Answer: b
Step-by-step explanation:
becuz now brainliest
The transformation of a function may involve any change. The correct option is A.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function of f(x) as sin(x), Now it can be seen the graph of the two functions is parallel, but the function f(x) has a y-intercept of 0, while h(x) has a y-intercept of 1. Therefore, we can write,
h(x) = f(x) + 1
The function is shifted up by 1 unit.
Hence, the transformation of the function is correctly described in the first option.
Learn more about Transforming functions:
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factorise the following expressions;
1. 8x + 6 2. 4x + 2
Answer:
Step-by-step explanation:
1. 8x + 6
2(4x+3)
2.4x+2
2(2x +1)
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
1. [tex]\boxed{Factorise \ = \ 8x + 6}[/tex]
⎆To factorise this, you have to take the common factor out. In this case, it's 2.
[tex]8x + 6 \\ = 2(4x + 3)[/tex]
[tex]\boxed{Answer \ = \ 2(4x + 3)}[/tex]
2) [tex]\boxed{Factorise \ = \ 4x + 2}[/tex]
⎆To factorise this, you have to take the common factor out. In this case also, it's 2.
[tex]4x + 2 \\ = 2(2x + 1)[/tex]
[tex]\boxed{Answer \ = \ 2(2x + 1)}[/tex]
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
ღ [tex]RainbowSalt2^{2}2^{2} [/tex]
An equation is shown below: −2(4x − 1) − 7 = 5 Which statement shows a correct next step in solving the equation? (1 point)
A)The equation can become −2(4x − 1) = −2 by applying the distributive property.
B)The equation can become −2(4x − 1) = 12 by applying the addition property of equality.
C)The equation can become −2(4x − 1) = 12 by applying the commutative property of addition
D)The equation can become −2(4x − 1) = −2 by applying the subtraction property of equality.
Answer:
B
Step-by-step explanation:
Add both sides of the equation by 7, which satisfies the definition of the addition property of equality.
What is the image of (-8,-8) after dilation by a scale factor of {1/4} centered at the origin?
Answer:
(-2, -2)
Step-by-step explanation:
To scale a factor by 1/4, you just need to divide the numbers by 4, or multiply them by 1/4.
-8/4=-2
Answer:
It would be (-2, -2)
Find the range of the given data set. 5/8,3/4,1 1/8,1 1/4
plzz help everything is due tonight! 29 pointssss
Answer:
Step-by-step explanation:
given= -3(2n-3)=25-8n
distributive property=-6n+9=25-8n
subtraction property= 2n+9=25
division property =2n=16
n=8
