The function, [tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex] has a limit that is undefined (does not exist) as x approaches 0. The correct option therefore option b;
b. As x approaches 0, the limit of p(x) does not exist
What is a function in mathematics?The given function is presented as follows;
[tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex]
Required;
The limit of the function as x approaches (zero) 0
Solution;
The limit of a function at a given point within the domain of the function is the value of the function as the function's argument approaches a.
Therefore, the limit of the given function at the point x = 0 is given by the function's value as the argument of the function, x approaches 0.
cos²(0) = 1
sin(2×0) = sin(0) = 0
Therefore;
[tex]\displaystyle { p(x) = \frac{ {cos}^{2}0 }{sin(2 \times 0)} = \frac{ 1 }{0} = \infty}[/tex]
Therefore, the limit of the function does not exist as x approaches 0
The correct option is therefore, option b
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Multiply using the associative property.
Enter your answer by filling in the boxes.
(7×5) x2=
(7×5) x2=7x
(7 × 5) x 2 =
X
x 2)
Answer this problem
The answer of (7 ×5) ×2 using associative property is 70.
What is associative property?
(a ×b) ×c = a ×(b ×c) and (a+b)+c = a+(b+c)
Addition and multiplication are supported by the associative property but not division and subtraction.
Using associative property ,
(7 ×5) ×2 = 7×(5 ×2)
(7 ×5) ×2 = 7×10
(7 ×5) ×2 = 70
Therefore, the answer of (7 ×5) ×2 using associative property is 70.
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The value of a, b, c and d are 25, 3, 14 and 7 such that the sum of all rows, columns and diagonals are 48.
Given to us a magic square in which the sum of all rows, columns and diagonals are same. Then, we have to complete the missing numbers i.e., a, b, c and d respectively.
Let's proceed to solve this magic square accordingly.
First let's calculate that what will be the sum of all rows, columns and diagonals.
From the figure of magic square one diagonal is completely filled from that we can easily calculate the sum of the diagonals.
Sum = 5+16+27 = 48
Then, we can find the value of a, b, c and d easily.
5+a+18 = 48
23+a = 48
a = 48-23
a = 25
Therefore, the value of a is 25.
29+16+b = 48
45+b = 48
b = 48-45
b = 3
Therefore, the value of b is 3.
Now, 5+29+c = 48
34+b = 48
c = 48-34
c = 14
Therefore, the value of c is 14.
Then, we have
c+d+27 = 48
14+d+27 = 48
41+d = 48
d = 48-41
d = 7
Therefore, the value of d is 7.
Hence, we have completed the magic square in which the sum of all rows, columns and diagonals are 48.
Therefore, the value of a, b, c and d are 25, 3, 14 and 7 respectively.
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Help pls!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
it should be 180
9 1/4 to 9
20 stays the same
Translate the phrase into an Algebraic expression The sum of 6 and b
The translation of the phrase into an algebraic expression which is the sum of 6 and b is 6+b.
What is an algebraic expression?It should be noted that an algebraic expression is used in Mathematics to show the relationship between the terms that are given. The concept of utilizing letters or alphabets to convey numbers without defining their exact values is known as algebraic expressions.
We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
In this case, we want to translate the phrase into an algebraic expression. The phrase is the sum of 6 and b. This will simply be:
= 6 + b
Therefore, the expression is 6+b.
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Every month, Omar buys baskets of wings to serve at a party for his friends. In May, he bought three more than twice the number of baskets of wings he bought in April. If Omar bought 15 baskets of wings in May, how many did he buy in April?
*Use distributive property*
Answer:
33
Step-by-step explanation:
If Gabriella has 3 more nickels than dimes and they have a combined value of 90 cents, how many of each coin does she have?
Correct dimes
nickels
If Gabriella has 3 more nickels than dimes and they have a combined value of 90 cents, The number of coin she have is; 4 nickels and 7 dimes.
Nickels and dimesx = number of nickels that Gabriella has
x +3 =number of dimes that Gabriella
Hence,
0.05x + 0.10 ( x + 3 ) = 0.9
Solving for x
Multiply both sides of the equation by 100 so as to eliminate two decimal places
5x + 10x + 30 = 90
Collect like terms
15x = 60
Divide both side by 15x
x = 60/15
x = 4 nickels
So,
x + 3 where x = 4
4 + 3 =7 dimes
Therefore she has 4 nickels and 7 dimes.
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Clancy has 423 cups of yogurt to share with his friends at a party. Each guest will receive 1 serving of yogurt which is 34 of a cup.
Write a multiplication equation to determine the number of people, p, who can be invited to the party.
Answer: Around 141 guests can be invited
Explanation: 423 divided by 3/4 is 141, and 141 x 3/4 is 423
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
The final expression that represent the total owed is 3c + 25
How to represent mathematical expression?He owed 3 months cable at a price of c dollars for each month, plus a one-time equipment fee of $25,
Therefore, the situation can be expressed as follows:
For a single month he pays c dollars
Hence, 3 month will be 3 × c.
Recall he also needs to pay a one time fees of 25 dollar.
Therefore, the final expression that represent the total owed is as follows:
total owed = 3c + 25
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It takes 4 cups of sugar to make 6 batches of cookies. How many cups of sugar is needed for 15 batches of cookies?
Answer:
10 cups
Step-by-step explanation:
6 divided by 4 is 1.5 and if you take 15 divided by 1.5 it'd be 10
Answer:
10 cups of sugar
Step-by-step explanation:
you can easily make it into a ratio.... ( the amountof sugar needed to make 15 batches of cookies is x)
x/15 = 4/6
when you multiply you get 6x = 4 × 15
6x = 60, then you divide by 6
giving you x=10
simplify the expression -1.1 + (-3.9). On the test, when tom simplified the expression he got -2.8. What mistake did tom likely make when he simplified the expression?
Answer:
the answer is -5.0
Step-by-step explanation:
Tom subtracted -1.1 from -3.9 instead of adding them together
A train travels along a straight piece of track between 2 stations
A and B. The train starts from rest at A and accelerates at
1.25m/s² until it reaches a speed of 20m/s. Find the distance
from A to B.
Answer:
v=20m/s ,u= 0m/s( from rest) a=1.25m/s Distance s=?
V²= UT +2as
make s subject
2as=v²-u²
S= v²-u²/2a
S =20²-0²/2*1.25
S=400/2.5
S= 160m
what are the domain and range of the function?
The domain and range are the set of all real numbers, so:
Domain: x ∈ R
Range: x ∈ R
Thus, the correct option is the second one
What are the domain and range of the function?
For any function y = f(x), we define the domain as the set of the possible values of x (the ones on the horizontal axis) and the range is the set of the possible values of y (vertical axis).
In this case, we have a linear equation (you can see that the lines extend to the bottom left and the top right)
So both domain and range are the sets of all real numbers.
Thus, the correct option is the second one.
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What is 581/14 in partial quotients?
The quotient of 581 and 14 has a value of 40.07
How to evaluate the expression using partial quotients?The quotient expression is given as
581/14
Next, we express 581 as the sum of a multiple of 14 and another number
Say 581 = 280 + 280 + 1
So, we have the following equation
581/14 = (280 + 280 + 1)/14
Expand the bracket
So, we have the following equation
581/14 = 280/14 + 280/14 + 1/14
Evaluate the quotients
581/14 = 20 + 20 + 0.07
Evaluate the sum
581/14 = 40.07
Hence, the value of the quotient expression is 40.07
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shade the portion of this figure that represents 14/4
14/4 = ?
There are 4x5 = 20 squares
Then 14/4 = 3 + 2/4
also 14/4 = 70/20 = 7/2
Take 14 squares, from figure
Now graph portion shade
A baker sells muffins in boxes that contain exactly 9 muffins each. Can the baker place 576 muffins in boxes with none left over. Explain
The baker can put all the 576 muffins in the box that contains exactly 9 muffins with none left over.
Can the baker put all the muffins in the box with none left over?In order to determine if the baker can put all the 576 muffins in the box that contains exactly 9 muffins with none left over, divide 576 by 9. If 9 perfectly divides 576, then there would be no remainder.
Division is the process in mathematics that is used to group a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other operations in mathematics are addition, subtraction and multiplication.
Number of boxes needed = number of muffins / capacity of each box
576 / 9 = 64
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RS has endpoints R(-11, 10) and S(-6, -5). Point T divides RS such that ST:TR is 2:3.
What are the coordinates of T?
Write your answers as integers or decimals.
()
Check the picture below.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ S(-6,-5)\qquad R(-11,10)\qquad \qquad \stackrel{\textit{ratio from S to R}}{2:3} \\\\\\ \cfrac{S\underline{T}}{\underline{T} R} = \cfrac{2}{3}\implies \cfrac{S}{R} = \cfrac{2}{3}\implies 3S=2R\implies 3(-6,-5)=2(-11,10)[/tex]
[tex](\stackrel{x}{-18}~~,~~ \stackrel{y}{-15})=(\stackrel{x}{-22}~~,~~ \stackrel{y}{20}) \implies T=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-18 -22}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-15 +20}}{2+3} \right)} \\\\\\ T=\left( \cfrac{ -40 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} T=(-8~~,~~1) \end{array}}[/tex]
Which of the following are the coordinates of point F' , the image of point F, after a rotation of 90° about (1 point)
the origin?
Answer:
(3, 0)
Step-by-step explanation:
I assume this means a clockwise rotation.
let's think this through logically :
the last option (0, 3) cannot be right, because that is F before the rotation. to go back to the original position requires a full rotation of 360° (remember, a circle has 360°, and that means to travel one complete time around the circle).
(0, -3) cannot be right, because this is just mirrored down, and would represent a turn of 180° (a half-circle).
for the other options imagine you use a math compass, put the pin on the origin, and the writing arm on F. and the you draw a circle through F.
(3, 0) is the result of the clockwise (right) turn of 90°, (-3, 0) would be the result of a counterclockwise (left) turn of 90°.
so, if my assumption above is incorrect, please pick (-3, 0) for the counterclockwise solution.
If 6times a number is added to -3, then the results is equal to 9 times the number. Find the number
To determine the missing number:
[tex]\text{Let the missing number = x}[/tex][tex]\begin{gathered} 6\text{ times a number = 6x} \\ 6x+(-3)=9x \\ 6x-3=9x \end{gathered}[/tex]collect like terms
[tex]\begin{gathered} 6x-9x=3 \\ -3x=3 \\ \text{divide both side by -3} \\ -\frac{3x}{-3}=\frac{3}{-3} \\ x=-1 \end{gathered}[/tex]Therefore the missing number = -1
Please help I’ll mark you as brainliest if correct!
Answer:
21 Degrees.
Step-by-step explanation:
It was 22 degrees by noon, by then the temperature had already risen by
eight degrees, but since we are going back in time, we would subtract the eight degrees.
22 - 8 = 14.
Now we are at 9 A.M, it is 14 degrees. But, the temperature had doubled from 5-9 A.M, so we would divide our fourteen by two in order to half it.
14 ÷ 2 = 7.
Now we are at 5 A.M.
From midnight to 5 A.M the temperature dropped fourteen degrees so we would add that fourteen back into the equation.
7 + 14 = 21.
Hope this helped!!
use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval.
The two approximations of the region's area between the graph of the function and the x-axis over the given interval are 14.31 < AREA < 17.01
We have :
f(x) = 9 -x [ 2, 4 ], 6 rectangles.
Here, a = 2 and b = 4 , n = 6
The width of the rectangles will be
x' = [tex]\frac{b-a}{n}[/tex]
x' = [tex]\frac{4-2}{6} = \frac{2}{6} = \frac{1}{3} = 0.33[/tex]
Now, The given function is f(x) = 9 -x
[tex]f(x_{i}) = x_{i} - 9[/tex]
For [tex]x_{0} = 0[/tex], [tex]f(x_{0} ) = 9[/tex]
For [tex]x_{1} = 0.3[/tex], [tex]f(x_{1} ) = 9 -0.3 = 8.7[/tex]
For [tex]x_{2} = 0.6[/tex], [tex]f(x_{2} ) = 9 -0.6 = 8.4[/tex]
For [tex]x_{3} = 0.9[/tex], [tex]f(x_{3} ) = 9 -0.9 = 8.1[/tex]
For [tex]x_{4} = 1.2[/tex], [tex]f(x_{4} ) = 9 -1.2 = 7.8[/tex]
For [tex]x_{5} = 1.5[/tex], [tex]f(x_{3} ) = 9 -1.5 = 7.5[/tex]
For [tex]x_{6} = 2.1[/tex], [tex]f(x_{3} ) = 9 -2.1 = 7.2[/tex]
Now, The area by using an approximation using 6 approximating rectangles and right endpoints is given by.
A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6})x'\\[/tex]
A = (8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3
A = 47.7*0.3 = 14.31
The area by using an approximation using 6 approximating rectangles and left endpoints is given by:
A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{0} + f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6} } )x'\\[/tex]
A = (9+8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3
A = 17.01
Thus 14.31 < AREA < 17.01
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Please help with number 8 step by step
Answer:
It is a function because circles are functions
Step-by-step explanation:
the formula for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k) = center
r=radius
radius is 4 because diameter is 8
Center is (2,1)
plug it into the equation:
[tex](x-2)^2+(y-1)^2=16[/tex]
A cashier has 35 bills, all of which are $10 or $20 bills. The total value of the money is $520. How many of each type of bill does the cashier have?
After solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.An operation of arity zero also referred to as a nullary operation, is a constant.The mixed product is an illustration of an operation of arity 3, also referred to as a ternary operation.So, the total value of money by 35 bills is $0, and $20 is $520.
Now, we know that: 20 × 18 = 360Similarly, we know that: 10 × 16 = 160Sum of 360 and 160: 360 + 160 = $520So, 185 bills of $20 and 16 bills of $10.Therefore, after solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.
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Find the slope from the given table. Simplify your answer. Hint: Make Time (x) and Distance (y). Does it matter which two points you use? Type yes or no.
m = 15/8 and yes it dep
Here, we want to find the slope from the given table
Mathematically, that could be calculated using the formula;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ we\text{ can select any two points} \\ \\ \text{let us select the first and the last;} \\ \\ m\text{ = }\frac{17-2}{9-1}\text{ = }\frac{15}{8}\text{ } \end{gathered}[/tex]Now, we want to find out if it differs if we use any other random two points
Let us select the 1st and the 3rd point
Mathematically, the slope here would be;
[tex]m\text{ = }\frac{12-2}{6-1}\text{ = }\frac{10}{5}\text{ = 2}[/tex]From these, we can see that the value of the slope obtained depends on the two points that are selected
graph AgraphwebImaginary A3222Real342 3 4-123graphAe7in A22Reals+3212343a-44which graph depicts a complex number with as the imaginary partA graphOgraphCCgraph
Graph (D) shows a complex number with an imaginary component, i.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. Bar graphs, circle graphs, and line graphs are the three most frequently used types of graphs.Different types of data can be displayed using different types of graphs.So, we are aware that a complex number is shown as:
z= x+iyWhere x stands for a number's real value and y for a number's imaginary value.
Which stands for the point (x,y)As a result, the number I is written as:
z=0+1.iThis indicates that the symbol for the number I is a point (0,1).
Therefore, the number I has a value of 1 on the hypothetical axis.So, Graph D is the appropriate selection.Therefore, graph (D) shows a complex number with an imaginary component, i.
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The complete question is given below:
Which graph depicts a complex number with i as the imaginary part?
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use * for multiplication between all factors.)[tex]z = x^{7}y^{7}, x = s cos(t), y = s sin(t)[/tex]
Applying the Chain Rule, the derivatives are given as follows:
[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex][tex]\frac{\partial z}{\partial t} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]What is the derivative of Z as a function of s?
The function Z is defined as follows:
z = x^7y^7.
The variables x and y are functions of variables s and t, as follows:
x = s cos(t).y = s sin(t).Hence the derivative of z as a function of s is given as follows:
∂z/∂s = (dz/dx)(dx/ds) + (dz/dy)(dy/ds).
Hence, applying the derivative rules for the exponents, and for the exponents, we have that:
[tex]\frac{\partial z}{\partial s} = 7x^6y^7\cos{(t)} + 7y^6x^7\sin{(t)} = 7x^6y^6(y\cos{t} + x\sin{t})[/tex]
Replacing the values of x and y, we have that:
[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex]
What is the derivative of Z as a function of t?We follow the same logic as above, only that now the inside derivatives, that is, the derivatives of x and y, are as function of t and not of s, hence:
∂z/∂t = (dz/dx)(dx/dt) + (dz/dy)(dy/dt).
Then:
[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7sx^6y^6(-y\sin{t} + x\cos{t})[/tex]
Then, replacing x and y as functions of s and t, we have that:
[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]
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You put some money in a bank account one year ago. You have not done anything with it since. The bank takes out a low balance fee of $0.25 each month. After 8 months, you had $28 in the account. Choose the equation that best shows the money in your bank account over time. CLEAR CHECK Balance=−0.25⋅Months Balance−28=−0.25(Months−8) Balance−8=−0.25(Months−28) Balance−28=−0.25(Months+8)
Answer:
Step-by-step explanation:
The cost of 8 shirts is $72 find the cost of 12 shirts
Answer: $108
Step-by-step explation:
El volumen de un cubo que tiene como arista 14 cm es?
1000 cm3
2.744 cm3
216 cm3
The volume of the cube is 2744 cm³.
QuadrilateralsThere are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square all angles are 90° and all sides present the same value.
A square is a 2D figure, when the square is associated a 3D figure, the figure is called a cube. The cube presents 6 faces with length (l) , height (h) and width (w) equal. Thus, the cube presents congruent edges.
The volume is given from the formula V=a³, where a is a congruent edge.
The question gives:
edge=14 cmTherefore,
V=a³
V=14³
V=14*14*14
V=2744 cm³
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A hat costs $10.95 and a T-shirt costs $14.20. How much change will you receive if you pay for both items with a $50 bill?
Pls give a good explanation
Answer: $24.85
Step-by-step explanation:
10.95+14.20= 25.15
25.15+24.85= 50
Answer:
24.35
Step-by-step explanation:
Add 10.95 to 14.20:
10.95+14.20=25.15
Then subtract the answer 25.15 from 50
50-25.15=24.35
[tex] \rm \int_0^1 \frac{ {x}^{3} - {x}^{2} - 1 }{ {x}^{2} - x - 1 }dx \\ [/tex]
Simplify the integrand.
[tex]\displaystyle \frac{x^3-x^2-1}{x^2-x-1} = x + \frac{x-1}{x^2-x-1}[/tex]
Expand into partial fractions, recalling that [tex]\phi[/tex] and [tex]-\frac1\phi[/tex] are roots to the quadratic in the denominator.
[tex]\dfrac{x-1}{(x - \phi) \left(x + \frac1\phi\right)} = \dfrac1{1+\phi^2} \left(\dfrac1{x-\phi} + \dfrac{\phi^2}{x + \dfrac1\phi}\right)[/tex]
Then the integral is
[tex]\displaystyle I = \int_0^1 \frac{x^3-x^2-1}{x^2-x-1} \, dx \\\\ ~~~~ = \int_0^1 x \, dx + \frac1{1+\phi^2} \int_0^1 \left(\frac1{x-\phi} + \frac{\phi^2}{x+\frac1\phi}\right) \, dx \\\\ ~~~~ = \frac12 + \frac{1}{1+\phi^2} \left(\ln|1-\phi| + \phi^2 \ln\left|1 + \frac1\phi\right| - \ln|-\phi| - \phi^2 \ln\left|\frac1\phi\right|\right)[/tex]
and this reduces significantly, when we recall that [tex]\phi = 1 + \frac1\phi[/tex], to
[tex]\displaystyle I = \boxed{\frac12 + \frac{2\phi}{1 + \phi^2} \ln(\phi)}[/tex]