f ' ( x ) = 1 ( x + 1 ) 2
Explanation:
differentiating from first principles
f ' ( x ) = lim h → 0
f ( x + h ) − f ( x ) h
f ' ( x ) = lim h → 0
x + h x + h + 1 − x x + 1 h
the aim now is to eliminate h from the denominator
f ' ( x ) = lim h =0
( x + h ) ( x + 1 )− x ( x + h + 1) h ( x + 1 ) ( x + h + 1 )
f ' ( x ) = lim h → 0
x 2 + h x + x + h − x 2 − h x − x h ( x + 1 ) ( x+h + 1 )
f ' ( x ) = lim h → 0
h 1 h 1 ( x + 1 ) ( x + h +1 )
f ' ( x ) = 1 ( x + 1 ) 2
James ate 4/5 of his banana and Eric ate 7/9 of his banana. Who ate more of their banana?
Answer:
James
Step-by-step explanation:
4/5 = 80% of banana
7/9 = 77.77% of banana
4/5 is greater than 7/9, so James ate more of his banana.
Please mark Brainliest if it helped you.
Answer:
James
Step-by-step explanation:
Because when reduce 4/5= 0.8
And 7/9= 0.77778
Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season started, the pond was 10 feet deep. What is the equation that best represents the depth of the pond each week? Hint: Use the formula y = P(1 + r)x. y = 10(0.03)x y = 10(0.3)x y = 10(1.3)x y = 10(1.03)x
Answer:
y = 10(1.03)^x
Step-by-step explanation:
In the formula y = p(1 + r)^x, p is the starting amount and r is the growth rate.
In this problem, the starting amount is 10. So, p = 10.
The growth rate is 3% each week, which is the same as 0.03 as a percentage. So, r = 0.03.
Plug these into the equation:
y = 10(1.03)^x will be the equation for this situation
The equation that best represents the depth of the pond each week is y = 10(1.03)× option (D) is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
We have:
A pond increases 3% each week.
The exponential growth is represented by:
y = p(1 + r)×
p = 10 feet
r = 3% = 0.03
y = 10(1 + 0.03)×
y = 10(1.03)×
Thus, the equation that best represents the depth of the pond each week is y = 10(1.03)× option (D) is correct.
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What is the scale factor of triangle ABC to triangle DEF?
Answer:
Second option, scale factor is 2.5
Step-by-step explanation:
We see that ∠B ≅ ∠E and ∠C ≅ ∠F, therefore, ΔABC ~ ΔDEF by the AA Similarity for Triangles Theorem which states that if two pairs of corresponding angles are congruent in two triangles, then those two triangles are similar. To find the scale factor, all we have to do is DF / AC = 5/2 or 2.5.
A triangle has a base of 16 inches and a height of 18 1 8 inches. What is its area?
Answer:
144 in²
Step-by-step explanation:
area of a triangle = 1/2 * base * height
area = 1/2 * 16 * 18
area = 144 in²
A wheel with a radius of 7 inches is rotating at 4 revolutions per second. What is the linear speed v, in feet per second
The linear speed of the wheel is v=175.84 inches inches per second.
The radius of the wheel (r) is 7 inches.
We know the circumference of a circle is given by: [tex]\pi\times2r[/tex]
Therefore the circumference of the wheel is [tex]\pi\times2\times 7[/tex] inches
= [tex]14\pi[/tex] inches
The wheel revolves at 4 revolutions per second.
Hence the wheel will go forward [tex]4\times14\pi[/tex] inches in one second
That is, [tex]56\pi[/tex] inches in one second.
Use the value [tex]\pi = 3.14[/tex]
[tex]56\times 3.14[/tex] inches
175.84 inches
Hence, the linear speed of the wheel is v=175.84 inches inches per second.
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Write the equation of the line that has a slope of -5 that goes through (-4,7)
Answer:
y = -5x + 7
Explanation:
Slope is given -5
7 is the y-intercept.
which model of 85% is shaded
Answer:
You have no examples of models
Step-by-step explanation:
What are the measures of x,y & z?
Answer:
x=33
y=57
z=80
Step-by-step explanation:
For x you take 90-57 because it is a right angle(90 degrees) and that equals 33
For y you say 180-(33+90) because 180 is the net area of a triangle and the answer is 57
For z you say 180-(43+57)
What is the measure of AngleDCF? Three lines extend from point C. The space between line C D and C E is 75 degrees. The space between lines C E and C F is 54 degrees. The measure of AngleDCF is degrees.
Answer:
129 degrees
Step-by-step explanation:
Space from D and E = 75
Space from E and F = 54
Space from D and F = 75 + 54
=> Space from D and F = 129 degrees
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The measure of ∠DCF is 132°.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The diagram for the given explanation can be made as shown below.
Given the measure of ∠DCE and ∠ECF as 78° and 54°, respectively. Therefore, we can write,
∠DCF = ∠DCE + ∠ECF
= 78° + 54°
= 132°
Hence, the measure of ∠DCF is 132°.
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What are the four branches of Mathematics?
Answer:
Algebra.
Geometry.
Trigonometry.
Calculus.
Statistics and Probability
Step-by-step explanation:
that is all the branches.
To find out how many rabbits were in a park students tagged 10 rabbits. They later came back to the park and counted 200 total rabbits and 5 of them were tagged. Using this information, what is the best estimate for the total number of rabbits in the park? Can someone help explain this? Not just answer it but actually explain the reasoning?
Answer:
400
Step-by-step explanation:
The assumption behind mark-recapture methods is that the proportion of marked individuals recaptured in the second sample represents the proportion of marked individuals in the population as a whole. In algebraic terms, This method is called the Lincoln-Peterson Index of population size.
Find the solution (in explicit form) for the following initial value problem: y 0 = xy3 (1 + x 2 ) − 1 2 y(0) = 1.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The solution is [tex]y^2 = \frac{1}{ 3 - 2 (1 + x^2 ) ^{\frac{1}{2} }}[/tex]
Step-by-step explanation:
From the question we are told that
The function is [tex]\left \{ {{y' = xy^3 (1 + x^2)^{-\frac{1}{2} }} \atop {y(0) = 1}} \right.[/tex]
Generally the above equation can be represented as
[tex]\frac{dy}{dx} = xy^3 (1+ x^2)^{- \frac{1}{2} }[/tex]
[tex]=> \frac{dy}{y^3} = \frac{x}{ (1 + x^2)^{\frac{1}{2} }} dx[/tex]
[tex]\int\limits { \frac{dy }{y^3} } \, = \int\limits {\frac{x}{(1 + x^2) ^{\frac{1}{2} }} } \, dx[/tex]
=> [tex]- \frac{1}{2y^2} = (1 + x^2)^{\frac{1}{2} }+ C[/tex]
From the question we are told that at y(0) = 1
[tex]- \frac{ 1}{2 * (1) } = (1 + (0)^2)^{\frac{1}{2} } + C[/tex]
[tex]C = - \frac{3}{2}[/tex]
So
[tex]- \frac{1}{2y^2} = (1 + x^2)^{- \frac{1}{2}} - \frac{3}{2}[/tex]
[tex]\frac{1}{y^2} = 3-2(1 + x^2)^{\frac{1}{2} }[/tex]
[tex]y^2 = \frac{1}{ 3 - 2 (1 + x^2 ) ^{\frac{1}{2} }}[/tex]
If y = 9x − 7, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs? A) {(0, −7), (1, 2), (−1, −16)} B) {(−7, 0), (2, 1), (−16, −1)} C) {(1, 9), (2, 7), (3, 16)} D) {(7, 9), (8, 10), (9, 11)}
Answer:
0,-7 8,567;7,57,6,6,6,6,6,78,3,5
Elizabeth is selling jam at a farmers market, and she earns $5.00 for each jar of jam that she sells. Her goal for the weekend is to earn at least $450.00, and she has already made $95.00 from jam sales as well as $24.00 from leading a demonstration. What is the minimum number of jars Elizabeth must sell at this point to reach her goal?
Answer:
66 jars of jam
Step-by-step explanation:
Elizabeth is selling jam at a farmers market.
She earns $5 for each jar of Jan that she sells
Her goal is to earn $450 during the weekend.
Elizabeth has already made $95 from the sale of her jams and $24 from leading a demonstration
Therefore the total amount that has been made is
= $95 + $24
= $119
Since her target is $450 and she has already made $119 then the amount remaining to complete the target can be calculated as follows
= $450 - $119
= $331
The minimum number of jars that Elizabeth must sell to realize her goal can be calculated as follows
= 331/5
= 66
Hence Elizabeth must sell 66 jars of jam to reach her goal.
Solve each of the following equations. a. 24 = -3 + 3n b. 11 + 4x = x - 10 c. -216 = 1 + 7(1 + 8m) d. 3p - 3(2 - 2p) = 34 + 4p You must show all of your work to receive credit.
Answer:
a. 24 + 3 =3n
27=3n
27/3 =3n/3
9=n
b.4x-x = -10 -11
3x = -21
3x/3 = -21 / 3
x = -7
c. -216 = 1 + 7 + 56m
-216 - 1 - 7 = 56m
- 224 = 56m
- 224 / 56 = 56m / 56
- 4 = m
d. 3p - 6 + 6p = 34 + 4p
3p + 6p - 4p = 34 + 6
5p = 40
5p / 5 = 40 / 5
p = 8
this is the digit that tells you whether to round up or down
When you want to round up or down numbers focus on only two digits,which is the digit in place that you are rounding to and the digit to it's immediate right which tells you whether to round up or down.When the number you are rounding is between 0-4, you round down to the next lowest number. When the number is 5-9,you round the number up to the next highest number.
For example: If you have 25 and you want to round it up then it will be rounded up to 3 because 5 can be rounded up to the next number which is 2 to make it 3.But when you have 23,then you can't round it up which means you will have to round it down to 20 since the 3 behind the 2 can't round up.
I hope this helps......
5:30PM
You run to the store on your way home from school. You want to buy some Doritos. Should you buy
the regular size bag or the party size bag? Calculate the unit price for each size and determine which
one is the better buy.
15 oz. Party Size Doritos $3.98
9.75 oz. Doritos $2.98
The Unit Price is just a Ratio with a denominator of 1. Your textbook has information about ratios on
pgs. 305-307
Answer:
The regular size bag of doritos is a better deal, I believe. Hope this helps!
Step-by-step explanation:
Write the following radical expression using exponents.
1 divided by square root of 3
Answer:
The square root of 3 is 9
A test consists of 20questions. Multiple choice questions earn 4points for a correct answer, and free response questions earn 8points for a correct answer. If the test is out of 100points, how many of each type of question are on the test?
Answer:
15 multiple choice questions
5 free response questions
Step-by-step explanation:
This is basically a systems of equations word problem.
To solve this, we need to create two equations that represent this scenario. Let's suppose [tex]m[/tex] represents the amount of multiple choice questions and [tex]f[/tex] represents the amount of free-choice questions.
We can create the following equations:
[tex]4m + 8f = 100[/tex]
[tex]m+f=20[/tex]
To solve for m and f, we can use elimination.
Let's multiply the equation [tex]m+f=20[/tex] by -4.
[tex]-4m - 4f = -80[/tex]
Great! Now let's add this equation to our first one, [tex]4m + 8f = 100[/tex].
[tex]4m + 8f = 100[/tex]
[tex]-4m - 4f = -80[/tex]
___________________
[tex]0m + 4f = 20[/tex]
[tex]4f=20[/tex]
Dividing both sides by 4 get us [tex]f=5[/tex].
So there are 5 free choice questions. To find m, we can substitute inside the equation [tex]m+f=20[/tex]
[tex]m+5=20\\\\m=20-5\\\\m=15[/tex]
So there are 15 multiple choice questions.
Hope this helped!
Which of the following statements is false? -(-5) = 5 |-5| = -5 -|-5| = -5 -|5| = -5
Your question has been heard loud and clear.
Well -(-5)=5
5/-5/= -5
/-5/5= -5
So basically , the statement is false because -5(-5) not equal to -5/-5/
Thank you
From the given options |-5|=-5 is false. Therefore, option B is the correct answer.
We need to identify the false statement from the given options.
What is an absolute value?The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To find the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value. The absolute value of a positive number is the number itself, that of a negative number is the number without a negative sign, and the absolute value of 0 is 0.
From option (A):
-(-5)=5 is true
From option (B):
|-5|=-5 is false
From option (C):
-|-5| = -5 is true
From option (D):
-|5| = -5 is true
From the given options |-5|=-5 is false. Therefore, option B is the correct answer.
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A football field is shaped like a
rectangle. It has a of 3x and a length
of 6x. Find the area of the field.
Answer:
18x^2
Step-by-step explanation:
You're basically just multiplying them together :)
How long would three 4 foot long pieces of rope be if they were laid end to end?
Which of the following expressions represents the verbal description below?
the product of 5 and the difference of 7 times the square of x and 3
5(7-3x^2)
5-7(x^2-3)
5(7x^2-3)
5-7x^2-3
Answer: C. 5(7x² - 3)
Step-by-step explanation:
Product means multiplication
Difference means subtraction
square means "to the power of 2"
Product of 5 and _______ --> 5(__)
Difference of 7 ... and 3 --> 7... - 3
7 times the square of x ---> 7x²
Put it together to get: 5(7x^2 - 3)
Answer:
D is the correct answer
Step-by-step explanation:
I got it right
What is the value of x?
Answer:
it's not even in the pic
Step-by-step explanation:
the q isn't even there
Eric, Cam, and Brooke are playing mini golf on a computer. The game stores objects in terms of x xx- and y yy-coordinates. The graph below shows the position of each player's ball and the hole marked X Xstart text, X, end text at ( 3 , 2 ) (3,2)left parenthesis, 3, comma, 2, right parenthesis.
Answer:
Its Eric 9.8m
Step-by-step explanation:
Answer:
9.8
Step-by-step explanation:
khan academy
compare the following fraction
4/3 and 5/2
-3/2. -4/5
Answer:
Step-by-step explanation:
to compare them, we need to convert them into like fractions
4/3 and 5/2
lcm of 3 and 2 is 6
4/3 × 2/2 = 8/6
5/2 × 3/3 = 15/6
15/6 is greater than 8/6
so 5/2 is greater than 4/3
similarly,
-3/2 and -4/5
we need to convert them into like fractions
lcm of 2 and 5 is 10
-3/2 × 5/5 = -15/10
-4/5 × 2/2 = -8/10
-8/10 is greater than -15/10
so -4/5 is greater than -3/2
Hope this helps
plz mark as brainliest!!!!
here it the following question
Answer:
1/3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
x^5=-243
so we find the prime factorization of 243
its 3^5 so the answer is -3
-4|2x+5|=-12 solve please
Answer:
x=-4
Step-by-step explanation:
1. Distribute.
|-8x-20|=-12
2. Make it positive.
8x+20 = -12
3. Inverse operations.
8x = -32
4. Divide.
x = -4.
Kenji walks 44 feet in 10 seconds. At this rate, how many miles does Kenji walk in an hour? show your work. (1 mile = 5,280 feet)
Answer:
Kenji walks 3 miles in an hour.
Step-by-step explanation:
1 hour = 3600 seconds
3600/10 = 360
So there are 360 increments of 10 in an hour. Multiply 44 by 360 to find the amount of feet in an hour:
(44)(360) = 15840
Now we have to divide 15,840 by the amount of feet in a mile (5,280):
15840/5280 = 3
So Kenji walks 3 miles in an hour.
Kenji walks 3 miles in one hour.
We know that,
1 hours = 60 minutes = 3600 seconds
Since, Kenji walks 44 feet in 10 seconds
Kenji walks in 1 second,[tex]=\frac{44}{10}=\frac{22}{5}feet[/tex]
Kenji walks in 3600 seconds , [tex]=\frac{22}{5}*3600=15840feet[/tex]
Given that, 1 mile = 5,280 feet
So that, [tex]15840feet=\frac{15840}{5280}=3miles[/tex]
Thus, Kenji walks 3 miles in one hour.
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what is the gcf of 54, 72 and 108
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{18}}}}}[/tex]
Step-by-step explanation:
The GCF of any numbers can be obtained by using two methods. They are :
Prime factorization methodDivision methodNow, I am going to find out the GCF of 54 , 72 and 108 using these both methods :
Let's find out using the prime factorization method
First of all , find the prime factor of each numbers
54 = 2 × 3 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
108 = 2 × 2 × 3 × 3 × 3
Take out the common prime factors of given numbers
Common prime factors = 2 , 3 and 3
Multiply those common prime factors and the number obtained is G.C.F
GCF = Common prime factors
= 2 × 3 × 3
= 18
-----------------------------------------------------------
Now,let's find out using another method i.e division method
Steps for finding G.C.F by using division method:
Step 1 : Divide the larger number by smaller one.
Step 2 : In case of remaining remainder, divide the first division by that remainder.
Step 3 : Again if remainder leaves, divide the second divisor by the remainder.
Step 4 : Repeat the process until the remainder becomes the zero. So , that the last divisor is the G.C.F
( See attached picture )
Hope I helped!
Best regards!!