Step-by-step explanation:
If the equation is
[tex] \sqrt{x + 2} [/tex]
Then, here is the answer.
The definition of a derivative is
[tex] \frac{f(x + h) - f(x)}{h} [/tex]
Also note that we want h to be a small, negligible value so we let h be a value that is infinitesimal small.
So we get
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} [/tex]
Multiply both equations by the conjugate.
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \times \frac{ \sqrt{x + h + 2} + \sqrt{x + 2} }{ \sqrt{x + h + 2} + \sqrt{x + 2} } = \frac{x + h + 2 - (x + 2)}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{h}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{ \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
Since h is very small, get rid of h.
[tex] \frac{1}{ \sqrt{x + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{2 \sqrt{x + 2} } [/tex]
So the derivative of
[tex] \frac{d}{dx} ( \sqrt{x + 2} ) = \frac{1}{2 \sqrt{x + 2} } [/tex]
Part 2: If your function is
[tex] \sqrt{x} + 2[/tex]
Then we get
[tex] \frac{ \sqrt{x + h} + 2 - ( \sqrt{x} + 2) }{h} [/tex]
[tex] \frac{ \sqrt{x + h} - \sqrt{x} }{h} [/tex]
[tex] \frac{x + h - x}{h( \sqrt{x + h} + \sqrt{x}) } [/tex]
[tex] \frac{h}{h( \sqrt{x + h} + \sqrt{x} ) } [/tex]
[tex] \frac{1}{ \sqrt{x + h} + \sqrt{x} } [/tex]
[tex] \frac{1}{2 \sqrt{x} } [/tex]
So
[tex] \frac{d}{dx} ( \sqrt{x} + 2) = \frac{1}{2 \sqrt{x} } [/tex]
A train leaves Philadelphia at 2:00 PM. A second train leaves the same city in the same direction at 4:00 PM. The second train travels
52 mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains?
Answer: First train speed shall be 42 mi/hr
Second train speed shall be 84 mi/hr
Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.
Step-by-step explanation:
What is the 1st train's head start in miles?
Let +s+ = the speed of the 1st train in mi/hr
From 2PM to 4PM is 2 hrs
+d%5B1%5D+=+s%2A2+
---------------------
Let +d+ = distance the 2nd train travels until
it overtakes the 1st train
From 4PM to 6PM is 2 hrs
Start time when the 2nd train leaves
---------------------
Equation for 1st train:
(1) +d+-+2s+=+s%2A2+
Equation for 2nd train:
(2) +d+=+%28+s%2B42+%29%2A2+
--------------------
Substitute (2) into (1)
(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+
(1) +2s+%2B+84+-+2s+=+2s+
(1) +2s+=+84+
(1) +s+=+42+
and
+s%2B+42+=+42+%2B+42+
+s+%2B+42+=+84+
------------------
The 1st train's speed is 42 mi/hr
The 2nd train's speed is 84 mi/hr
---------------------------
check:
(2) +d+=+%28+s%2B42+%29%2A2+
(2) +d+=84%2A2+
(2) +d+=+168+
and
(1) +d+-+2s+=+s%2A2+
(1) +d+-+2%2A42+=+42%2A2+
(1) +d+=+84+%2B+84+
(1) +d+=+168+
3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations described below. a. The account pays 3% annual interest compounded monthly. b. The account pays 4% annual interest compounded continuously.
Answer:
Part A)
About $3767.34.
Part B)
About $3692.47.
Step-by-step explanation:
Part A)
Recall that compound interest is given by the formula:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
To obtain $4000 after two years, let A = 4000 and t = 2.
Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.
Substitute and solve for P:
[tex]\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}[/tex]
In concluion, about $3767.34 should be deposited.
Part B)
Recall the formula for continuous compound:
[tex]\displaystyle A = Pe^{rt}[/tex]
Where e is Euler's number.
Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:
[tex]\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}[/tex]
In conclusion, about $3692.47 should be deposited.
how does the distributive property work
Explanation:
The distributive property tells you that multiplication distributes over addition. In equation form, it looks like ...
a(b +c) = ab +ac
__
Groups and Multiples of GroupsThe parentheses are a grouping symbol. In the above equation, they indicate that the sum (b+c) is to be treated as a group. When it is multiplied by 'a', everything in the group is multiplied by 'a'.
In the real world, there are many ways things are grouped. Baseball cards are packaged together with bubble gum; Cracker Jacks® are packaged together with a prize; left gloves are packaged together with right gloves; a bicycle is a package that has a frame, 2 wheels, a seat, handlebars. If you purchase a number of any of these packages, each of the items in the package is part of your purchase that number of times.
For example, 3 bicycles will have 3 frames, 3×2 = 6 wheels, 3 seats, 3 sets of handlebars. In algebraic form, this might look like ...
3(f +2w + s + h) = 3f +6w +3s +3h
__
Eliminating ParenthesesUsing the distributive property to eliminate parentheses is like regrouping the contents of the packages so like items are grouped together. In our above example, the 3 frames were grouped together when we considered that part of the group of 3 bicycles. The multiplier multiplies every member of the group.
__
Adding ParenthesesThe reverse of the distributive property tells us we can regroup items into sets. It tells us we can take 3 frames, 6 wheels, 3 seats, and 3 handlebars and group them together in a way that makes 3 bicycles, each having a frame, 2 wheels, a seat, and handlebars.
3f +6w +3s +3h = 3(f +2w + s + h)
Often, we're asked to choose the multiplier to be the greatest common factor (GCF) of the numbers of things in the group. That makes each group as small as possible. The multiplier only needs to be a common factor, not necessarily the greatest common factor.
>> The total cost of a pizza and 3 drinks is $19. The price of the pizza is $10 and each drink is the
same price, d.
Which model represents the situation?
10
d
d
d
19
.) What is the price of one drink?
d
?
Answer:
d = 3
Step-by-step explanation:
According the figure:
10 + d + d + d = 19d = 3Answer Check Below:
⇒ 10 + 3 = 13
⇒ 13 + 3 = 16
⇒ 16 + 3 = 19
Therefore, d = 3.Answer:
$3
Step-by-step explanation:
⇒ 10 + 3d = 19 is represented by the figure⇒ 3d = 9⇒ d = 3The price of one drink is $312) Write the equation of a rational function
Vertical asymptote at x = 0 and x = -1
Horizontal asymptote at y = -4
Hole at x = 12
X-intercepts at x = 5, x=-7 L
Answer:
[tex] \frac{4(x - 5)(x + 7)(x - 12)}{(x + 1)(x)(x - 12)} [/tex]
Step-by-step explanation:
A rational function is
[tex] \frac{p(x)}{q(x)} [/tex]
where q(x) doesn't equal zero.
If p is a asymptote, or hole at that value, then we will use
[tex](x - p)[/tex]
Step 1: We have asymptote as 0 and -1 so our denomiator will include
[tex](x - 0)(x - ( - 1)[/tex]
Which is
[tex](x)(x + 1)[/tex]
So our denomator so far is
[tex] \frac{p(x)}{x(x + 1)} [/tex]
Step 2: Find Holes.
Since 12 is the value of the hole,
[tex](x - 12)[/tex]
is a the binomial.
This will be both on the numerator and denomator so qe have
[tex] \frac{(x - 12)}{x(x + 1)(x - 12)} [/tex]
Step 3: Put the x intercepts in the numerator.
Since 5 and -7 is the intercepts,
[tex] \frac{(x - 12)(x - 5)(x + 7)}{x(x + 1)(x - 12)} [/tex]
Step 4: Horinzontal Asymptotes,
Multiply the numerator and denomiator out fully,
[tex] \frac{ {x}^{3} - 10 {x}^{2} - 59x + 420 }{ {x}^{3} - 12 {x}^{2} + x - 12} [/tex]
Take a L
look at the coefficients,
Notice they have the same degree,3, this means if we divide the leading coefficents, we will get our horinzonral asymptote.
Multiply the numerator by 4.
[tex] \frac{4(x - 12)(x - 5)(x - 7)}{x(x + 1)(x - 12)} [/tex]
Above is the function,
Whats the value of the question
Answer:
8
----
125
Step-by-step explanation:
(2/5)³
2 2 2 8
--- x --- x --- = ---------
5 5 5 125
I hope this helps!
Solve and verify your answer.
A sludge pool is filled by two inlet pipes. One pipe can fill the pool in 11 days and the other pipe can fill it in 24 days. However, if no
sewage is added, waste removal will empty the pool in 32 days. How long (in days) will it take the two inlet pipes to fill an empty pool
Answer:
' =9 93/107 days
Step-by-step explanation:
1/11+1/24
one day =35/264
35/264 -1/32
=107/ 1056- fraction of rem in a day
1 day= 107/1056
x = 1
=107/1056x=1
x=1÷107/1056
1056÷107
=9 93/107 days
164 hundreds - 12 hundreds
Answer:
152 hundred
Step-by-step explanation:
164 hundred - 12 hundred = 152 hundred
Please rate!
Answer:
1.52
Hope this helps :)
Step-by-step explanation:
step one:
put them as decimals which would be 1.64 and 0.12
step two:
subtract which would be 1.64 - 0.12
step three:
solve your answer would be 1.52 or 152 hundredths
i need help on a math question thank u
Answer:
XZ is longer than XY
Step-by-step explanation:
First we can notice all of the answers consist of knowing the lengths, so we must now find the lengths for each segment. To do this, we must use the pythagorean theorem.
(1, -1) and (-5, -5)
-5- -1 = -4
-5-1 = -6
-4^2+-6^2 = c^2
16+36 = c^2
52 = c^2
7.21110255 = c
So, the length of XZ is 7.21110255 units long
(1, -1) and (8, -2)
8-1 = 7
-2--1 = -1
7^2+-1^2 = c^2
49+1 = c^2
50 = c^2
7.07106781 = c
So, the length of XY is 7.07106781 units long.
XZ is longer than XY
A 40-kilogram bag of seed is spread evenly about the entire yard. How much, in kilograms, of the seed will NOT be watered? Use: Percentage = watered squares / Total # of Square X 100
The computation of the percentage shows that the kilograms of seed that won't be watered is 12 kilograms.
How to calculate the percentage?Your information is incomplete. Therefore an overview will be given. Let's assume that the watered squares are 35 while the total squares are 50.
Then, the percentage of the watered squares will be:
= 35/50 × 100
= 70%
Therefore, the percentage of the unwatered squares will be:
= 100% - 70%
= 30%
Then, the kilograms of the seed that won't be watered will be:
= Percentage of unwatered seed × Entire kilograms of seed
= 30% × 40kg
= 12kg
In conclusion, the seed that won't be watered is 12 kg.
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18.
Given that sin x =
8
and sin y = , where x and y are acute, find the value of cos (x + y).
17
A.
B.
130
221
140
221
140
204
220
22
C.
D.
Answer:
B
Step-by-step explanation:
[tex]\sin{x}=\frac{5}{13}, \cos{x}=\sqrt{1-(\frac{5}{13})^2}=\frac{12}{13}[/tex]
[tex]\sin{y}=\frac{8}{17}, \cos{y}=\sqrt{1-(\frac{8}{17})^2}=\frac{15}{17}[/tex]
[tex]\cos(x+y)=\cos{x}\cos{y}-\sin{x}\sin{y}\\=\frac{12}{13}\times\frac{15}{17}-\frac{5}{13}\times\frac{8}{17}\\=\frac{140}{221}[/tex]
The equation to model Exponential Growth is:
y= a(1+r)*
y= total amount
a= starting amount
r= the growth rate as a decimal
t= number of growth periods
Question 2 (1 point)
You have been gotten a job offer and the company wants to start you out at $45,000
and will give you a 5% raise every year. Write an equation you could use to
determine how much you would be making after x number of years.
Your salary in x years is modeled an the exponential growth
The equation that determines your salary in x years is y = 45000(1.05)^x
How to model the salary growth?The model of the exponential growth is given as:
y = a(1 + r)^x
From the question, we have:
Initial salary, a = 45000
Raise, r = 5%
So, the equation becomes
y = 45000(1 + 5%)^x
Evaluate the sum
y = 45000(1.05)^x
Hence, the equation that determines your salary in x years is y = 45000(1.05)^x
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Eva filled a bucket with 7 gallons of water. A few minutes later, she realizes only 1 3/5 of water remained. How much water had leaked out of the bucket?
Answer:
[tex]6 \frac{2}{5}[/tex]Step-by-step explanation:
[tex]7 - 1 \frac{3}{5} = 6 \frac{2}{5}[/tex]
hey guys can you please help me with these questions please explained them
B for question 12
B for question 13
Step-by-step explanation:
U = Union
n= intercestion
B'= not b
A"= not a
so AnB'
should be B
if 2.50 = 1
2.50x8=
20
1×8 =
8
should be $8
What is the solution to use the following equation 5(2x-6)+20=10
Answer:
first you distribute the five making it 10x-30+20=10
second you combine like terms making it 10x-10=10
third you isolate the variable making it 10x=20
Finally you divide both terms by ten giving you x=2 as your answer.
A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white?
A.1
B.6
C.12
D.13
Answer: D
Step-by-step explanation:
21=7+6+neither-5
7+6=13-5=8
21-8=13
Simplify (cosx)(tanx)(cscx)
[tex]❖\qquad\qquad\huge\underline{{\sf Answer}} \qquad \normalsize❖[/tex]
Let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \cos(x) \times \tan(x) \times \csc(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: \cancel{ \cos(x) }\times \dfrac{ \cancel{ \sin(x)} }{ \cancel{ \cos(x) }} \times \dfrac{1}{ \cancel{\sin(x)} } [/tex]
[tex]\qquad \sf \dashrightarrow \:1[/tex]
The equivalent value is 1
For a class activity, a teacher put students into teams of 5. The teams were made up of 2 students randomly chosen from group A and 3 students randomly chosen from group B.
If group A has 4 students and group B has 6 students, how many different team combinations were possible?
Enter your answer as a number, like this: 42
Answer:
120
Step-by-step explanation:
6p3 = 120
The number of the different combinations of the teams will be 26.
What are permutation and combination?A permutation is an act of arranging objects or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.
Given that for a class activity, a teacher put students into teams of 5. The teams were made up of 2 students randomly chosen from group A and 3 students randomly chosen from group B. If group A has 4 students and group B has 6 students,
The number of possible combinations will be calculated as,
C = ⁶C₃ + ⁴C₂
C = ( 4 x 3 ) / 2 + ( 6x 5 x 4 ) /( 3x 2 )
C = 6 + 20
C = 26
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6 · 6 · 6 · 6 = 1,296. Using exponents, write two more expressions that also have a value of 1,296.
Marcus has 127 baseball cards in his collection. Gabriel has 56 cards in his collection. Gabriel divides his collection evenly among Marcus and 7 other friends. How many baseball cards does Marcus have now?
Use the drop-down menu to show the correct answer.
Marcus has
Choose...
baseball cards now.
Answer:
134
Step-by-step explanation:
Gabriel has 56 cards and divides them evenly among 8 friends, which means each person has 56/8= 7 cards.
So Marcus has 127 + 7 = 134 cards
Oxygen flows through one tube into a liter flask filled with air, and the mixture of oxygen and air (considered well stirred) escapes through another tube. Assuming that air contains 4% oxygen, what percentage of oxygen will the flask contain after 5 L have passed through the intake tube?
The amount of oxygen in the flask through the intake tube illustrates proportions
The flask 99.35% will contain of oxygen after 5L have passed through the intake tube
How to calculate the percentage of oxygen?
To do this, we make use of the following representations
P for the proportion of oxygenV for te volume of oxygenx for the proportion of oxygen in the flask after 5 L passed throughSo. we have the following derivative
dP = dV - P * dV
Divide through by dV
dP/dV = 1 - P
Next, we set up the integral
[tex]\int\limits^x_{0.040} \frac {1}{1 - P}dP= \int\limits^5_0 {dV}[/tex]
Integrate both sides
[tex]-\ln(|P - 1|)|\limits^x_{0.04} = 5[/tex]
Expand
-ln(|x - 1|) + ln(|0.04 - 1|) = 5
Evaluate the difference
-ln(|x - 1|) + ln(|-0.96|) = 5
Express as a fraction
ln(0.96/|x - 1|) = 5
Express both sides as exponents with a base of 2
e^ln(0.96/|x - 1|) = e^5
Solve for x
x = 1 - 0.96/e^5
Evaluate the difference
x = 0.9935
Express as percentage
x = 99.35%
Hence, the flask 99.35% will contain of oxygen after 5L have passed through the intake tube
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If log_10(x) = 3 + log_10(y), then find x/y
Answer:
1000Step-by-step explanation:
[tex]log_{10}x = 3 + log_{10}y[/tex][tex]log_{10}x - log_{10}y = 3[/tex][tex]log_{10}(x/y) = 3[/tex][tex]x/y = 10^3[/tex][tex]x/y = 1000[/tex]Answer:
x/y = 10^3 = 1000
Step-by-step explanation:
The rules of logarithms tell you ...
log(x/y) = log(x) -log(y)
__
Here, we have ...
log(x/y) = log(x) -log(y)
= (3 +log(y)) -log(y) = 3 . . . . . . . . substittute for log(x)
Taking the antilog, we get ...
log(x/y) = 3
x/y = 10^3 = 1000
_____
Additional comment
The expression log(x) is often used to refer to the "common log" of x, which is the logarithm to the base 10. This lets us avoid the cumbersome notation log_10(x).
In more formal mathematics, log(x) may be used to refer to the natural log. The distinction is usually made in high school algebra by referring to the natural log using ln(x).
10ft,10ft,4ft what is the area
Answer:
400 ft sq
Step-by-step explanation:
Area = Length x Width x Height
10 x 10 x 4
100 x 4
400
Have a great day!!
Please rate and mark brainliest!!
José plotted points on a coordinate plane to represent the vertices of a rectangle. The first
two points José plotted are shown below.
Jose's rectangle must have equal and parallel opposite sides
The coordinates of the other points could be C(7,5) and D(7,1)
How to determine the other points?The coordinates are given as;
A = (2,5).
B = (2,1).
To form a rectangle, each of the remaining points must have the same y-coordinates as points A and B.
So, we have:
C = (x,5)
D = (x,1)
Also, the remaining points must have the same x-coordinates.
i.e.
Cx = Dx
From the list of options, we have:
C(7,5) and D(7,1)
Hence, the coordinates of the other points could be C(7,5) and D(7,1)
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Given that the width is 4.5 units and the length can be represented by x + 3, which answer choice shows the correct expression of the area below?
Please just explain step by step how you got the answer.
!!! I WILL GIVE YOU 50 POINTS IF YOU SOLVE IT!!!
Step-by-step explanation:
the area of a rectangle is
length × width
that is in our case
(x + 3) × 4.5 = 4.5x + 4.5 × 3 = 4.5x + 13.5
remember, when multiplying 2 expressions, you multiply every term of one expression by every term of the other expression and then you add all these individual results up by considering the signs, of course.
find the value of x
Answer:
See below, please
Step-by-step explanation:
[tex](2x + 9) + (4x - 3) = 90[/tex]
[tex]6x + 6 = 90[/tex]
[tex]6x = 90 - 6 = 84[/tex]
Hence
[tex]x = 14[/tex]
a recipe for 5 people calls for 1.5 kg of meat. How much meat is required if the receipe is adapted to feed 8 people
Answer:
2.4 kg
Step-by-step explanation:
1.5 divided by 5 is 0.3 and 0.3 multiplied by 8 is 2.4
In the diagram, the length of Line segment Y Z is twice the length of Line segment A Z.
Triangle X Y Z is shown. Angle X Y Z is a right angle. An altitude is drawn from point Y to point A on size Z X to form a right angle.
Line segment Y A is an altitude of ΔXYZ. What is the length of Line segment Y A?
5 StartRoot 3 EndRoot units
10 StartRoot 3 EndRoot units
15 units
20 units
Answer:
5 startrood 3 endroot units .
The length of YA from the figure is 10√3 units
Pythagoras theoremAccording to the pythagoras theorem;
YZ² = AZ² + YA²
Given that YZ = 2AZ, hence;
20² = 10² + YA²
YA² = 400 - 100
YA² = 300
YA = √300
YA = 10√3 units
Hence the length of YA from the figure is 10√3 units
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Evaluate 3x2−9
when x=−2
Answer:
3
Step-by-step explanation:
substitute x = - 2 into the expression
3x² - 9
= 3(- 2)² - 9
= 3(4) - 9
= 12 - 9
= 3
Calculate the determinant of this matrix:
What is the first step?
Step 1: Augment the matrix by copying columns 1 and 2 to the right of the matrix
Step 2: Find the products along the main diagonals
d1= 4
d2= 0
d3= 3
Step 3: Find the products of the minor diagonals
e1= 0
e2= 16
e3= 2
Step 4; Perform the final calculation
d1+d2+d3-e1-e2-e3= -11
(Got them all right on edge 2022)
Why did you ask this, but also answer it?- Lol thank you for the points though I guess...
Answer:
thank you they are all correct!
Step-by-step explanation: