Answer:
the answer is 77
Step-by-step explanation:
suppose the answer is z and the width is x
the perimeter would be 4x+8 = 36
4x = 28
x=7
7+4=11
7*11=77
simplify the expression - 4 1/2 ( - 2.5n + 3n - 4 ) .
Answer:
-2.25n + 18
Step-by-step explanation:
- 4 1/2 ( - 2.5n + 3n - 4 )
4 1/2 = 9/2
-9/2 (-2.5n + 3n - 4)
-9/2(0.5n - 4)
-2.25n + 18
b) Town A has a rectangular park.
The length of the park is .xm.
The width of the park is 25 m shorter than the length.
The area of the park is 2200 m².
(i) Show that x²-25x-2200 = 0.
This might be written as x2-25x-2200 = 0, since the park's area is 2200 m2, and its length is.xm.
what is rectangle ?A rectangle is a polygon with four direction perpendicular in Euclidean plane geometry. You may also refer to it as an equiangular quadrilateral, meaning that every one of its vertices are equal. A straight angle may also present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90º vertices and equivalent parallel sides make up a quadrilateral with the characteristics of a rectangle. As a result, it's also known as a georeferencing rectangle. A rectangle is also referred to as a parallelogram since its separate angles are parallel and equal.
given
Park's rectangular length is x meters.
Park width is equal to (x-25)m since width is 25 m shorter than length.
The park has a 2200 m2 area.
Rectangle's area is known to be length times breadth.
Therefore;
x*(x-25)=2200 about division x²-25x = 2200
This might be written as x2-25x-2200 = 0, since the park's area is 2200 m2, and its length is.xm.
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Emma practiced piano for 75% of the time that Olivia practiced. Emma practiced for 90 minutes. How long did Olivia practice?
Lauren worked for [tex]$7 / 24$[/tex] th of a day.
What is fraction?An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters. A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.A fraction is a concept where some portions of a full item are expressed in fraction form or division form. For example, if there are 150 students and 98 of them are female, the fraction can be written as follows. Similarly,
24 hours make up the entirety of a day.
In the morning, 1(1/4) hours, which equates to 5/4 hours, in the afternoon, 3 hours, and in the evening, 2 hours and 45 minutes, respectively, which may be stated as
=(2+45/60)
=2+3/4
=11/4hours
So, the total no of hours Lauren practised will be
Total [tex]$=\frac{5}{4}+3+\frac{11}{4}$[/tex]
[tex]$=\frac{5+12+11}{4}$[/tex]
[tex]$=\frac{28}{4}$[/tex]
[tex]$=7$[/tex] hours
Now we can express it in fraction form,
Fraction[tex]$7 / 24$[/tex]
Hence, Lauren worked for [tex]$7 / 24$[/tex]th of a day.
The complete question is,
Lauren practiced playing the piano 1 1/4 hours in the morning, 3 hours in the afternoon, and 2 hours and 45 minutes in the evening. For what fraction of the day did she practice?
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Pls Help
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale of 67 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
Find all points (a, b, c) in space for which the system has at least one solution.
x + 2y + 3z = a
4x + 5y + 6z = b
7x + 8y + 9z = c
The system of equations has at least one solution if the determinant of the coefficient matrix is not equal to zero.
A system of linear equations is a set of two or more linear equations with the same variables. These equations can be solved to find the values of the variables that satisfy all the equations simultaneously.
In this problem, we have a system of three linear equations: x + 2y + 3z = a, 4x + 5y + 6z = b, and 7x + 8y + 9z = c.
The goal is to find all the points (a, b, c) in space for which the system has at least one solution.
To find the points (a, b, c) in space, we need to find out if the system of equations is consistent or inconsistent. If the system is consistent, it means that there exists at least one solution to the system of equations.
This can be determined by finding the determinant of the coefficient matrix, which is the matrix formed by the coefficients of the variables in the system of equations.
If the determinant is not equal to zero, then the system is consistent, and it has at least one solution.
This means that the points (a, b, c) in space are those for which the system of equations is consistent and has a solution.
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a motor has several pieces of shim stock under one corner of its base to level it. they are 0.25 inch, 0.75 inch, 0.065 inch, and 0.010 inch in thickness. how thick is the total shim when they are stacked up?
The total thickness of the shim when they are stacked up under one corner to its base to level it is 1.075 inch.
The smallest of an object's three descriptive dimensions—height, breadth, and length—is referred to as thickness. If a rectangular prism's volume and one side's area are known, you may use those two figures to determine the thickness of the prism. For instance, you can determine the thickness of the cement slab that forms your driveway if you know its volume and the size of its surface area. Simply ensure that the object's area and volume are given in the same units of measure.
There are four shim stock under one corner of its base,
0.25 inch, 0.75 inch, 0.065 inch, and 0.010 inch in thickness
So total thickness be,
0.25 + 0.75 + 0.065 + 0.010
= 1.075 inches.
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Kala wrapped 48 gifts. Kala wrapped 6 times as many gifts as Juan. Let n be the number of gifts that Juan wrapped.
Answer:
Juan wrapped n gifts.
Kala wrapped 6n gifts. (because she wrapped 6 times as many gifts as Juan)
Kala wrapped 48 gifts in total (as stated in the problem)
So, 6n = 48
n = 8 (by dividing both sides by 6)
So, Juan wrapped 8 gifts.
Answer:
8 gifts.
Step-by-step explanation:
If Juan wrapped n gifts, then Kala wrapped 6n gifts because Kala wrapped 6 times as many gifts as Juan.
And we know that Kala wrapped 48 gifts, so we can set up an equation:
6n = 48
To find the number of gifts Juan wrapped, we can divide both sides of the equation by 6:
n = 48/6
n = 8
So Juan wrapped 8 gifts.
Which expressions are equivalent to 10a - 25 + 5b?
The expressions are equivalent to 10a - 25 + 5b are option A, C and D.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
Given that the expression is 10a - 25 + 5b.
For the given options, simplify each individual expression to determine the answer:
A. 5(2a−5+b)
= 10a - 25 + 5b
Equivalent
B. -2(-5a-25+5b)
= 10a + 50 - 10b
Not equivalent
C. 10×(a − 2.5 + 0.5b)
= 10a - 25 + 5b
Equivalent
D. (−2a + 5 − b)⋅(−5)
= 10a - 25 + 5b
Equivalent
E. −10⋅(−a−2.5−0.5b)
= 10a + 25 + 5b
Not equivalent
Hence, the expressions are equivalent to 10a - 25 + 5b are option A, C and D.
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Write a numerical tatement to repreent the problem. Then implify the numerical expreion to anwer the quetion. After dieting for 30 day, Ignacio ha lot 12 pound. What number decribe hi average weight change per day?
The number which describes the average change in weight per day of Ignacio is equal to 0.4 pounds per day.
Number of days Ignacio done the dieting is equal to 30 days
Total weight lost by Ignacio in 30 days = 12 pounds
Let 'x' be the change in weight per day of Ignacio after dieting.
Weight lost in 30 days = 12 pounds
Average weight change per day is:
⇒ 1 day = ( 12 / 30 ) pounds per day
⇒ 1 day = ( 2/ 5 ) pounds per day
⇒ 1 day = ( 0.4 ) pounds per day
Therefore, the average weight change per day by Ignacio is equal to 0.4pounds per day.
The above question is incomplete, the complete question is:
Write a numerical statement to represent the problem. Then simplify the numerical expression to answer the question. After dieting for 30 day, Ignacio has lost 12 pound. What number describe his average weight change per day?
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A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon
of gas. During one particular week, the two cars went a combined total of 2475 miles, for a total gas consumption of 65 gallons. How many
gallons were consumed by each of the two cars that week?
First car: ___ gallons
Second car:___ gallons
Answer:
first car: 25 gallons
second car: 40 gallons
Step-by-step explanation:
1) 35 miles/gallon consumption=distance/volume
2) 40 miles/gallon distance=consumption*volume
2475 miles = d1 + d2
= 35*v1 + 40*v2
v1 + v2 = 65
v2 = 65 - v1
2475 = 35*v1 + 40*(65 - v1)
2475 = 35*v1 + 2600 - 40*v1 /-2600
-125 = -5*v1
v1 = 25 gallons
v2 = 65 - v1
v2 = 40 gallons
A 40% sugar solution is added to an 85% sugar solution to create 1000 mL of a 60% solution. How
much of each solution is used?
Number of ml of 40% sugar = x = 1000mL
Number of ml of 85% sugar used = y = 800mL
How to find the value of x?A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x. To determine the answer, simplify the values.
Let the number of ml of 40% sugar be x and 85% sugar used be y
System of equations is given as:
x + y = 1800mL ....... (1)
x = 1800 - y
40% × x + 85% × y = 60% × 1800mL
0.4x + 0.85y = 1080.... (2)
We substitute 1800 - y for x in (2)
0.4(1800 - y) + 0.85y = 1080
simplifying the above equation, we get
720 - 0.4y + 0.85y = 1080
- 0.4y + 0.85y = 1080 - 720
0.45y = 360
y = 360/0.45
y = 800mL
Solving for x
x = 1800 - y
substitute the value of y in the above equation, we get
x = 1800 - 800
x = 1000mL
Therefore, the number of ml of 40% sugar = x = 1000mL
Number of ml of 85% sugar used = y = 800mL.
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pls help meee i dont understand this
Answer:
I think the y= (-7)
PLEASE SHOW WORK…… I WILL GIVE BRAINLIEST
Answer:
11. 15°
I haven't learned how to find sides with only one side given yet I'm so sorry!!
Which list of numbers is ordered from least to greatest?
Answer: I want to say is this one: -6, -3, 2, 5
Step-by-step explanation: That one just look like its the one because the first option it goes from greatest to least and then repats itself so i know if not that one. then the next one also looks wrong. I saw is the 3rd one.
Find the length of the circumferences of the circles whose diameters is 49
The diameters is 49 be the circumference of the circle is 154 cm.
What is meant by circumference of the circle?When it comes to geometry, a circle's or ellipse's circumference is its perimeter. In other words, the circumference would be the length of the circle's arc if it were opened out and straightened out to a line segment. The radius surrounding any closed figure is known as its perimeter more generally.
The distance in a straight line around a circle is known as its circumference. Or, to put it another way, the circumference of a circle is the length of a straight line formed by opening up the circle.
A circle's perimeter is referred to as its circumference. By calculating the length it would take to walk around the world, we may determine the size of the earth.
Given : Diameter of the circle [tex]$=49 \mathrm{~cm}$[/tex] and value of [tex]$\pi=\frac{22}{7}$[/tex]
The circumference of the circle is given by [tex]$C=2 \pi r$[/tex] or in the form of a diameter the circumference of the circle is [tex]$C=\pi d$[/tex]
Now, we have given [tex]$\mathrm{d}=49 \mathrm{~cm}$[/tex] and value of [tex]$\pi=\frac{22}{7}$[/tex]
Substitute the value in the formula,
[tex]$& C=\pi d \\[/tex]
substitute the values in the above equation, we get
[tex]$& C=\frac{22}{7} \times 49 \\[/tex]
simplifying the equation, we get
C = 22 × 7
C = 154 cm
Therefore, the circumference of the circle is 154 cm.
The complete question is:
Find the circumference of circle whose diameter is 49cm, pi = 22 by 7
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56% of men do not look forward to going clothes shopping for themselves. You randomly select 8 men. Find the probability that the number of men who do not look forward to going clothes shopping for themselves is EXACTLY FIVE.
Salut/Hello!
Answer: 0.625
Step-by-step explanation:
The probability will be 5 men in a selection of 8 random men
so 5/8 is equal to 0.625 which shows the probability.
I hope it was helpful! :]
The vertices of a triangle are located at (-4, 1). (0, -2) and (3, 2). Select the correct option from the drop-down to complete the sentence.
The triangle is
Answer:
Isosceles Right Triangle.
Step-by-step explanation:
Let the points be A, B and C where A = (-4, 1), B = (0, -2) and C = (3, 2)
Slope of AB = (-2-1)/(0- -4) = -3/4
and its length = √(-2-1)^2 + (0- -4)^2 = √25 = √5.
Slope of BC = (2 - -2)/(3 - 0) = 4/3
and its length = √(2 - -2)^2 + (3)^2 = √25 = √5
Slope of AC = ((2-1)/3- -4) = 1/7
and its length = √((4--4)^2 + (2-1)^2 = √17
The product of the slopes of AB and BC = -3/4 * 4/3 = -1 so
m < ABC = 90 degrees.
Also, the sides AB and BC are equal in length
So. the Triangle is an isosceles right triangle.
Fill in the blanks
Divide
A.5
B.54
C.546
Goes in the _____ Place
A.hundreds
B.tens
C.ones
Answer:
hundreds
Step-by-step explanation:
Triangle ABC has sides AB= 17cm, AC= 13cm and BC= 23cm, as shown
below.
13 cm
23cm
17 cm
Diagram not drawn to scale
Calculate the size of angle CAB to the nearest integer.
(3 marks)
Answer:
[tex]\boxed{m \angle CAB =99^{\circ}}[/tex]
Step-by-step explanation:
We can use the law of cosines to determine measure of ∠CAB
If a, b and c are the three sides of a triangle and C is the angle opposite side c then the law of cosines says
c² = a² + b² - 2ab cos(C)
Here we are asked to find m∠CAB
The side opposite ∠CAB is BC which is 23 cm long. This is c in the formula
The other two sides, a and b are 13 cm and 17 cm
Applying the formula, using C to represent m∠CAB
[tex]23^2=\:13^2+\:17^2-\:2\:\cdot 13\cdot 17\cdot \cos \left(C\right)[/tex]
First switch sides:
[tex]13^2+17^2-2\cdot \:13\cdot \:17\cos \left(C\right)=23^2[/tex]
[tex]\rightarrow 69+289-442\cos \left(C\right)=529\\\\\rightarrow 458 -4 42\cos \left(C\right) = 529\\[/tex]
[tex]\rightarrow -442\cos \left(C\right) = 529-458\\\\\rightarrow -442\cos \left(C\right) = 71\\\\[/tex]
[tex]\rightarrow \cos \left(C\right)=-\dfrac{71}{442}\\\\\rightarrow \cos \left(C\right) = - 0.16063\\\\[/tex]
[tex]\rightarrow C = \cos^{-1} (-0.16063)[/tex]
[tex]\rightarrow C = 99.2437^{\circ}[/tex]
Rounded to the nearest integer, this would become
[tex]\rightarrow C = \boxed{99^{\circ}}[/tex]
6²- (8 x 3)+2² (7 x 3)
Answer:96
Step-by-step explanation:36-8(-3)=9
a student was adding the numbers 1, 2, 3, 4, and 5. they wrote: assuming these numbers are adjectives modifying the same noun, discuss what is incorrect about their equation.
The student's equation is incorrect because it contains only one part, and an equation requires two parts to be valid.
An equation is a statement that two things are equal, and it must contain two different parts. A single number, such as the five numbers that this student used, can't make an equation. The student was using the numbers as adjectives, which modify nouns, but adjectives can't be added to make an equation.
In order to have a proper equation, the student must have two parts, each with its own number or variable. For example, the student could have used 2 + 3 = 5, which is an equation with two parts.
The left side of the equation (2 + 3) is the sum of the two numbers, and the right side of the equation (5) is the result of that sum.
This equation would be correctly written and would produce the correct result.
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A road i inclined at an angle of 3°. After driving 5403 feet along thi road, find the driver' increae in altitude. Round to the nearet foot. Ue ine coine and tangent
The increase in driver's altitude will be 283 feet based on the mentioned angle of elevation and distance travelled.
The road will represent hypotenuse and the altitude will represent the height of the triangle. Based on this, the formula to be used for calculation is -
sin theta = perpendicular ÷ hypotenuse, where theta is the angle of elevation.
sin 3° = altitude ÷ 5403
Rewriting the equation
Altitude = sin 3 × 5403
Keep the value of sine angle
Altitude = 0.05 × 5403
Performing multiplication
Altitude = 282.7 feet
Rounding off we get = 283 feet.
Thus, the altitude will be 283 feet.
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true or false (if false, explain why)? ||αu v||2 = α 2 ||u||2 ||v||2 , where || · || denotes euclidean norm, α is a scalar, u and v are vectors
The equation ||αu v||^2 = α^2 ||u||^2 ||v||^2 does not hold in general.
Therefore the answer is False.
The left side of the equation is the square of the Euclidean norm of the product of a scalar and two vectors, which is ||αu v||^2 = (αu)^T (αu) = α^2 u^T u v^T v = α^2 ||u||^2 ||v||^2. The Euclidean norm, also known as the L2 norm, is a measure of the magnitude of a vector in a multi-dimensional space. It is defined as the square root of the sum of the squares of the vector's components.
The right side of the equation is the product of the squares of the norms of two vectors, which is not equal to the square of the norm of their product in general.
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Write your own word problem that involves a multistep linear equation. Then translate your problem into its resulting math equation. What steps would you then follow to solve for the variable? Be sure to list your steps in the correct order.
Word problem with steps for linear equation is given below.
What is linear equation?An equation containing variables with its highest power as one is called linear equation.
Question:
Mother is as five times as old as daughter. After 3 years, the mother will be four four times as old as her daughter. What are their present age?
Solution
Let x represents the age daughter.
Mother is as five times as old as daughter. i.e., 5x
After 3 years, the mother will be four four times as old as her daughter.
⇒5x+3=4(x+3)
5x+3=4x+12
⇒5x-4x=12-3
⇒x=9.
Their present age of daughter is 9 and mother is 5*9=45.
Hence, present age of mother and daughter is 45 and 9 respectively.
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if the mean of a set of six numbers is 15, and the given numbers in the set are 5, 14, 10, 22, and 23, what is the value of the sixth number in the set? : * a) 0 b) 16 c) 22 d) 24
The value of the sixth number in the set of numbers is 16
The correct answer is an option (b)
Let us assume that 'p' be the value of the sixth number in the set.
So, the set of numbers is { 5, 14, 10, 22, 23, p}
The mean of a set of six numbers is 15.
We know that we can find the mean or average of a data set by adding all numbers in the data set and then dividing by the total number of values in the set.
Let m be the mean of set of numbers { 5, 14, 10, 22, 23, p}
So, m = 15
Here, the total number of values in set = 6
Using the formula for mean,
m = (5 + 14 + 10 + 22 + 23 + p)/6
15 = (5 + 14 + 10 + 22 + 23 + p)/6
15 × 6 = (5 + 14 + 10 + 22 + 23 + p)
90 = 74 + p
90 - 74 = 74 + p - 74
p = 16
Therefore, the sixth number is 16
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Use the Binomial Theorem and substitution to expand each Binomial. Show your step.
A) (3x+y)^4
B) (x-2y)^6
The value of the equation from binomial expansion is
a) A = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴
b) B = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶
What is Binomial Expansion?The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
A = ( 3x + y )⁴
On simplifying the equation , we get
From binomial expansion , ( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Substituting the values in the equation , we get
( 3x + y )⁴ = ⁴C₀ ( 3x )⁴ ( y )⁰ + ⁴C₁ ( 3x )³ ( y ) + ⁴C₂ ( 3x )² ( y )² + ⁴C₃ ( 3x ) ( y )³ + ⁴C₄ ( 3x )⁰ ( y )⁴
On further simplification , we get
( 3x + y )⁴ = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴
Hence , the equation is A = 81x⁴ + 108x³y + 54x²y² + 12xy³ + y⁴
b)
B = ( x - 2y )⁶
On simplifying the equation , we get
From binomial expansion , ( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Substituting the values in the equation , we get
( x - 2y )⁶ = ⁶C₀ ( x )⁶ ( -2y )⁰ + ⁶C₁ ( x )⁵ ( -2y ) + ⁶C₂ ( x )⁴ ( -2y )² + ⁶C₃( x )³(-2y)³ + ⁶C₄ ( x )² ( -2y )⁴ + ⁶C₅ ( x )¹ ( -2y )⁵ + ⁶C₆ ( x )⁰ ( -2y )⁶
On further simplification , we get
( x - 2y )⁶ = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶
Hence , the equation is
B = x⁶ - 12x⁵y + 60x⁴y² - 160x³y³ + 240x²y⁴ - 192xy⁵ + 64y⁶
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if 20 men can complete a piece of work in 16 days how many men should be exiled to finish the work in 20 days?
Answer: 16 men should be assigned to finish the work in 20 days.
Step-by-step explanation:
Let's assume that the number of men needed to complete the work in 20 days is y. Then, the rate of work done by each man is given by 20/16=5/4 units of work per day.
So, the rate of work done by y men is given by 5/4 * y units of work per day.
Since the total work is constant, we have 20 men * 20/16 units of work per day = y men * 5/4 units of work per day.
Dividing both sides by 5/4, we get:
y = 20 * 20/16 / (5/4) = 20 * 4/5 = 16 men.
Therefore, 16 men should be assigned to finish the work in 20 days.
For the following exercises, find the level curves of each function at the indicated value of c to visualize the given function.14. z(x, y) = y²x², c = 115. z(x, y) = y²x², c = 416. g(x, y) = x² + y²; c=4,c=9
The level curve for the function z(x, y) = y²x², at the value c = 115 are the points that satisfy the equations y = (√115)/x and y = -(√115)/x .
The Level Curves of a function z(x,y) at a constant value "c" are defined as the set of points (x,y) where z(x,y) = c.
So, to find the level curves of z(x,y) = y²x² at the indicated value of c = 115, we need to solve the equation y²x² = 115 for x and y.
Starting with y²x² = 115,
Simplifying ,
we get ;
⇒ y² = 115/x²
Taking the square root(√) of both sides:
that means ⇒ |y| = sqrt(115/x²) ;
Since y can be either positive or negative, we have two equations:
⇒ y = sqrt(115/x²) ⇒ y = -sqrt(115/x²)
⇒ y = (√115)/x ⇒ y = -(√115)/x .
Therefore , the level curve for c = 115 is the set of points that satisfy either of these two equations.
The given question is incomplete , the complete question is
Find the level curves of each function at the indicated value of c to visualize the given function. z(x, y) = y²x², c = 115 .
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4 of 8 Work out the area of the shaded shape. 5m 12m 8m 9m The diagram is not drawn to scale. 2
The area of the shaded shape is 60 [tex]m^{2}[/tex].
What is the area of shaded shape?This question uses the area formula for rectangles, which states that the area of a rectangle is equal to its length multiplied by its width.
The formula for the area of a rectangle is A = lw, where l is the length of the rectangle and w is the width of the rectangle
To work out the area of the shaded shape, we need to calculate the area of the rectangle (5m x 12m) and subtract the area of the smaller rectangle (8m x 9m).
The area of the rectangle = 5m x 12m = 60[tex]m^{2}[/tex]
The area of the small rectangle = 8m x 9m = 72[tex]m^{2}[/tex]
Therefore, the area of the shaded shape = 60[tex]m^{2}[/tex] - 72[tex]m^{2}[/tex] = -12[tex]m^{2}[/tex]
The answer is 60[tex]m^{2}[/tex].
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scalcet9 10.2.033. my notes ask your teacher practice another at what point(s) on the curve x = 9t2 2, y = t3 − 9 does the tangent line have slope 1 2 ?
The tangent line to the curve x = 9t^2 + 2, y = t^3 − 9 at the point (83, 18) has a slope of 1/2.
The slope of the tangent line to a curve at a point (x₀, y₀) can be found by taking the derivative of the equation for the curve at that point and evaluating it at x₀.
Given the curve x = 9t^2 + 2, y = t^3 − 9, we can find the derivative with respect to t, which is the slope of the curve at any point (x, y).
dx/dt = 18t
dy/dt = 3t^2
So, the slope of the tangent line at point (x₀, y₀) on the curve is given by:
m = dy/dt * (dt/dx) = (3t^2) * (1/18t) = (1/6) * t
To find the point(s) on the curve where the tangent line has slope 1/2, we set m = 1/2 and solve for t:
(1/6) * t = 1/2
t = 3
Substituting t = 3 back into the equation x = 9t^2 + 2, y = t^3 − 9, we get the point (x₀, y₀) = (83, 18).
--The question is incomplete, answering to the question below--
"at what point(s) on the curve x = 9t^2 + 2, y = t^3 − 9 does the tangent line have slope 1/2 ?"
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