Answers
From the definition, we have
[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{f(x) - f(10)}{x - 10}[/tex]
With [tex]f(x)=\sqrt{x-1}[/tex], we get [tex]f(10)=\sqrt{10-1}=\sqrt9=3[/tex]. So the limit we want to compute is
[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{\sqrt{x-1} - 3}{x - 10}[/tex]
Rationalize the numerator by multiplying by its conjugate:
[tex]\displaystyle \frac{\sqrt{x-1} - 3}{x - 10} \times \frac{\sqrt{x-1}+3}{\sqrt{x-1}+3} = \frac{\left(\sqrt{x-1}\right)^2-3^2}{(x-10)\left(\sqrt{x-1}+3\right)} = \frac{x-10}{(x-10)\left(\sqrt{x-1}+3\right)}[/tex]
x is approaching 10, which is to say x ≠ 10, so we can cancel the factors of x - 10 and remove the discontinuity.
Then we're left with
[tex]\displaystyle f'(10) = \lim_{x\to0} \frac1{\sqrt{x-1}+3} = \frac1{\sqrt{10-1}+3} = \frac1{\sqrt9+3} = \frac1{3+3} = \boxed{\frac16}[/tex]
evaluated by direct substitution, which we can do since the limand is continuous.
Related Questions
Find the volume of the sphere. Round your answer to the nearest tenth.
Answers
Answer:
20
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME WITH THIS
Answers
Answer:
7a is not a factor because it doesnt divide into anything.
7a is not a term because it is not only the variable.
3 is a constant because it is a number in the expression.
7a is not a coefficient because it is not just the number.
8b and 5b are like terms because they have the same variables.
None of these are true Thats false because some of the answers are right
40 PTS PLS HELP! The figure shown is formed by a square and a semicircle. Line segment BC is 4 cm. Find the area of the figure.
Question 5 options:
14.28 cm2
22.542
20.56 cm2
32.642
Answers
Answer:
1.1458
2.
3.14.14 cm2
4.20035
di ako sure correct me if i wrong
The area of the figure formed by the square and semicircle is T = 22.28 cm²
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the area of the square be represented as A
Now , the value of A is
Let the area of the semicircle be S
Let the total area of the figure be T = S + A
where A = ( 4 )² = 16 cm²
And , S = ( πr² ) / 2
S = 3.14 x ( 2 )² / 2
S = 6.28 cm²
So , the total area T =6.28 cm² + 16 cm² = 22.28 cm²
Hence , the area of the figure is T = 22.28 cm²
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The complete question is attached below :
The figure shown is formed by a square and a semicircle. Line segment BC is 4 cm. Find the area of the figure.
A) 22.28 cm2
B) 22.542
C) 20.56 cm2
D) 32.642
A factory’s production is modeled by function f(x) where f(x) is the number of parts produced per hour and x is the number of people working during production choose the ordered pair that represents a posible domain and range of the function
Answers
Answer:
5,10
Step-by-step explanation:
this is the answer
Solve for the missing components
Answers
Side B= 48 degrees
Side C= 90 degrees, automatically seen by the square
5) Angle B= 53 degrees
Side A= 37 degrees
Side C= 90 degrees, being a right angle
All right triangles equal to 180 degrees, in which those answers do for each problem.
0.46 + (-0.642)
Please help!! Thank you!!
Answers
Answer:
-0.182
Step-by-step explanation:
Given expression:
0.46 + (-0.642)It should be noted that;
1. Positive integer + (Negative integer) = Positive integer - Positive integer
a + (-b) = a - b2. Positive integer - (Negative integer) = Positive integer + Positive integer
a - (-b) = a + bOur case is point 1. Therefore,
⇒ 0.46 + (-0.642)⇒ 0.46 - 0.642⇒ -0.1822x - 8 + 3x + 2 = 4x + 10 + 3x - 6
Answers
Answer:
x = 10/-6 or 5/-3
Step-by-step explanation:
2x - 8 + 3x + 2 = 4x + 10 + 3x - 6
x - 6 = 7x + 4
+6 +6
---------------------
x = 7x + 10
-7x -7x
---------------------
-6x = 10
x = 10/-6 or 5/-3
I hope this helps!
Can I? I really need your help, b'coz, I can't understand how to solve it.
Answers
Answer:
See below ~
Step-by-step explanation:
1. D. cylinder
2. A. pyramid
3. E. rectangular prism
4. C. cone
5. F. cube
Find the equation of a line parallel to y=4x+2 that contains the point (−2,−3). Write the equation in slope-intercept form.
Answers
Answer:
y = 4x + 5
Step-by-step explanation:
Use point-slope formula to plug in the known point and slope.
What is the value of 14 × 10,000?
140
1,400
14,000
140,000
Answers
Answer:
140000
Step-by-step explanation:
Hewo Yuri-san here Allow me to help! :3
Answer:
-140,000
Step-by-step explanation:
Here's a trick I learned in 5th grade.
You see all the zero's behind the number 10,000 just add them onto the back of the number you're mutliplying with and it gives you the answer.
In this case, we have the number 10,000 with 4 zero's and we're going to add that to the back of 14 which gives us the answer 140,000 And they both have 4 zero's. :)
Therefore, the answer is 140,000
Hope this Helps!
Have a great day!
-Yuri-san
The linear function y 2.5x + 3.94 represents the amount of revenue in millions since 2000. What
was the revenue in millions in 2010?
Answers
Answer:
i dont know what will i do that plss help me
Identify and correct the error. B 50° A 50
Answers
Answer:
30 degrees
this is a guess but an educated one because the total angle adds up to 180 deg so one i assume is around 100 plus 50 plus 30 makes sense
PLEASE HELP
Estimate the square root to the nearest (a) integer and (b) tenth.
Answers
22points) what’s 1+1?
A=1
B=2
C=-2
D=11
E=21
F=77
G=I don’t know
Answers
Step-by-step explanation:
1 plus 1 equals 2
It's addition so u just add
1 + 1 = 2
Pls mark me brainiest
find the surface area of each shipping package. Which package has the greater surface area? Does the same package have a greater volume?
package A: 14 x 12 x 3
package B: 11 x 6 x 8
Answers
Answer:
greater area: Ano, B has the greater volumeStep-by-step explanation:
The relevant area and volume formulas are ...
A = 2(LW +H(L +W))
V = LWH
When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.
Figure A has the larger area.
Figure B has the larger volume.
__
Additional comment
The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)
If you randomly select a letter from the phrase "Brandon loves to eat at Red Robin," what is the probability that you select a consonant? (Your answer must be in the form of a reduced fraction.)
Answers
Answer:
16/27
Step-by-step explanation:
Formula for probability:
favourable outcomes/possible outcomes
using this we can find the answer.
let's first count all the consonants. there are 16 consonants and 27 total letters. that means that your answer would be 16/27.
9. How can you better manage stress and feelings related to anxiety?
O A.By working more hours
O B. By understanding your own emotions
O C.By improving your grades
O D. By having a stricter social schedule
Mark for review (Will be highlighted on the review page)
Answers
Answer:
B. By understanding your own emotions
Step-by-step explanation:
Other options seem unrealistic so B would be best.
A doughnut shop made 32 chocolate doughnuts one morning. The chocolate
doughnuts were 40% of the total number of doughnuts made that morning. How
many doughnuts were made, in all?
3
Answers
80 donuts were made
i hope this helps !
can you help me to solve this problem
g ( t ) = | t | - 3 ; find g ( 3 ) , g ( -5 ) , and g ( 0 )
Answers
Answer:
g(3) = 0. g(-5) = 2. g(0) = -3
Step-by-step explanation:
simply put whatever is inside the brackets, into where t is in the equation
e.g:
|t| - 3 for g(3) is: |3| - 3 = 0
the two lines around t just mean that whatever is inside you should always turn positive. so |-1| = 1 and |-3 + 1| = 2
Find the determinant of this matrix:
[tex]\left[\begin{array}{ccc}0&6\\5&0\end{array}\right][/tex]
Answers
Answer:
-30
Step-by-step explanation:
Apply the formula
[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc[/tex]
0(0)-6(5)
-30
What is the value of the expression.
20 + 12 ÷ 1/4 x 3
Answers
Answer:
164
Step-by-step explanation:
[tex]20 + 12 \div \frac{1}{4} \times 3 \\ \\ = 20 + 12 \times 4 \times 3 \\ \\ = 20 + 144 \\ \\ = 164[/tex]
Write the algebraic expression that matches each graph.
Answers
Answer:
f(x) = |x - 2| - 2
Step-by-step explanation:
Based on the shape of the graph, it's an absolute value function.
so the template for it is f(x) = |x|
From there, you can make some additions to show how much the graph has shifted from the template equation
since the graph went over to the left by 2 units and down by 2 units, this is added into the equation as follows:
f(x) = |x - 2| - 2
could someone please help me with this super quickly? only real answers please
optionally you could check out some of my previous questions such as with https://brainly.com/question/27457567 it gives 50 points as well
Answers
Answer:
Axis of symmetry: x = 5
Vertex form: y = -4(x - 5)² + 3
Step-by-step explanation:
Given ordered pairs: (2, -33) (3, -13) (4, -1) (5, 3) (6, -1)
Axis of Symmetry
As this is a parabola, it will be symmetrical.
To determine the axis of symmetry, identify two ordered pairs that have the same y-values and find their midpoint.
Two ordered pairs with the same y-value: (-4, 1) and (6, -1)
Midpoint of x = 4 and x = 6 is: x = 5
Therefore, the axis of symmetry is x = 5
Vertex form
Vertex form of a quadratic equation: y = a(x - h)² + k
(where (h, k) is the vertex)
The axis of symmetry is the x-value of the vertex of the parabola.
As we have been given the point when x = 5, the vertex is: (5, 3)
Substituting this into the formula:
⇒ y = a(x - 5)² + 3
To find the value of a, substitute any of the other points into the formula and solve for a.
Using (4, -1)
⇒ a(4 - 5)² + 3 = -1
⇒ a(-1)² = -4
⇒ a = -4
Therefore, the vertex form of the parabola is:
y = -4(x - 5)² + 3
PLEASE HELP NOW
HURRY
Answers
Answer:
13
Step-by-step explanation:
we us the pythagorean theorem
sqrt( 144 + 25) = 13
Find the area and circumference of each shaded sector. Use 3.14 for . Round to the
nearest tenth.
Answers
Answer:
Area = 226.1 ft^2
and circumference = 61.7 ft.
Both to the nearest tenth.
Step-by-step explanation:
The area of shaded part
= 1/2 *3.14 r^2
= 1/2 * 3.14 * 12^2 = 226.1 ft^2.
Circumferences of the shaded part = diameter + length of the semicircle
= 2 *r + 3.14 * r
= 2*12 + 3.14 * 12
= 61.68 ft.
A boat travels 1/5 of a mile on 7/9 gallon of gas. How many miles can the boat travel on 1 gallon of gas
Answers
Answer:Since we know the boat uses 25 gallons of gas per 64 miles, we can divide 64 miles by 25 gallons to get the rate of gallons per hour.
64 ÷ 25 = 2.56 gallons of gas every hour.
Using this information, we can multiply the amount of gas used for one hour, 2.56 gallons, by the 125 gallons of gas that the problem suggests, 125, to find the number of miles the boat can travel on the amount of gas.
2.56 x 125 = 320 miles
Answer: The boat can travel 320 miles on 125 gallons of gas.
A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape. (a) What is the probability that both grapes are green? (b) What is the probability that Henry eats a red grape then a green grape?
Answers
Answer:
A. 28/253
B. 60/253
Step-by-step explanation
A. first step is to add all the grapes up which = 23
then you would put the
green grapes/ the total which would be 8/23
since henry ate one grape you would subtract 8-1 and then 23-1 and you would get 7 and 22
then you would put 7/22 and multiply 8/23 which gets you 28/253
B. first you put red grapes over total grapes which are 15/23
then,
you would do the green grapes which are 8/22
you would multiply 15/23 and 8/22 which = 60/253
1.
Use trigonometry to work out the value of x.
Not drawn accurately.
Help pls
Answers
Answer:
20cos(39) or 15.543 (3 d.p.)
Step-by-step explanation:
Use SOHCAHTOAYou want to find A and have an angle of 36° and HSo use CAHcos(39) = x / 20x = 20cos(39)Which table shows a data o for an antenna that revolves at exactly twice the rate of the antenna described in the graph?
Answers
The table shows a data for an antenna that revolves at exactly twice the rate of the antenna described in the graph is Table D.
How to illustrate the rate?The formula to calculate the rate will be:
= Change in revolution/Change in time
The rate of the given antenna will be:
= (60 - 30)/(4 - 2)
= 30/2
= 15
Also, the rate of antenna 1 is 23, antenna 2 is 25, antenna 3 is 2. The rate for antenna 4 will be:
= (720 - 660)/(24 - 22)
= 60/2
= 30
It can be seen that 30 is double of 15.
Therefore, table D revolves at exactly twice the rate of the antenna.
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Given that the expression 2x² -2.9x-3.6 can be factorized into the form 0.1(px+q)(rx+s), where p, q, r and s are integers, find the value of p + q + r + s.
Answers
[tex]~~2x^2-2.9x-3.6\\\\=\dfrac{20}{10}x^2 - \dfrac{29}{10} x-\dfrac{36}{10} \\\\=\dfrac 1{10} (20x^2 -29x -361)\\\\=0.1(20x^2-29x-36)\\\\=0.1(20x^2-45x+16x-36)\\\\=0.1[5x(4x-9)+4(4x-9)]\\\\=0.1(5x+4)(4x-9)\\\\\text{Where,}~ p=5, ~ q=4,~ r=4~,s=-9\\\\\text{Hence,}~ \\\\p+q+r+s \\\\ = 5+4+4 -9 \\\\=13-9 \\\\ =4[/tex]
The value of p + q + r + s in the equation 0.1{(5x + 4)(4x - 9)}.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, 2x² - 2.9x - 3.6.
Now, 0.1(20x² - 29x - 36).
= 0.1{4x(5x + 4) - 9(5x + 4)}.
= 0.1{(5x + 4)(4x - 9)}.
∴ p + q + r + s = 5 + 4 + 4 - 9.
p + q + r + s = 4.
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