Need a good explanation. Struggling with derivative basics.

Need A Good Explanation. Struggling With Derivative Basics.

Answers

Answer 1

5 IS THE DERIVATIVE OF k(x)= 5x at x=10

WHAT ARE DERIVATIVES ?

The rate at which a function alters in relation to a variable is known as a derivative in mathematics. Problems involving calculus and differential equations need the use of derivatives.

CALCULATION

f(x)=5x

∴f'(10)=f(10+h)−f(10)h

=5(10+h)−5(10)

= h→0/h

=[tex]\lim_{h\to 0}[/tex]5h/h

=[tex]\lim_{h\to 0}[/tex]5

=5.

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Related Questions

a measurement that can be repeated is said to be and one that is close to the accepted or actual value is

Answers

A measurement that can be repeated is said to be precise and one that is close to the accepted or actual value is approximate.

Given that,
The incomplete statement is given we have to complete the statement.

What is standard measurement?

All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.

Here,

A measurement that can be repeated is said to be precise values
A measurement that is close to the accepted or actual value is approximate.

Thus, the required words are precise and approximate.

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What does pin stand for? a. principal investment number b. permission initiating number c. percent increase number d. personal identification number please select the best answer from the choices provided a b c d

Answers

Answer:

The answer is D.

Step-by-step explanation:

Answer:

in this case the answer is D

Step-by-step explanation:

your welcome

two accountants, lee and johnson, went to a business meeting together. lee drove to the meeting and johnson drove back from the meeting. if lee and johnson each drove 140 kilometers, what was the average speed, in kilometers per hour, at which lee drove? 1) the average speed at which johnson drove was 70 kilometers per hour 2) lee drove for exactly 2 hours

Answers

The average speed of Lee is 70 km/hr.

To clear up this trouble we want to understand the concept of average speed.

average speed is given while we divide the overall distance blanketed with the aid of the total time taken.

right here, it's miles given that Lee and Johnson each drove a hundred and forty Km. additionally, it's miles given that lee drove for two hours.

So, average speed of Lee = [tex]\frac{140}{2}[/tex]

                                         = 70 km/hr

Here, the average speed at which Lee drove the car and went to business meeting is 70 km/hr.

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find the slope of the line that goes through the points (4,-6) and (3,7)

Answers

Answer:

m=-13

Step-by-step explanation:

the formula for getting the slope is[tex] = \frac{y 2- y1}{x2 - x1} \\ = \frac{7 - ( - 6)}{3 - 4} \\ = \frac{7 + 6}{ - 1} \\ = \frac{13}{ - 1} \\ = - 13[/tex]Hope this helps

Question 2 (1 point)
Given the following points, are lines CD and EF parallel, perpendicular, or neithe
A(1,2) B(3,4) C(5,2) D(8,3) E(3,8) F(-6,5)
a
b
C
parallel
perpendicular
neither?

Answers

Given lines CD and EF are parallel. Therefore answer is (a)

How to find slope of  two lines and check whether they are parallel or perpendicular

Given are two points P (x₁, y₁) and Q ( x₂, y₂)

Then slope of the line  PQ is given by  (y₂-y₁)/(x₂-x₁)

If two lines have slopes m₁ and m₂ respectively

Then the lines are parallel when their slopes are equal i.e. m₁=m₂

and  the lines are perpendicular when m₁*m₂= -1

Given C(5,2), D(8,3),E(3,8) F(-6,5)

Then,

Slope of CD = (3-2)/(8-5)= 1/3

Slope of EF = (5-8) / (-6-3)  = 1/3

Slope of CD=Slope of EF

Therefore CD and EF are parallel

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HELP ME PLEASE I need this rn!!!!! SOMEONE ANYONE PLEASEEEEE
question 4
Jeremy is 80 ft from a wall. Each time he moves toward the wall he reduces his distance from the wall by half. Which graph best models the situation?
the four photos are to this question



question 5
Which expressions describe the end behavior of the graph?
the 5 photo is to this one
Select EACH correct answer.

Answers

Using a geometric sequence, we have that:

Graph 1 models the situation.

The end behavior of the graph is given as follows:

As x decreases, y approaches the line y = 2.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, hence the second term is the first multiplied by q, the third is the second multiplied by q, and so on.

For item 4, we have that:

The first term is of 80.The common ratio is of 0.5.Hence when x = 2, y = 40, when x = 3, y = 20, and so on.

This means that the first graph is correct.

What is the end behavior of a function?

The end behavior of a function is given by the limits of the function when x goes to infinity.

Hence, from the final graph, we have that:

As x decreases, y approaches the line y = 2. (lim x -> negative infinity = -2).As x increases, y decreases without bound. (lim x -> infinity = - infinity, not an option but just to explain).

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Which transformation will preserve distance between points when applied to a figure
in the (x, y) -coordinate plane?
A . (x,y) → (x + 2,- 3y)
B . (x,y) → (-x+ 2, y + 7) C . (x,y) → (2x,- 3y)
D. (x,y) → (2x, y)
1 pts. PLEASE HELP FOR TEST

Answers

The transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)

How to determine the transformation will preserve distance between points when applied to a figure in the (x, y) -coordinate plane?

Let the coordinate be represented as

(x, y)

For a transformation to preserve distance between points when applied to a figure in the (x, y)-coordinate plane, the transformation must be any of the following:

ReflectionRotationTranslation

From the list of options, we have

B . (x,y) → (-x+ 2, y + 7)

This transformation is a translation

Hence, the transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)

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Please help and answer the parts A and B

Answers

A> The equation for the line is y = -0.1x + 2600

B> The value of the car is $16,500

From the table, we know that for every 6000 miles added there is a decrease in the value by $600.

A> So it is the function of one order

y = kx + b

25500 = 5000k + b

24800 = 12000k + b

After equating it we get

b = 26000 and k = -0.1

Now put the value of b and k in the equation, and we get

y = -0.1x + 26000

Therefore the equation is y = -0.1 + 26000

B> When we put the value of x = 95000, we get

y = -0.1 × 95000 + 26000

  = 16500

Therefore the cost of the car is $16,500

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Altogether, tom and sarah have 32 baseball cards. if sarah has three times as many baseball cards as tom, how many does each of them have

Answers

tom has 8 cards and sarah has  24 cards .

Explain how many  cards sarah and tom has?

tom and sarah total baseball cards =32

sarah has three times as many baseball cards as tom

The 2 equations are

1. sarah + tom = 32

2. sarah = [tex]3 \times tom[/tex]

substitute equation 2 in 1.

[tex]3\times tom +tom= 32[/tex]

4 tom = 32

tom = 32/4

tom = 8 cards

sarah = [tex]3\times tom[/tex]

         = [tex]3\times 8[/tex]

sarah = 24 cards

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If 4 is subtracted from the numerator of a fraction, its value becomes 1/3. If 5 is added to the denominator of the original fraction its value becomes 1/2. What is the original fraction. ​

Answers

Answer:

79

Step-by-step explanation:

Let the numerator of the original fraction be 'x' and the denominator be 'y'. So, the original fraction becomes xy

According to the question,

Condition I,

If 4 is subtracted from the numerator of a fraction, its value becomes 1/3.

or,x−4y=13

or,3(x−4)=y

or,y=3x−12

Condition II,

If 5 is added to the denominator of the original fraction, the value becomes 1/2.

or,xy+5=12

or,2x=y+5

Put value of y from equation (i) in equation (ii), we get,

or,2x=(3x−12)+5

or,2x=3x−12+5

or,3x−2x−7=0

∴x=7

Put value of x in equation (i), we get,

or,y=3×7−12

or,y=21−12

∴y=9

So, (x,y) = (7,9)

Therefore, the required original fraction is 79.

Evaluate 15 − 6(7 + 5) ÷ 32.

Answers

The answer will be 12.75
Explain the answer
15 − 6(7 + 5) ÷ 32
15- (6 x 12) divide by 32
15-72 divide by 32
15-2.25
12.75
Hope it helps:)

Given , find the average rate of change of f(x)=[tex]f(x)=\frac{1}{x+5}[/tex] on the interval
[1,1+h]. Your answer will be an expression involving h.
Pls halp

Answers

The average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex]  on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]

Given,

The function = [tex]\frac{1}{x+5}[/tex]

We know the average rate of change of the function is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Where a and b are the intervals

a= 1

b=1+h

f(a) =f(1)= [tex]\frac{1}{1+5}[/tex]

=[tex]\frac{1}{6}[/tex]

f(b)= f(1+h)

=[tex]\frac{1}{1+h+5}[/tex]

=[tex]\frac{1}{6+h}[/tex]

f(b)-f(a)= [tex]\frac{1}{6+h}-\frac{1}{6}[/tex]

[tex]=\frac{6-(6+h)}{6(6+h)} \\=\frac{6-6-h}{36+6h}\\ =-\frac{h}{36+6h}[/tex]

Then,

[tex]\frac{f(b)-f(a)}{b-a} =\frac{-\frac{h}{36+6h} }{1+h-1}[/tex]

[tex]=\frac{-\frac{h}{36+6h} }{h} \\=-\frac{1}{36+6h}[/tex]

Hence, the average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex]  on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]

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HELP...........................! !

Answers

Answer:

[tex] \sf \large( \frac{2}{5} ) {}^{14} [/tex]

Step-by-step explanation:

=((2/5)^4(2/5)^3)^2

=((2/5^4+3))^2

=((2/5^7))^2)

=(2/5)^14

what is 9/7 divided by 6

Answers

So the reciprocal of the division will make 6 to be 1/6
So 9/7 * 1/6 = 9/ 7* 6= 9/ 42
In simplest form = 3 / 14
I hope it helped:)

please solve u r the best thx

Answers

Answer:13

Step-by-step explanation:

Answer:

There are no values of f to make this equation true.

Hope this helps.

Step-by-step explanation:

In the second part of the equation, 6( 1/16f  - 3 ), 6 * 1/16f is 3/8f. If both sides subtract a 3/8f and both sides add 18, you get 18.5 = 0 meaning there are no values of f to make this equation true.

help please
just tell the answer get it right for brainliest!​

Answers

Answer:

pretty sure its 2.9

Step-by-step explanation:

Answer:2.92 or just 3

Step-by-step explanation:

btw read your lesson and pay attentiom

PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT

Answers

Let f(x) be the integrand.

[tex]f(-2)=-8 \\ \\ f(0)=0 \\ \\ f(2)=8 \\ \\ f(4)=64 \\ \\ \implies \int^{4}_{-2} x^3 \text{ dx}=\approx \frac{1}{2}(2)[-8+64+2(0+8)] \\ \\ =\boxed{72}[/tex]

can someone please anwser (5z+y)/7 (the number values of z and y are in the picture)

Answers

Answer:

2

Step-by-step explanation:

First substitute the values of z and y in the expression.

Use PEDMAS. We have to multiply 5 and 3, which gives 15. Subtract 1 from 15 and then divide the result by 7.

[tex]\sf \dfrac{5z + y}{7}= \dfrac{5*3 + (-1)}{7}\\\\[/tex]

          [tex]\sf = \dfrac{15 - 1}{7}\\\\ = \dfrac{14}{7}\\\\= 2[/tex]

What is the length of the shorter leg?
____________________________
What is the length of the longer leg?
____________________________

Answers

The shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.

How to get the length of the legs of the triangle?

Here we know that we have a right triangle, and we know that:The hypotenuse measures √130 units.

The perimeter measures 14 + √130 units.

If we define:

x = shorter leg.

y = larger leg.

Then, using the Pythagorean theorem, we can write:x^2 + y^2 = √130^2 = 130

And for the perimeter equation we know that:

perimeter = x + y + √130 = 14 + √130

We can simplify this equation to:x + y = 14Then we have the system of equations:

x^2 + y^2 = 130

x + y = 14

Isolating one variable in the second equation we get.

x = 14 - y

Replacing that in the other equation we get:

(14 - y)^2 + y^2 = 130

Now we can solve this for y.

196 - 28y + y^2 + y^2 = 130

2y^2 - 28y + 196 - 130 = 0

2y^2 - 28y + 66 = 0

y^2 - 14y + 33 = 0

Using Bhaskara's formula we can get:

y = (14 ± √( 14^2 - 4*1*33))/2*1y = (14 ± 8)/2

Now, remember that y is the larger leg of the triangle, then:y = (14 + 8)/2 = 11For the value of x we use:

x = 14 - y = 14 - 11 = 3x = 3the shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.

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jonathon wanted to know how far people could swim in 30 minutes. he collected data from 10 people about how many miles they could swim in 30 minutes and obtained the following results: 0.25 0.80 0.75 0.93 0.24 0.50 0.75 0.98 0.35 0.85 what is the range of the data jonathon collected?

Answers

The range of the data collected by Jonathon is [0.25,0.98]

Given that Jonathon wanted to know how far people could swim in 30 minutes. he collected data from 10 people about how many miles they could swim in 30 minutes and obtained the following results: 0.25 0.80 0.75 0.93 0.24 0.50 0.75 0.98 0.35 0.85 and asked to find the range of the data collected by Jonathon.

The minimum value of the data collected by Jonathon is 0.25 and the maximum value of the data collected by Jonathon is 0.98

The range of the given data:(minimum value,maximum value)

Here, The minimum value of the data collected by Jonathon is 0.25

The maximum value of the data collected by Jonathon is 0.98

Therefore,The range of the data collected by Jonathon is [0.25,0.98]

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I cant find my answer please help!

Answers

Answer:

Domain: 1 ≤ x ≤ 6

Range 10 ≤ M(x) ≤ 60

Step-by-step explanation:

M(x) = 10x where x represents the number of tickets bought

Assume nobody goes with Victoria. In that case she will go alone, only 1 ticket is bought and total cost = $10

Maximum 5 friends means total of 6 tickets purchased so total cost is $60

Domain refers to the possible input values ie possible x values. Here the domain is 1 ≤ x ≤ 6 also written as [1, 6]

The range is the total possible set of output values. Here output of the function is cost and cost ranges between 10 and 60 inclusive

So Range = 10 ≤ M(x) ≤60 also written as [10, 60]

The length of a rectangle is 4 inches more than 3 times its width. The perimeter of the rectangle is 48 inches. What are the length and width of the rectangle?​

Answers

The length and width of the rectangle is found as 19 inches and 5 inches respectively.

What is defined as the perimeter of rectangle?To calculate the perimeter, or distance all around rectangle, add all four side lengths. This can be done quickly by adding the width and height and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter = 2(length + width).

Now, as per the given question;

Let width of a rectangle = w inches

Then, length of a rectangle = 3w + 4

Perimeter of a rectangle = 2(length + width)

Substitute the values in the formula of perimeter.

48 = 2(3w + 4 + w)

48/2 = 4w + 4

24 = 4w + 4

20 = 4w

w = 5

Thus, the width of the rectangle is 5 inches.

Put w = 5 inches in its length.

l = 3w + 4

l = 3×5 + 4

l = 15 + 4

l = 19 inches.

Therefore, the length of rectangle is found as 19 inches.

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Ashley is constructing CD such that CD intersects AB at C and is the segment bisector of AB. Select the relationship that must be true.

A) Point C is equidistant from A and B.

B) Point D is equidistant from A and B.

C) Point A is equidistant from C and D.

D) Point B is equidistant from C and D

Answers

Answer:

Step-by-step explanation:

a,d

Answer:ad

Step-by-step explanation:

ad

What is the value of the expression below when w=7?
w² +3w - 10

Answers

Answer:

The value of the expression is 60.

Answer is 60

Step by step

Substitute 7 in place of variable “w” in the expression

7^2 + (3)(7) - 10

49 + 21 - 10

Answer is 60

can someone help me really quick

Answers

Shawn earn 11 per hour.

Hannah travel 25 miles in one gallon of gas.

What is graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

given:

According to the graph the y- axis shows the earnings.

So, we have the coordinates are

(1, 11), (2, 22) and (3, 33)

So, Shawn earn = 22 - 11 / 2 -1 = 11 per hour.

Now, in second case

The coordinates are

(3, 75), (5, 125), (6, 150), (10, 250)

So, m= (125 - 75) / (5-3)

m= 50/2

m=25

So, Hannah travel 25 miles in one gallon of gas.

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a password system uses four digits from 0 to 9. how many different four-digit passwords with no digit repeated are possible?

Answers

Total 5040 passwords can be generated when no digits are repeated

Permutation in mathematics is an arrangement of objects in an definite order. The elements or sets or things are arranged in sequential order or linear order.

• Permutation is classified into four types :

1) where repetition is not allowed

2) where repetition is allowed

3) objects that are non distinct  

4) circular permutation

• The formula for calculating permutation is n!/(n-r)!

As we are given that the password uses four digits from 0-9 and repetition is not allowed.

So, n = 10 and r = 4

Using the formula for permutation we get

= 10! / (10-4)!

= 10!/6!

= 10 * 9 * 8 * 7 * 6! / 6!

= 10 * 9 * 8 * 7

= 5040

Therefore, 5040 four digit passwords are possible when no digit is repeated.

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the perimeters of two squares are in the ratio 2 : 7. What is the ratio of the area of the smaller square to the area of the larger square

Answers

The ratio of the area of the smaller square to the area of the larger square = 4 : 49

Finding the area of a square from the perimeter

Let the perimeter of the small square be [tex]P_1[/tex]

Lethe the perimeter of the large square be [tex]P_2[/tex]

Perimeter of a square = 4 Length

[tex]P_1=4L_1\\\\P_2=4L_2[/tex]

The ratio of the perimeters = 2:7

[tex]\frac{4L_1}{4L_2} =\frac{2}{7} \\\\\frac{L_1}{L_2} =\frac{2}{7}[/tex]

The area of a square = L^2

[tex](\frac{L_1}{L_2} )^2=(\frac{2}{7} )^2\\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{2^2}{7^2} \\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{4}{49}[/tex]

Therefore, the ratio of the area of the smaller square to the area of the larger square = 4 : 49

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how many quarts of pure antifreeze must be added to 3 quarts of a ​40% antifreeze solution to obtain a 60​% antifreeze​ solution?

Answers

1.5 quarts of pure antifreeze must be added to 3 quarts of a ​40% antifreeze solution to obtain a 60​% antifreeze​ solution

Given;

Percentage of 3 quarts of antifreeze solution = 40%

We have to find,

Quarts to obtain the antifreeze solution of 60%

Now,

The 3 quarts of 40% antifreeze solution contains 0.4 x 3 = 1.2 quarts of pure antifreeze solute

Let,

x is the number of quarts of pure antifreeze needed to make a 60% solution

The equation to solve becomes, where x is the amount of pure antifreeze to be added is

(1.2 + x )/(3 + x) =0.6

(1.2 + x ) = 0.6 * (3 + x)

(1.2 + x ) = 1.8 + 0.6x

x-0.6x = 1.8 - 1.2

0.4x = 0.6

x = 1.5

Therefore,

1.5 quarts of pure antifreeze to the current solution to make a 60% solution

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Simplify fully

4x^+ 4x/-2x^-2

Answers

Answer: -12x

Step-by-step explanation: 4x +4 −2 −2x

Calculate x to the power of 1 and get x.

4x+4×( −2 −2x )

Calculate 2 to the power of −2 and get  41.

4x+4×( − 41x)

Divide x by − 41

​by multiplying x by the reciprocal of − 41 .

4x+4×( −1x×4)

Anything divided by -1 gives its opposite.

4x+4(−x×4)

Multiply 4 and −1 to get −4.

4x−4x×4

Multiply −4 and 4 to get −16.

4x−16x

Combine 4x and −16x to get −12x.

−12x

Eva’s phone is 4 times the number of songs on Hank’s phone.
• The total number of songs on both phones is 600 songs.

How many songs (N) are on Hank’s phone?

Answers

Answer:

120 songs

Step-by-step explanation:

         Eva=4u

       Hank=1u

Eva+Hank=5u

            5u=600

             1u=600/5

                 =120

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