The value of the derivatives is A'(12) = 24.
We have,
To find the derivative of the area function A(x) with respect to x, we can differentiate the equation for the area of a square:
A(x) = x^2
Using the power rule, we differentiate A(x) with respect to x:
A'(x) = 2x
To find A'(12), we substitute x = 12 into the derivative equation:
A'(12) = 2 * 12 = 24
Therefore,
The value of the derivatives is A'(12) = 24.
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Final answer:
To find A'(12), the rate at which the area A(x) changes when the side length x changes, take the derivative of A(x), which is 2x, and evaluate it at x = 12. The derivative of A(x) is 2x, so A'(12) = 2(12) = 24.
Explanation:
To find the rate at which the area A(x) changes with respect to a change in x, we need to take the derivative of A(x) with respect to x. In this case, A(x) represents the area of a square wafer of silicon with a side length x. The derivative with respect to x is A'(x), which represents the rate of change of the area.
We want to find A'(12), which means we want to find the rate of change of the area when the side length is 12 mm. To do this, we need to take the derivative of A(x) and then evaluate it at x = 12.
Since the side length of the wafer is very close to 12 mm, we can assume x = 12.
Let's find the derivative of A(x):
A(x) = x^2
A'(x) = 2x
Now we can evaluate A'(12):
A'(12) = 2(12) = 24
Use the dustributive property to express 16+48?
What is the value of x?
A.10
B.12
C.1
D.4
A clothing store is running a special in which customers receive a free pair of jeans with the purchase of 4 shirts. It costs the clothing company $3.46 to produce one shirt and $5.56 to produce one pair of jeans. The store is selling each shirt for $21.46. Approximately how much money will the company make if 42 customers take advantage of the special?
The clothing company will make approximately $214.60 if 42 customers take advantage of the special.
Explanation:To calculate the amount of money the company will make, we need to determine the total cost of shirts and jeans given out for free.
Each customer will receive a free pair of jeans for every 4 shirts purchased.
The cost of 1 shirt is $3.46 and the cost of 1 pair of jeans is $5.56.
So, the cost of 4 shirts is 4 x $3.46 = $13.84.
Therefore, for each set of 4 shirts, the company is losing $13.84 on production costs and gaining $21.46 on sales.
For 42 customers, the company will distribute 10 sets of 4 shirts and give away 10 pairs of jeans.
The total amount of money the company will make is (10 x $21.46) = $214.60.
I need help please and fast what is 3 1⁄8 − 1 7⁄8 =
help in algrebra, unsure how to do this kinda question and desperately need help.
1. The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
(b) Define your variables.
Answer:
a). Linear equation; y=1.25 x+12.5
b). The variable are x and y, where;
y is the total cost at the county fair
x is the number of tickets per ride
Step-by-step explanation:
Step 1: Define variable in the linear equation
y=mx+c
where;
y=The total cost at the county fair
x=the number of tickets per ride
m=Cost per ticket ride
c= fair admission price
Step 2: Derive linear equation
In or case;
y=$43.75
m=$1.25 per ticket ride
x=25 tickets
c=unknown
replacing;
43.75=(1.25×25)+c
c=43.75-31.25
c=12.5
The fair admission price=c=12.5
Replacing in the Linear equation;
y=1.25 x+12.5
Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:
Octagon ABCDEFGH with ordered pairs at A at 3, 1, at B 3, negative 1, C 1, negative 3, D negative 1, negative 3, E negative 3, negative 1, F negative 3, 1, G negative 1, 3, H 1, 3. Octagon A prime B prime C prime D prime E prime F prime G prime H prime with ordered pairs A prime 6, 2, at B prime 6, negative 2, at C prime 2, negative 6, at D prime negative 2, negative 6, at E prime negative 6, negative 2, at F prime negative 6, 2, at G prime negative 2, 6, at H prime 2, 6
If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated?
one half
2
4
one quarter
octagon ABCDEFGH was dilated by a scale factor of 2. Therefore, option 2 is the correct answer.
To find the scale factor by which octagon ABCDEFGH was dilated, we can compare the corresponding side lengths of the original octagon and the dilated octagon.
Let's take one side, for example, side AB. The length of side AB in the original octagon is the distance between points A(3, 1) and B(3, -1), which is 2 units.
The length of side A'B' in the dilated octagon is the distance between points A'(6, 2) and B'(6, -2), which is also 4 units.
By comparing the side lengths, we can see that side A'B' is twice as long as side AB.
Therefore, the scale factor by which octagon ABCDEFGH was dilated is 2.
In conclusion, octagon ABCDEFGH was dilated by a scale factor of 2.
Therefore, option 2 is the correct answer.
The octagon ABCDEFGH was dilated by a scale factor of 2. This means each coordinate in the original octagon was multiplied by 2 to obtain the corresponding point in A'B'C'D'E'F'G'H'.
The scale factor of dilation between octagon ABCDEFGH and its dilated counterpart A'B'C'D'E'F'G'H' can be determined by comparing corresponding side lengths. Taking one side as an example, the original octagon has a side connecting points A(3, 1) and B(3, -1) with a length of 2 units (vertical distance). In the dilated octagon, the corresponding side connecting A'(6, 2) and B'(6, -2) has a length of 4 units (vertical distance). The scale factor (k) is then calculated as the ratio of the length in the dilated octagon to the length in the original octagon: [tex]\( k = \frac{4}{2} = 2 \)[/tex].
Therefore, octagon ABCDEFGH was dilated by a scale factor of 2 from its original position to A'B'C'D'E'F'G'H'. This indicates that the coordinates of each point in the original octagon were multiplied by 2 to obtain the corresponding points in the dilated octagon. The scale factor, in this case, is 2, signifying a doubling in size during the dilation process.
What is mMHJ? Plz answer fast I have a time limit
Answer:
a) 35°
Step-by-step explanation:
Vertical angles are the opposite angles that form when two lines intersect.
The vertical angles are equal.
1. As vertical angles are equal first take the values of the two angles and put them in an equality as follows:
[tex]2x-20=x+15[/tex]
2. Then, solve for x:
[tex]2x-x=15+20[/tex]
[tex]x=35[/tex]°
Therefore the angle MHJ is 35°
What is the quotient? 2m+4/8÷m+2/6
Answer:
3/2 (D on Edge)
I️ need heLp evaluation
A local gym charges nonmembers $10 per hour to use the tennis courts. Members pay a yearly fee of $300 and $4 per hour for using the tennis courts. Write and solve an equation to find how many hours you must use the tennis courts to justify becoming a member.
Answer:
75 Hours
Step-by-step explanation:
75h x $4 = $300
You would need 75 hours to justify the $300 fee
Factor the expression. 3r2 – 75
(3r –5)(r + 5)
(3r +5)(r – 5)
3(r – 5)(r + 5)
3(r – 5)(r – 5)
factor 3r^2-75
you would move the 3 to the outside of the parenthesis
then you have 5*5 = 25 and multiply that by the 3 to get the 75
3(r-5)(r+5)
Answer:
What he said.
Step-by-step explanation:
5.4 = a - (-1.8) solve for a.
Simplify 7(n - p) + 5p.
-7n - 12p
7n - 12p
7n - 2p
Answer:
7n - 2p
Step-by-step explanation:
Fill in the missing reason in the proof
a.definition of straight angles
b.alternate interior angles are congruent
c.supplementary angles sum up to 180°
d.complementary angles sum up to 180°
Answer:
The Answer is A
Step-by-step explanation:
I took the test in usa test prep.
_________ is the ratio of the vertical change to the horizontal change between any two points on a line.
You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y=2x+4y=2x+4. There is a tree in your yard at the point (−4, 11)(−4, 11). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the tree from the zip line? Round your answer to the nearest tenth.
Solving this problem actually requires us the use of the distance formula of point to a line.
The formula is:
distance = | a x + b y + c | / sqrt (a^2 + b^2)
So we are given the equation:
y = 2 x + 4
rewriting:
y – 2 x – 4 = 0 --> a = -2, b = 1, c = -4
We are also given the points:
(-4, 11) = (x, y)
Using the distance formula at points (x, y):
distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 + (1)^2]
distance = 15 / sqrt (5)
distance = 6.7
So the tree is about 6.7 ft away from the zip line.
The question is an illustration of distance between a point and a line.
The distance between the zip line and the tree is 6.70 feet
The zip line equation is given as:
[tex]\mathbf{y = 2x +4}[/tex]
The coordinates of the tree is given as:
[tex]\mathbf{(x,y) = (-4,11)}[/tex]
The distance (d) between an equation and a point is:
[tex]\mathbf{d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}}[/tex]
Where:
[tex]\mathbf{ax +by + c = 0}[/tex]
Rewrite [tex]\mathbf{y = 2x +4}[/tex] as [tex]\mathbf{ax +by + c = 0}[/tex]
[tex]\mathbf{2x - y + 4 = 0}[/tex]
By comparison:
[tex]\mathbf{a =2, b = -1, c = 4}[/tex] and [tex]\mathbf{(x,y) = (-4,11)}[/tex]
So, we have:
[tex]\mathbf{d = \frac{|2 \times -4 -1 \times 11 + 4|}{\sqrt{(2)^2 + (-1)^2}}}[/tex]
[tex]\mathbf{d = \frac{|-15|}{\sqrt{5}}}[/tex]
Evaluate square root
[tex]\mathbf{d = \frac{|-15|}{2.24}}[/tex]
Remove absolute bracket
[tex]\mathbf{d = \frac{15}{2.24}}[/tex]
[tex]\mathbf{d = 6.70}[/tex]
Hence, the distance between the zip line and the tree is approximately 6.70 feet
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Eric and six friends spent a day at the musement park at the end they decided to pair up for roller coaster rides so that each friend would ride with each others exactly once how much rides would be taken
A golfer takes a swing from a hill twenty feet above the cup with an initial upwards velocity of 32 feet per second. How long does it take the ball to land on the ground near the cup?
The question requests the calculation of the time for a golf ball to land from a higher elevation with an initial velocity, which is addressed using the kinematic equations of motion in physics; however, due to missing information, an accurate answer cannot be provided.
Explanation:Projectile Motion of a Golf Ball
The question involves calculating the time it takes for a golf ball to land on the ground when hit from an elevated position with an initial upwards velocity. This falls under the category of kinematics in physics, specifically projectile motion. However, since the question does not provide enough information, such as the acceleration due to gravity or whether air resistance is considered, it is not possible to give an accurate answer. Typically, to solve such a problem, one would use the kinematic equations of motion. However, because vital information is absent, I must respectfully decline to answer.
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A projectile is thrown upward so that its distance above the ground after t seconds is h = - 16t2+ 440t. After how many seconds does it reach its maximum height?
PLEASE HELP!!
To the nearest square unit, what is the area of the regular heptagon shown below?
A. 2772 square units
B. 1572 square units
C. 792 square units
D. 5545 square units
Answer:
1572 Square Units
Step-by-step explanation:
First, find the perimeter by multiplying 20.8 * 7 which is 145.6. Then multiply the perimeter with the apothem. After that, you divide by 2.
So, 145.6*21.6/2= 1572.
Through a given point p on a plane how many lines can be drawn that are perpendicular to that plane
What is the perimeter of trapezoid JKLM?
+ units
2 + + units
9 + units
9 + + units
answer is D
Perimeter is the sum of the length of the sides used to make the given figure. The correct option is D.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
The length of the different sides of the trapezoid can be written as,
JK = 3 units
KL = √(2² + 1²) = √5 units
LM = 6 units
JM = √(1² + 1²) = √2 units
Now, the perimeter of the trapezoid JKLM is,
Perimeter JKLM = 3 + √5 + 6 + √2 = (9 + √5 + √2) units
Hence, the perimeter of the trapezoid JKLM is (9 + √5 + √2) units.
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A plot of land is about 13,000 ft by 8000 ft. Approximately how many square miles is this? Round to the nearest whole number.
Answer:
4 square miles
Step-by-step explanation:
A plot of land is about 13,000 ft by 8000 ft.
1 mile = 5280 ft
To convert feet to miles we divide by 5280
13000 ft = [tex]\frac{13000}{5280}=2.4621[/tex]
8000 ft = [tex]\frac{8000}{5280}=1.5152[/tex]
Now we find the area
To find area we multiply the miles
2.4621* 1.5152= 3.73057392
When we round to nearest whole number it becomes
4 square miles
Given segment aed and bfc, ae=bf and ed=fc prove ad=bc
What is 4???
An orthocenter is the intersection of three
An orthocenter is the intersection of three:
Altitudes in a triangle.
Step-by-step explanation:Altitude--
An altitude is a line segment that originates from a vertex and is perpendicular to the line segment opposite to that vertex.
Orthocenter--
An orthocenter of a triangle is a point where the three altitudes of a triangle meet or intersect.
In a right angled triangle the orthocenter is the vertex of the triangle where the right angle is formed.
The correct answer is not provided in the given options.
Explanation:The volume of a cylinder can be calculated using the formula V = πr^2h, where π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.
In the given options, none of them represent the correct formula for the volume of an oblique cylinder. Therefore, the correct answer is not provided in the given options.
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I don't know what the symbol means or what to do.
Answer:
Step-by-step explanation:
That weird symbol means "element". In our case, the elements of the domain (the x-values) are -15, -6, -1. Which tells us that we are going to sub each one of the numbers into the equation and solve it for the corresponding y value. That in turn gives us the coordinate point. The equation is
x + y = 6
Subbing in first -15 for x:
-15 + y = 6 and
y = 6 + 15 so
y = 21 and the coordinate point is (-15, 21).
Subbing in -6 for x:
-6 + y = 6 and
y = 6 + 6 so
y = 12 and the coordinate point is (-6, 12).
Subbing in -1 for x:
-1 + y = 6 and
y = 6 + 1 so
y = 7 and the coordinate point is (-1, 7)
The second choice is the one you want.
Just remember that x is the domain and any elements in the domain go in for x.
Also remember that y is the range and any elements in the range go in for y
If your brother is 12 years old and you are 10 years old. How old will you have to be to be half your brother's age?
Answer:
6
Step-by-step explanation:
help quick
Divide and give the answer in scientific notation.
8.4 x 10^7
________
3 x 10^3
A) 5.4 x 10-4
B) 5.4 x 1021
C) 2.8 x 10-4
D) 2.8 x 104
Put the numbers in order from smallest to largest.
3.6
4.9
4.2
3.1
5.0
4.5