Differentiation from First Principles is a formal method for determining a tangent's gradient.
What is meant by differentiation?
Finding a function's derivative is the process of differentiation. It is also the process of determining how quickly a function changes in relation to its variables.
According to the Sum rule, a sum of functions' derivatives equals the sum of those functions' derivatives. The derivative of two different functions is the difference of their derivatives, according to the Difference rule.
Differentiation from First Principles is a formal method for determining a tangent's gradient. The straight line connecting any two locations on the curve that are fairly near to one another will have a gradient that is similar to that of the tangent at those places.
s(t) = ∫vdt = ∫sin(πt)dt = (-cos(πt))/π + c
substituting the values t = 3, we get
s(-3) = (-cos(-3π))/π + c = 0
simplifying the above equation, we get
(-cos(3π))/π + c = 0
1/π + c = c
c = -1/π
Therefore, the correct answer is s(t) = (-cos(πt))/π - 1/π = (-cos(πt) - 1)/π.
The complete question is:
Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0
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Suppose the demand curve for pencils is QD = 200 - 4P. What is the exact own price elasticity of demand at P-$30?A. -0.67B. -10.67C. -0.09D. -1.5
The exact own price elasticity of demand is (A) -0.67.
The own price elasticity of demand measures the responsiveness of the quantity demanded to changes in price. It can be calculated using the formula:
epsilon = (dQ/dP) * (P/Q)
where dQ/dP is the derivative of the demand curve with respect to price and P/Q is the price elasticity of demand.
In this case, the demand curve is QD = 200 - 4P, so dQ/dP = -4. When P=$30, Q = 200 - 4 * 30 = 140. So,
epsilon = (-4) * (30/140) = -0.67
Hence, the exact own price elasticity of demand at P=$30 is -0.67, so the answer is A. -0.67.
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if 0≤b≤2, for what value of b is ∫b0cos(ex)dx a minimum?
The value of b for which ∫b0cos(ex)dx is minimum is π/2e..
To find the value of b for which the definite integral ∫b0cos(ex)dx is a minimum, we can find the critical points (i.e. local extrema) of the integrand cos(ex) in the interval [0, 2].
Since cos(ex) is a periodic function with period 2π/e, it suffices to consider the interval [0, 2π/e]. In this interval, cos(ex) has its maximum value of 1 at x = 0, and its minimum value of -1 at x = π/2e and x = 3π/2e.
Since e is positive, the function cos(ex) is increasing on the interval [0, π/2e) and decreasing on the interval (π/2e, π/e].
Therefore, if b is in the interval [0, π/2e), the integral is minimized when b = 0. If b is in the interval [π/2e, π/e], the integral is minimized when b = π/2e.
Since the maximum value of b is 2, and 2 < π/e, it follows that the integral ∫b0cos(ex)dx is minimized when b = π/2e.
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distinct vertices of an octagon are chosen at random. what is the probability that they are adjacent?
If distinct vertices of an octagon are chosen at random , then the probability that they are adjacent is 2/7 .
An Octagon has 8 vertices, so there are 8 possible vertices to choose from. To find the probability that two chosen vertices are adjacent, we need to determine the number of ways in which two adjacent vertices can be chosen,
Since there are 8 vertices and each vertex has 2 adjacent vertices,
The total number of pairs of vertices in octagon is = ⁸C₂ = 28;
the possible Adjacent pairs are : {(1,8),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8)} ;
So , probability of vertices being adjacent is = 8/28 ;
Simplifying further , we get ;
Probability ⇒ 2/7 .
Therefore , the probability that vertices are adjacent is 2/7 .
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A drone is flying at the altitude of 16 1/4 feet above sea level a groundhog is directly below the drone at an altitude of 7 3/8 feet below sea level what is the distance between the drone and the groundhog
one is above sea level the other below sea level, so their distance is just their sum from sea level, so hmmm let's convert the mixed fractions to improper fractions and then sum them up.
[tex]\stackrel{mixed}{16\frac{1}{4}}\implies \cfrac{16\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{65}{4}} ~\hfill \stackrel{mixed}{7\frac{3}{8}} \implies \cfrac{7\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{59}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{65}{4}+\cfrac{59}{8}\implies \cfrac{(2)65~~ + ~~(1)59}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{130+59}{8}\implies \cfrac{189}{8}\implies 23\frac{5}{8}[/tex]
coins are tossed. a. give an example of a simple event. b. give an example of a joint event. c. what is the complement of getting on the coin? d. what does the sample space consist of?
Coin tossing has a simple event of heads or tails, a joint event of multiple coin combinations, the complement of heads is tails, and sample space is {heads, tails}.
a. A simple event in coin tossing is getting either heads or tails on a single coin flip.
b. A joint event in coin tossing is getting heads on one coin and tails on another coin, for example.
c. The complement of getting heads on a coin flip is getting tails. The complement of getting tails is getting heads.
d. The sample space in coin tossing consists of all the possible outcomes of a single coin flip. This can be represented as a set, such as {heads, tails}. The sample space is the set of all possible outcomes of the experiment.
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There are 136 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 38 fans?
The ratio of the ide length of Square A to the ide length of Square B i 4:9. The ide length of Square A i 12 yard. What i the area of Square B ?
Area of square B is 729.
Now, According to the question:
A square is a two-dimensional figure with four sides. It is also known as a quadrilateral. The area of a square is defined as the total number of unit squares in the shape of a square. In other words, it is defined as the space occupied by the square.
"Information available from the question"
We have been given that the ratio of the side length of square a to the side length of square b is 4:9. The side length of square a is 12 yards.
First of all, we will find the side length of square b using proportions as:
[tex]\frac{a}{b} = \frac{4}{9}[/tex]
[tex]\frac{12}{b}=\frac{4}{9}[/tex]
Cross multiplying the equation:
4b = 108
b = 108/4
b = 27
We know that area of a square is [tex]side^2[/tex]
=> b = 27
Area of square = [tex]27^2[/tex]
Area of square = 729
Hence, Area of square B is 729.
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Write the equation for the linear function shown in the table
Answer:
y = 6x
Step-by-step explanation:
Each value of x is multiplied by 6 to get the corresponding y value
The price for gasoline is represented by the equation y = 2.72x, where y r represents the total price for x gallons of gasoline The graph goes through (5.44,2) and (8.16,3)
The graph goes through (5.44,2) and (8.16,3) is false.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given that price for gasoline is represented by the equation y = 2.72x,
where y r represents the total price for x gallons of gasoline
We have to check whether the line passes through (5.44,2) and (8.16,3)
From the equation the slope is 2.72.
Now let us check whether the two points gives the same slope.
m=3-2/8.16-5.44
=1/2.72
=0.36
Hence, the graph goes through (5.44,2) and (8.16,3) is false.
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Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.
y = 5 (2 Superscript x Baseline)
a.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 1) and approaches x = 1 in quadrant 1.
y-intercept = 1
c.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 2) and approaches x = 1 in quadrant 1.
y-intercept = 1
b.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 1) and (2, 4) in quadrant 1.
y-intercept = 2
d.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 5) through quadrant 1.
Answer: The equation y = 5 * 2^x represents an exponential function where the base is 2 and the y-intercept is 5.
The graph that best fits this equation is:
d. On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 5) through quadrant 1.
y-intercept = 5
So, the correct answer is d.
Step-by-step explanation:
a function satisfies the differential equation (a) what are the constant solutions of this equation? separate your answers by commas.
The solutions are decreasing when y is in the set (1,3).
(A) Equilibrium solutions, also known as constant solutions, fulfill dy/dx=0.
When the right-hand side of the equation is taken into account, we have
dy/dx equals y2(y-1) (y-3). We get the constant solutions y=0, y=1, and y=3 by setting the right side to zero.
(b) Solutions rise when dy/dx exceeds 0. For the set of y values (-,0) (0,1) (3,) see that dy/dx > 0. Therefore, when y in is the set (-,0) (0,1) (3,), solutions are growing.
(c) When dy/dx 0, solutions are decreasing, and dy/dx 0 when 1 y 3. That is, while y is in the set, solutions are decreasing (1,3).
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Increase R245 in the ratio 5:6.
Answer:
To increase R245 in the ratio 5:6, you can add an amount proportional to the ratio 5:6 to R245.
Let's say you want to increase R245 by x.
The new value for 5 parts will be 5x + 245, and the new value for 6 parts will be 6x + 245.
So, the new ratio would be (5x + 245) : (6x + 245), which is still 5:6.
Therefore, to increase R245 in the ratio 5:6, you would add x to R245.
The table shows the parts of powder and water used to make gelatin.
Boxes of Gelatin Powder (oz) Water (cups)
3 9 6
8
At this rate, how much powder and water will Jeff use to make 8 boxes of gelatin?
To make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given table, we have
Boxes Gelatin Powder (oz) Water (cups)
3 9 6
Here,
Gelatin Powder = 3 × Boxes
Water = 2 × Boxes
The equations for 8 boxes is
Gelatin Powder = 3 × 8
= 24 oz
Water = 2 × 8
= 16 cups
Hence, to make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.
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0.800 in fraction form
Answer:8/
Step-by-step explanation: It is because any number after decimal point contains zero at it's end then the number is considered as it is. For example here 0.800 so after decimal point is 8, and after 8 there are zero's. So numerically, it is 0.8 or 0.800 both are same . Hence it's fraction form would be 8/ 10.
Answer:
4/5
Step-by-step explanation:
0.800 = 800/1000 = 8/10 = 4/5
Let U and V be nxn orthogonal matrices. Explain why UV is an orthogonal matrix. [That is, explain why UV is invertible and its inverse is (UV)"]
Why is UV invertible?
A. Since U and V are nxn matrices, each is invertible by the definition of invertible matrices. The product of two invertible matrices is also invertible.
B. UV Is Invertible because it is an orthogonal matrix, and all orthogonal matrices are invertible.
C. Since U and V are orthogonal, each is invertible by the definition of orthogonal matrices. The product of two invertible matrices is also invertible.
D. UV is invertible because the product of any two matrices is always invertible
For the orthogonal matrices, the product of two invertible matrices is also invertible.
Orthogonal matrices are matrices that have a special property: the dot product of each of their rows or columns is equal to 0.
The dot product of two vectors is equal to 0 when the vectors are orthogonal to each other, meaning they are perpendicular.
Since U and V are orthogonal matrices, each is invertible by the definition of orthogonal matrices.
The inverse of an orthogonal matrix is its transpose.
This is because the dot product of each row (or column) with itself is equal to 1, so the transpose of an orthogonal matrix is its inverse.
The product of two invertible matrices is also invertible, so UV is invertible.
Answer C is correct.
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5x - 6 = 44. what is x
Answer:
[tex]5x - 6 = 44 \\ \longrightarrow \: 5x = 44 + 6 \\ \longrightarrow \: 5x = 50 \\ dividing \: both \: sides \: by \: 5 \: \\ \\ \longrightarrow \: \cancel\frac{5x}{5} = \cancel\frac{50}{5} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]
hope helpful! :)
Answer:
x = 10
Step-by-step explanation:
5x - 6 = 44. what is x
5x - 6 = 44
add 6 on both sides5x = 50
divide each side by 5x = 10
---------------------
check
5 x 10 - 6 = 44 (remember pemdas)
44 = 44
the answer is good
Write 8 3/4 as an improper fraction
Answer: 35/4
Step-by-step explanation:
8x4=32
32+3=35
in town A , the population increased from 2000 to 2400 in 2 years. In town B, the population increased from 1800 to 2300 during the same time period. In which town is the percentage increase in population greater?
Answer: Town B
Step-by-step explanation:
Town A -
2400 - 2000 = 400
percentage increase = 400/2000x100
= 20 %
Town B -
2300 - 1800 = 500
percentage increase = 500/1800x100
= 27. 78 %
2. În triunghiul ABC, AB=3√7 cm, BC = sqrt(17) cm şi AC= 4√5 cm. Verificați dacă triunghiul este dreptunghic cu catetele AB şi BC.
Answer: it’s b
Step-by-step explanation:
your welcome
Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires
attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two
wires cross.
Answer:
You provided plenty of background information, but please provide a question to be answered.
draw a triangle in which angleXYZ=30degree, angleYZX=75degree and side YZ=8.5cm
Answer:
see attached
Step-by-step explanation:
You want to draw a triangle with angle measures 30° and 75° at vertices Y and Z, and the length of YZ as 8.5 cm.
Third angleThe third angle of the triangle will be 180° -30° -75° = 75°. This means the triangle is isosceles, and the two congruent sides are both 8.5 cm.
ProtractorOnce you measure the length YZ as 8.5 cm, you can draw angles at 30° and 75° from points Y and Z, respectively. A protractor is a suitable tool for the purpose. The point of intersection of these rays is X, giving you the desired triangle XYZ.
ConstructionA right triangle with hypotenuse 8.5 cm will have the leg opposite the 30° angle as 4.25 cm, half the hypotenuse. This offers opportunities to construct the triangle several ways.
Here's one. Draw an arc (or circle) of radius 8.5 cm centered at point Y. Mark a point Z on the arc. Using the same radius, draw an arc that intersects the first one at point A. Angle ZYA is 60°, as is angle YZA. Now, you can bisect angle ZYA, or segment ZA, or you can simply measure off 4.25 cm on segment ZA. The point halfway between Z and A can be marked point B. Where ray YB intersects the original arc (or circle) centered at Y, is point X of your triangle XYZ.
__
Additional comment
We used a geometry program to draw the triangle in the attachment. It conveniently provided angles with the necessary measures. In terms of the construction described above, the vertex of the right angle is point B.
Another way to start is by identifying right angle lines BZ and BY on grid paper. Once you locate point Z 4.25 cm from B, you can draw an arc centered at Z with radius 8.5 cm that intersects line BY at Y. Then an arc with the same radius centered at Y will identify the location of point X.
Write y=2/5x−2 in standard form.
Answer:
2x - 5y = 10
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
y = [tex]\frac{2}{5}[/tex] x - 2 ( multiply through by 5 to clear the fraction )
5y = 2x - 10 ( subtract 2x from both sides )
- 2x + 5y = - 10 ( multiply through by - 1 )
2x - 5y = 10 ← in standard form
In baeball, each time a player get to hit the ball, it i recorded. The ratio of hit compared to total attempt i their batting average. Each player on the team want the to have the highet batting average to help their team the mot. So far Jana ha hit the ball 7 time out of 10 and Taha ha hit th ball 10 out of 16 time. Which player ga a ratio that mean they have a better batting average?
The player who has better batting average is Jenna
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Jenna = 7 times / 10 timeTasha = 10 times / 16 timesRatio = ?Calculating the ratio of both players we get:
Jenna ratio = 7/10
Jenna ratio = 0.7
Taha ratio = 10/16
Tasha ratio = 0.63
0.7 > 0.63
7/10 > 10/16
Jenna > Tasha
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Correctly written question:
In baseball each time a player get to hit the ball it is recorded. The ratio of hit compared to the total attempt is their batting average. Each player on the team wants to have the highest batting average to help their team the most. So far Jenna has hit the ball 7 times out a 10 and Tasha has hit the ball 10 out of 16 time. Which player has a ratio that mean they have a better batting average?
Yvonne is using Triangle PQR with Altitude QS¯¯¯¯¯ shown below to prove the Pythagorean Theorem.
Given △PQR∼△QSR∼△PSQ, which conclusion about these triangles could Yvonne use in her proof of the Pythagorean Theorem?
Responses
PQQR=QSPS and QRPR=RSQR
P Q Q R = Q S P S and Q R P R = R S Q R
PQPR=PSPQ and QRPR=RSQS
P Q P R = P S P Q and Q R P R = R S Q S
PQPR=PSPQ and QRPR=RSQR
P Q P R = P S P Q and Q R P R = R S Q R
PQQR=QSSR and QSSR=PSQS
P Q Q R = Q S S R and Q S S R = P S Q S
The conclusions with regards to the similar right triangles, Yvonne needs to prove the Pythagorean Theorem are;
PQ/PR = PS/PQ and QR/PR = RS/QR
What is the Pythagorean Theorem?Pythagorean Theorem outlines the relationship between the length of the hypotenuse side and the lengths of the legs of a right triangle. The theorem states that the sum of the squares of the lengths of the legs of a right triangle, is equivalent to the square of the length of the hypotenuse side.
The specified similar triangles are;
ΔPQR ~ ΔQSR ~ ΔPSQ
PQ/PS = PR/PQ...(1)
(PQ)² = PS·PR
QR/RS = PR/QR...(2)
(QR)² = RS·PR
(PQ)² + (QR)² = PS·PR + PR/RS = PR·(PS + RS) = PR×PR = (PR)²
(PQ)² + (QR)² = (PR)²
Equations (1) and (2), can be expressed as follows;
PQ/PS = PR/PQ...(1)
Multiply both sides by PS/PR
PQ/PS × (PS/PR) = PR/PQ × (PS/PR)
PQ/PS × (PS/PR) = PQ/PR
PR/PQ × (PS/PR) = PS/PQ
Therefore;
PQ/PR = PS/PQQR/RS = PR/QR...(2)
Multiplying both sides by (SR/PR). we get;
QR/SR × (RS/PR) = QR/PR
PR/QR × (RS/PR) = RS/QR
QR/PR = RS/QRTherefore, the conclusions about the triangles, Yvonne can use in her proof of the Pythagorean Theorem are;
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A coin of questionable fairness is tossed 10 times per set of trials for two sets of trials. the outcomes are ththththht and ttthtthtth (t = tails; h = heads). which model can you most likely rule out on the basis of this simulation?
The model that is most likely rule out on the basis of this simulation is 40%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
First set of trials: ththththht ( where T = Tails ; H = Heads)
Number of heads = 5
Number of outcomes = 10
Second set of trials: ttthtthtth
Number of heads = 3
Number of outcomes = 10
Total number of heads = 5 + 3 = 8
Total number of outcomes = 10 + 10 = 20
Probably of heads = 8/20 * 100%
Probably of heads = 0.4*100%
Probably of heads = 40%
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I really need help with this question please and thank you
Answer:
8.5
Step-by-step explanation:
this is a right triangle so we could use the formula, which is Pythagorean theorem
so it is [tex]13.5^{2} -10.5^{2} =72\\\sqrt{72} =8.5[/tex]
Are -20 degrees and 340 degrees co-terminal angles? Why? Show your work to earn full credit.
Yes -20 degrees and 340 degrees are co-terminal angles
What are co-terminal angles?are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330°.
The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. All of these angles are coterminal angles.
co-terminal angles are found by adding or subtracting 360° to the angles.
for example the co-terminal angles of -10° = -10° + 360 = 350°
Similarly The co-terminal angles of -20 = -20+360 = 340°
therefore the -20 and 340 are co-terminal angles
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PLEASE HEEEEEEEEEEEEEEEEEEEEEEEEEEEELP
Find the error in the following equations:
2. 4a ^ 2 * 3a ^ 5 = (4 + 3) * a ^ (2 + 5) = 7a ^ 7
3. x ^ 6 * x * x ^ 3 = x ^ (6 + 3) = x ^ 9
4. 3 ^ 4 * 2 ^ 3 = 6 ^ (4 + 3)
The errors in the equation is shown below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
4a² x 3[tex]a^5[/tex]
= 4 x 3 x [tex]a^{2 + 5}[/tex]
= 12 [tex]a^7[/tex]
[tex]x^6[/tex] x (x) x x³
= [tex]x^{6 + 1 + 3}[/tex]
= [tex]x^{10}[/tex]
[tex]3^4[/tex] x 2³
= 3 x 3 x 3 x 3 x 2 x 2 x 2
= 81 x 8
= 648
Thus,
The equation is solved correctly above.
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What is the sum of the first 20 multiples of five?
Answer:
1050
Step-by-step explanation:
Answer:
the answer is: 1050
Step-by-step explanation:
hope it helped you mark brainliest
write the equation with the least degree and integer coefficients that has the roots listed
3, 2 +-3i
The polynomial function is f(x) = (x - 3)((x - 2)² + 9)
How to determine the polynomial from the zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: x=3, 2 +-3i
The polynomial can be repesented as
f(x) = product of (x - zeros)
using the above as a guide, we have the following:
f(x) = (x - 3)(x - (2 - 3i))(x - (2 + 3i))
This can be expressed as
f(x) = (x - 3)((x - 2)² + 9)
hence, the polynomial is f(x) = (x - 3)((x - 2)² + 9)
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