The company made 42 candles from 5040 cm³ of wax.
What is a rectangular prism?Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.
Given the dimensions of the candle, which is in the shape of rectangular prisms
let l be the length, b be width and h be the height,
length = 5 cm
width = 2 cm
height = 12 cm
total wax needed for 1 candle is calculated by the volume of candle,
V = l x b x h
V = 5 x 2 x 12
V = 120 cm³
number of candles made by 5040 cm³ wax
number of candles = 5040/120
number of candles = 42
Hence, 42 candles are made.
Learn more about rectangular prism;
https://brainly.com/question/21308574
#SPJ1
The complete question is,
A company makes wax candles shaped like rectangular prisms. Each candle is 5cm long, 2cm wide, and 12cm tall. If the company used 5040cm3 of wax, how many candles did they make?
A quare piece of cloth i ize 25 m quare i cut into rectangle trip of 50 50 cm wide find the number of tate and their total length in metre
All of the rectangles together measure 1250 meters in length.
A textile square with a 25 square meter surface area. We are aware that the area of a square is determined by multiplying one side's length by itself. The square root of 25 square meters, or 5 meters, is the length of one side of the square in this instance.
Secondly, we are aware that the fabric is being cut into 50 cm-wide rectangles. We can use the following formula to determine each rectangle's length:
(Rectangle width) x (Square cloth length) / (Width of square cloth)
The equation in this instance is (50 cm) x (25 m) / (5 m) = 2500 cm or 25 meters.
Therefore, each rectangle is 25 meters long.
We divide the square cloth's length by each rectangle's width to get the total number of rectangles.
25m / 0.5m (50cm) = 50 rectangles.
Finally, we multiply the quantity of rectangles by the average length of each rectangle to determine the total length of all the rectangles:
50 m x 25 m = 1250 m
Therefore, a square piece of fabric that is 25 square meters in size and has been divided into 50 rectangles, each measuring 50 cm wide and 25 meters long.
Therefore the rectangles together measure 1250 meters in length.
To know more about rectangle visit :
brainly.com/question/20693059
#SPJ4
claire jogs $6$ miles per hour and megan jogs $5$ miles per hour. they start together at their campsite and jog to an outpost $18$ miles away. when claire gets there, she immediately turns around and heads back towards megan. how many miles will they be from the outpost when they meet? express your answer as a mixed number.claire jogs $6$ miles per hour and megan jogs $5$ miles per hour. they start together at their campsite and jog to an outpost $18$ miles away. when claire gets there, she immediately turns around and heads back towards megan. how many miles will they be from the outpost when they meet? express your answer as a mixed number.
When Claire and Megan meet, they will be $13\frac{1}{2}$ miles away from the outpost.
What is speed?Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.
This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone $9$ miles, and Megan will have gone $8\frac{1}{2}$ miles. When they meet, they will have gone a total of $17\frac{1}{2}$ miles, leaving them $13\frac{1}{2}$ miles away from the outpost.
To know more about speed click-
https://brainly.com/question/25631156
#SPJ4
When Claire and Megan meet, they will be [tex]13\frac{1}{2}[/tex] miles away from the outpost. This can be solved by applying the concept of speed.
What is speed?Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.
This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone 9 miles, and Megan will have gone [tex]8\frac{1}{2}[/tex] miles. When they meet, they will have gone a total of [tex]17\frac{1}{2}[/tex] miles, leaving them [tex]13\frac{1}{2}[/tex]miles away from the outpost.
To know more about speed refer to-
brainly.com/question/25631156
#SPJ4
what are the composite factors of 12 ?
Answer:
The prime factors of 12 are 2 x 2 x 3.
So the composite factors of 12 are:
1, 2, 3, 4, 6 and 12.
Sue played four games of golf. For these games her modal score was 98 and her mean score was 100. Her range of scores was 10.
Answer
212
because I added the 98,4,100,10
Answer:
This question is based on the concept of mean. Therefore, the scores for the four games were 97, 98, 98, 107.
Given:
Sue played four games of golf. For these games her modal score was 98 and her mean score was 100. Her range of scores was 10.
According to the question,
If the modal score is 98 then, there must be two games where she scored 98.
The mean is the total of all of her scores divided by the number of games,
We get,
98+98+x+y=400
x+y= 204
As it is given that, the range is 10 and x is the lowest and y is the highest we can say that:
As we know that, her range of scores was 10,
97+10= 107
Therefore, the scores for the four games were 97, 98, 98, 107.
PLEASE HELP WITH EXPLAINING ill give brainliest!
After Ms. Wilson pays her federal taxes, D. She will receive a refund of $ 258.
Why will she receive a tax refund ?A tax refund is given when an individual or business overpays their taxes to the government during the year. It happens when the taxes that an individual or business paid through the year (withholding taxes or estimated taxes) are more than their actual tax liability for the year.
Going by the table, Ms. Wilson at her Single filling status was meant to pay the tax amount of $ 5, 086 in federal taxes and instead paid $ 5, 344. She will therefore get a refund of :
= 5, 344 - 5, 086
= $ 258
Find out more on tax refund at https://brainly.com/question/19577427
#SPJ1
Kabir paid an entrance of $5 plus an additional 0.75 per game at a local arcade. The next week, he and a friend went to another arcade where kabir paid $1.25 per game, but there was no entrance fee
How many games will kabir have to play at each arcade to spend the same amount of money at each arcade?
On solving the provided question, we can say that by equation so he has to play 10 games at each arcade, to spend the same amount of money at each arcade
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation that we can create here is
Kabir paid an entrance of $5 plus an additional 0.75 per game at a local arcade.
he and a friend went to another arcade where kabir paid $1.25 per game, but there was no entrance fee
let kabir played 10 games.
then at arcade 1 he spends $5 + (10*0.75) = 5 + 7.5 = $12.5
now at arcade 2 = 12.5/1.25 = 10 to spend the same amount of money at each arcade
so he has to play 10 games at each arcade, to spend the same amount of money at each arcade
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
I need help please help me?
Which of the following r values indicates the strongest relationship between two variables? +0.45
-0.30
+0.03
-0.45
According to the given option +0.03 is the r values that indicates the strongest relationship between two variables. The option 3 is correct.
The strength of the association between two variables is gauged using correlation coefficients. Although there are other kinds of correlation coefficients, Pearson's is the most widely used. A correlation coefficient frequently used in linear regression is Pearson's correlation. Correlation coefficients typically lie in the range of -1.00 to +1.00.
The closest value to +1 (positive correlation) or -1 is taken into consideration as the strongest correlation, per the rule of correlation coefficients (negative correlation).
A high correlation coefficient means that one variable's value is directly correlated with another.
There is no relationship between the two variables if the correlation coefficient is zero.
A negative correlation coefficient shows an adverse relationship between the values of the two variables.
According to the given option +0.03 is the r values that indicates the strongest relationship between two variables.
To learn more about correlation coefficients link is here
brainly.com/question/15577278
#SPJ4
I WILL MARK BRAINLIEST IMMEDIATELY PLSS
Using a system of equations, Christine's investments in account one were $4,000 and in account two $16,000.
What is a system of equations?A system of equations refers to simultaneous equations.
Simultaneous equations are two or more equations solved concurrently.
Total investment in two accounts = $20,000
The simple interest rate for account one, x = 8%
The simple interest rate for account two, y = 10%
Total interest for a year = $1,920
Let account one = x and account two = y
Equations:x + y = 20,000 ... Equation 1
0.08x + 0.1y = 1,920 ... Equation 2
Multiply Equation 1 by 0.08
0.08x + 0.08y = 1,600 ... Equation 3
Subtract Equation 3 from Equation 2:
0.08x + 0.1y = 1,920
-
0.08x + 0.08y = 1,600
0.02y = 320
y = 16,000
= $16,000
In Equation 1, x + y = 20,000, Substitute y = 16,000:
x + 16,000 = 20,000
x = 4,000
= $4,000
Check:
From Equation 2:
0.08x + 0.1y = 1,920
0.08(4,000) + 0.1(16,000) = 1,920
320 + 1,600 = 1,920
Thus, using simultaneous equations, we can conclude that Christine invested $4,000 in the first account and $16,000 in the second account.
Learn more about simultaneous equations at https://brainly.com/question/16863577
#SPJ1
Complete Question:Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?
First account:
Second account:
A) A contractor is buying a truck for work. They have saved $2,000.00 for the down payment. The remaining $4,000.00 will be financed through the dealership for three years at an interest rate of 2%. How much interest would they pay by the end of the finance?
Answer:
$240
Step-by-step explanation:
To calculate the interest, you need to multiply the principal (the amount financed, $4,000.00) by the interest rate (2%) and the number of years (3).
So, the interest would be: $4,000.00 x 0.02 x 3 = $240.00
The contractor would pay $240.00 in interest over the course of the 3-year financing.
algebra 25 focus: polynomial multiplication 66 3/3 correct problem level 25 algebra 125 xp resilience 86, stamina 95. suppose that $f$ is a quadratic polynomial and $g$ is a cubic polynomial, and both $f$ and $g$ have a leading coefficient of $1$. what is the maximum degree of the polynomial $(f(x))^3 - (g(x))^2 f(x) - 1$?
maximum degree f(x) = x2 + bx + c g(x) = x3 + wx2 + yx + z [f(x)]3 - [g(x)]2 + f(x) - 1 (x2+bx+c)3 - (x3+wx2..for the given polynomial
What is a polynomial class 9?
Polynomial Definition. Polynomials are expressions with one or more terms with a non-zero coefficient. A polynomial can have more than one term. An algebraic expression p(x) = a0xn + a1xn-1 + a2xn-2 + … an is a polynomial where a0, a1, ………. an are real numbers and n is non-negative integer.
Find the value of f(–9) and g(1) if f(x) = 8x + 6 and g(x) = 9x + 20x−2
polynomial f(x) = 8x + 6
f(–9) = 8(-9) + 6 = -66
g(x) = 9x + 20x − 2
g( 1 ) = 9( 1 ) + 20( 1 ) − 2 = 27
None of the given choices were correct (unless there's a typo error for — it's supposed to be g( 1 ) = 27 instead of 29?) because the value are: f(–9) = -66 and g( 1 ) = 27
f(–9) and g(–1) if f(x) = –3x – 2 and g(x) = 3x³ – 24x
f(x) = –3x – 2
f(–9) = –3(–9) – 2 = 25
g(x) = 3x³ – 24x
g(–1) = 3(–1)³ – 24(–1) = 21
Therefore, : f(–9) = 25, g(–1) = 21
learn more about of polynomial here
https://brainly.com/question/24960978
#SPJ4
Write an expression to represent the situation
Rhona got 114 more votes Tham Petro.
Matt took 10 minutes longer than twice as long as Bryce took to do his assignment.
A hamburger costs 29 cents less than half as much as a full meal.
someone please help asap tysm <333
The expression that represents the statements are
1. R = 114+P
2. M = 10+2B
3. H = 1/2M -29
What are linear expressions?Linear expressions are those statements that each term is either a constant or a variable raised to the first power.
In linear expressions, the highest power of the variable is 1.
In the first statement 'Rhona got 114 more votes Tham Petro'. Let's represent the votes for Rhona by R and for Pedro by P
therefore R = 114+ P
In the second statement 'Matt took 10 minutes longer than twice as long as Bryce took to do his assignment'
Let's represent the time it took Matt to do his assignment' by M and time it took Bryce by B.
then,
M = 10+2B
In the third statement 'A hamburger costs 29 cents less than half as much as a full meal'.
Let's represent the cost of hamburger by H and the cost of full meal' by M, then,
H = 1/2M -29
learn more about linear expressions from
https://brainly.com/question/2030026
#SPJ1
the half-life of strontium-90 is 28 years, meaning that after 28 years a given amount of the substance will have decayed to half the original amount. find the exponential decay midel of strontium-90
Answer:i had to
Step-by-step explanation: mb
How do you find the smallest and largest angle of a triangle?
To calculate measure of the angle of a given triangle apply cosine rule :
c² = a² + b² - 2abcos C
b² = a² + c² - 2ac cos B
a² = c² + b² - 2cbcos A and by comparison find the smallest and the largest angle.
As given in the question,
Consider a triangle ABC to determine the smallest and the largest angle of the triangle,
Side opposite to angle A = BC
Side opposite to angle B = AC
Side opposite to angle C = AB
Let
side AB = c
side AC = b
side BC = a
To determine the measure of the angle using side measurement apply
cosine rule :
c² = a² + b² - 2abcos C
b² = a² + c² - 2ac cos B
a² = c² + b² - 2cbcos A
Calculate measure of all the angles and compare them to determine smallest and largest angle of the triangle.
Therefore, to find the measure of the angle of a triangle use cosine rule and by comparison determine the smallest and the largest angle.
Learn more about triangle here
brainly.com/question/2773823
#SPJ4
2.7-6.8x=-6.8-5.1x round to the nearest tenth
The given algebraic expression when solved to the nearest tenth is 5.6
How to solve like terms?2.7 - 6.8x = - 6.8 - 5.1x
collect like terms
2.7 + 6.8 = -5.1x + 6.8x
9.5 = 1.7x
divide both sides by 1.7
x = 9.5/1.7
x = 5.6
Therefore, the algebraic expression is given by x = 5.6
Read more on like terms:
https://brainly.com/question/17471184
#SPJ1
helppppppppppppp pls.
someone asked tjis question before
Step-by-step explanation:
he needs 100ml to make 250ml, the explanation is somewhere on this app
Answer:
150ml
Step-by-step explanation:
250ml=100%
25ml=10%
times 25mls 6 times so that it become 60%=150ml
how many liters of 10% salt solution must be added to 5 liters of 25% salt solution to obtain a 15% salt solution?
Answer: 10 liters
Step-by-step explanation:
Let the number of liters of 10% solution be [tex]x[/tex].
[tex]0.10x+5(0.25)=0.15(x+5)\\\\0.10x+1.25=0.15x+0.75\\\\1.25=0.05x+0.75\\\\0.05x=0.50\\\\x=10[/tex]
7 less than the product of a number n and 1/5 is no more than 95 .
ANSWER:
STEP-BY-STEP EXPLANATION:
We must interpret each sentence mathematically, just like this:
Less then would be a subtract
Product would be a multiplication
No more than would be equal or less than
Answer:
.2n-7≤95
.2n≤102
n≤510
hope this helps
Find the length of the toothpick nearest millimeter
Answer:
85 Millimeters
Step-by-step explanation:
1 centimeter is equal to 10 millimeters. Hope this helped!
Do the sides 7 cm 24 cm and 25 cm form a right-angled triangle give reason?
The sides 7cm , 24cm and 25cm ; forms a right angled triangle because the condition of Pythagoras Theorem is satisfied .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the square of hypotnuse (longest sides) is equal to the sum of the square of the other two sides .
The sides are given as ⇒ 7cm , 24cm and 25cm ;
here the longest side (hypotnuse) is = 25 cm ;
According to Pythagoras theorem ,
⇒ [tex]25^{2} =24^{2} +7^{2}[/tex] ;
⇒ [tex]625=576+49[/tex] ;
⇒ [tex]625 = 625[/tex] ;
The condition of Pythagoras theorem is satisfied .
Therefore , the given sides can form a Right Angled Triangle .
Learn more about Right Angled Triangle here
https://brainly.com/question/30238309
#SPJ4
Aubree's car used 4 gallons to travel 120 miles. How many miles can the car go on one gallon of gas?
Aubree's car used 1 gallon to travel 30 miles.
The car used 4 gallons to travel 120 miles. We need to calculate the distance car can travel with 1 gallon of gas.
By unitary method;
The distance car can travel = (120/4)*1 =30
Aubree's car used 1 gallon to travel 30 miles.
Learn more about the unitary method,
https://brainly.com/question/19423643
On 1 gallon of gas, Aubree`s car can go 30 miles.
This is a question of the unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, [by dividing] and then finding the necessary value by multiplying the single unit value.
Aubree`s car used 4 gallons of gas to travel 120 miles. So, to find the miles it travelled on 1 gallon of gas. We can simply just divide the total miles the car travelled by the total litres of gas it used.
Therefore, 120/4=30 miles.
Learn more about the unitary method here:
https://brainly.com/question/22056199
Solve the system of equations – 8x + 6y = 14 and -5x + 2y = -7 by combining
the equations.
-
|(- 8x +y = 14)
(- 5a +2y =-7)
- 8x t6y = 14
-5 +2y =-7
0x + 0y
try
For the given system of equations the value of x is 0.27 and the value of y = 2.7.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.
The given equations are:
-8x + 6y = 14 and
-5x + 2y = -7
For the equation -5x + 2y = -7 isolate the value of x:
-5x = 7 - 2y
x = - (7 - 2y) / 5
Substitute the value of x in the equation -8x + 6y = 14.
[tex]-8 (\frac{7-2y}{5} ) +6y =14\\\\-11.2 + 3.2y + 6y =14\\\\9.2y = 14 + 11.2\\\\y = 2.7[/tex]
Substitute the value of y in any one of the equations:
-8x + 6(2.7) = 14
-8x = 14 - 16.2
x = 0.27
Hence, the value of x is 0.27 and the value of y = 2.7.
Learn more about system of equations here:
https://brainly.com/question/24065247
#SPJ4
Given the linear system:
5x + 3y = 17
-8x - 3y = 9
What is the correct formula for the solution to the linear system?
The solution to the linear system is [tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,\ y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
A linear system of equation:
Ax + By = C
Dx + Ey = F
Can be solved using:
[tex]x=\frac{\left[\begin{array}{cc}C&B\\F&E\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}A&C\\D&F\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]}[/tex]
Hence, for:
5x + 3y = 17
-8x - 3y = 9
[tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Answer:
C
Step-by-step explanation:
On the grid below, draw the graph of * + 2y = 3.
The graph of the linear equation can be seen in the image at the end.
How to graph the linear equation?
I assume that you want to graph the linear equation:
x + 2y = 3
To do so, you just need to find two points that lie on that line, to find them, just evaluate the linear equation in two different values of x (or y)
Remember that the point notation is (x, y)
if we use x = 0
0 + 2y = 3
2y = 3
y = 3/2 = 1.5
So we have the point (0, 1.5)
if x = 1
1 + 2y = 3
2y = 3 - 1
2y = 2
y = 2/2
y = 1
So the point is (1, 1)
Now that you have these two points, you can graph them on a coordinate axis, and connect them with a staright line.
The graph can be seen below.
Learn more about linear equations at:
https://brainly.com/question/1884491
#SPJ1
A line in the xy-plane passes through the origin and has a slope of 1/7 . Which of the following points lies on the line? a. (0,7) b. (1,7) c. (7,7) d. (14,2)
(14,2) is the point lies on the slope-intercept form, line .
What does the slope intercept form mean?
The formula for a straight line, written as y = mx + b, where m denotes the line's slope and b its y-intercept. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
In the slope-intercept form, the equation for the line is expressed as follows: y = mx + b, where m denotes the slope and b the y-intercept. We can observe that the line's slope is 3 from our equation, y = 3 x + 5.
All lines passing thru the origin should have a slope of y = mx + c
In this case, since the slope is 1/7 , the line will be y = 1/7x
Thus, it could observe which is the only point that satisfies this equation of the line out of all the points.
For choice "E" when x= 7 and y = 14 m = 1/7 and put the value in y = mx + c it will give 14 = 2 , which is wrong.
Learn more about slope intercept form
brainly.com/question/29146348
#SPJ4
What is the answer to simplifying this
The answer to the simplification is 56.
What is order of precedence?The order of precedence is the hierarchical order in which calculations are conducted. The simplest example of this is the way you always multiply before you add numbers.
In mathematics, you have BODMAS
B = Bracket
O = of
D = Division
M = Multiplication
A = Addition
S = Subtraction
From the equation;
7 x (-7 +15)
Removing the bracket
7 x (8)
Multiplying
56
Learn more about order of precedence here:https://brainly.com/question/1599125
#SPJ1
a library is having a book sale to raise money hardcover book scost $4 each and paperback books cost $2 each. a person spends $26 for 8 books. how many of each type of book did she buy
Answer: 5 hardcover and 3 paperback
Step-by-step explanation: To solve, we need to keep this question in mind:
"How many books can we buy for each without going over the initiate amount [$26]?"
So, let's start with the $4 books, so knowing our multiples of 4
ex. 4, 8, 12, 16, 20, 24, 28......
So, I listed the example of the multiples. So, it can be either 20 or 24. So, it would be 20, because it is under the initiate amount AND it is less with unincluded paperback books. So, 26-20 = 6. So, if each paperback book costs $2, we need to divide 6 by 2. That's 3. So, therefore, she can buy 5 hardcovers and 3 paperbacks by spending all the money. I hope this helps!
Find dy/dt for each pair of functions. y = x^2 - 2x, x = t^2 + 8 dy/dt =
[tex]dy/dt[/tex] for each pair of functions is [tex]4t^3 + 28t[/tex].
[tex]y[/tex] = [tex]x^2 - 2x[/tex]
[tex]x[/tex] = [tex]t^2 + 8[/tex]
[tex]y[/tex] = [tex](t^2+8)^2 - 2(t^2+8)[/tex]
[tex]dy/dt[/tex] = [tex]2(t^2+8)(2t) - 2(2t)[/tex]
= [tex]4t^3 + 32t - 4t[/tex]
[tex]dy/dt[/tex] = [tex]4t^3 + 28t[/tex]
The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.
When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable. The function closest to that input value is best approximated linearly by the tangent line.
To learn about Derivative :
https://brainly.com/question/23819325
#SPJ4
find a cartesian equation for the curve and identify it. r = 7 cos(θ)
The cartesian equation for the curve r = 7 cos(θ) is [x -(7/2)]²+y² = 49/4, which is the equation of a circle.
Given r =7 cosθ
Multiplying throughout by ‘r’,
r² =7r cos θ --- (1)
Consider x² + y² = r² and put x = r cos θ --- (2)
x² + y² = 7x
Using completing the square method:
x² - 7x + (7/2)² + y² = (7/2)²
[x - (7/2)]² + y² = 49/4
(x - 7/2)² + (y - 0)² = (7/2)²
This is the equation of the circle with a center (7/2, 0) and radius of 7/2.
To know more about the cartesian equation:
https://brainly.com/question/1503410
#SPJ4
A: -4p²q²-3pq
B: 4c²-12c to the 4th
C: 3m²+9m³
D: c³+c to the 7th
E:-24x to the 4th -16x to the 8th
PLEASE WRITE ALL AS A PRODUCT QUICK HELP
The required product are as follows,
A: -4p²q²-3pq = 4c²[1 - 3c²] B: 4c²-12c⁴ = 4c²[1 - 3c²]
C: 3m²+9m³ = 3m²{1 + 3m} D: c³+c⁷ = c³[1 + c⁴]
E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
(a)
Given expression,
-4p²q²-3pq = -pq (4pq + 3)
Similarly,
B: 4c²-12c⁴ = 4c²[1 - 3c²]
C: 3m²+9m³ = 3m²{1 + 3m}
D: c³+c⁷ = c³[1 + c⁴]
E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]
Thus, the required products has be illustrated above.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
