Existence and uniqueness of solutions are guaranteed for all of the given initial value problems.
1. dy/dx = 2x^2y^2: y(1) = -1
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, -1), the function f(x, y) = 2x^2y^2 is continuous and the partial derivative ∂f/∂y is also continuous.
2. dy/dx = x ln y: y(1) = 1
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 1), the function f(x, y) = x ln y is continuous and the partial derivative ∂f/∂y is also continuous.
3. dy/dx = cubicroot y: y(0) = 1
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = cubicroot y is continuous and the partial derivative ∂f/∂y is also continuous.
4. dy/dx = cubicroot y: y(0) = 0
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 0), the function f(x, y) = cubicroot y is continuous and the partial derivative ∂f/∂y is also continuous.
5. dy/dx = Squareroot x- y: y(1) = 2
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 2), the function f(x, y) = Squareroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.
6. dy/dx = Squareroot x - y: y(2) = 2
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (2, 2), the function f(x, y) = Squarroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.
7. dy/dx = Squareroot x - y: y(2) = 1
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (2, 1), the function f(x, y) = Squareroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.
8. y dy/dx = x - 1: y(0) = 1
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = x - 1 is continuous and the partial derivative ∂f/∂y is also continuous.
9. y dy/dx = x - 1: y(1) = 0
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 0), the function f(x, y) = x - 1 is continuous and the partial derivative ∂f/∂y is also continuous.
10. dy/dx = ln(1 + y^2): y(0) = 0
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 0), the function f(x, y) = ln(1 + y^2) is continuous and the partial derivative ∂f/∂y is also continuous.
11. dy/dx = x^2 - y^2: y(0) = 1
Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = x^2 - y^2 is continuous and the partial derivative ∂f/∂y is also continuous.
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Solve the system of equations using elimination. −2x + 3y = 15 x + y = 10 a. (2, 8)b. (3, 7) c. (6, 9) d. (9, 11)
The system of equations is:
-2x + 3y = 15
x + y = 10
We can use elimination to solve this system. One way to eliminate x is to multiply the first equation by -2 and add it to the second equation:
(-2) * (-2x + 3y = 15) + (x + y = 10)
4x - 6y + x + y = 15 + 10
5x - 6y = 25
5x = 25 + 6y
x = 5 + (6/5)y
Substituting x back into the second equation, we get:
x + y = 10
5 + (6/5)y + y = 10
Combining like terms:
y = 10 - 5 - (6/5)y
(11/5)y = 15 - 5
(11/5)y = 10
y = 10 * (5/11)
y = 10/11
Finally, substituting x = 5 + (6/5)y back into the equation we found earlier:
x = 5 + (6/5)y
x = 5 + (6/5) * (10/11)
x = 5 + (60/55)
x = 55/11 + 60/55
Combining like terms:
x = (55 + 60) / 55
x = 115/55
The solution to the system of equations is (x, y) = (115/55, 10/11).
So the answer is (d) (9, 11).
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Find missing length for similar triangle
On solving the provided question we can say that since it is given that triangles are similar and 1/2 of each other so DE will be = 13
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
since it is given that triangles are similar and 1/2 of each other
so DE will be = 13
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Write the equation of a line that is perpendicular to the line y = 3x +7 and has an
x-intercept of 12.
The line y = - (1 / 3) · x + 4 is a equation perpendicular to line y = 3 · x + 7.
How to derive the equation of a line perpendicular to another line
Algebraically speaking, lines are described by the following equation:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variable.y - Dependent variable.And two lines are perpendicular to each other if the product of their slopes is equal to:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.Now we proceed to determine the equation of the perpendicular line. First, write the slope of the original line:
m = 3
Second, calculate the slope of the perpendicular line:
m' = - 1 / 3
Third, find the y-intercept:
b = y - m' · x
b = 0 - (- 1 / 3) · 12
b = 4
Fourth, write the resulting equation of the line:
y = - (1 / 3) · x + 4
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9. Consider the following end behavior for a polynomial function.
I will give u 90 points, please I'm desperate...and please give the correct answer
Answer:
Jeremy is in the top 2%-----------------------------
Given:
Mean μ = 3.26,Standard deviation σ = 0.17,The score of x = 3.72.Find corresponding z-score:
z = (x - μ)/σz = (3.72 - 3.26)/0.17 = 2.76 (rounded)Find the percent value of z-score using z-table:
2.76 → 99.71%Jeremy is in the top 2% so he will receive a certificate.
Given the polynomial P(x) = 2x3+ 9x2 + 7x – 6, if (x+ 3) is one of its factors, then what are the other two factors of P(x)?
The other two factors of given polynomial are (x+2) and (2x-1).
What is polynomial?A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction Using the sum of powers in one or more variables multiplied by coefficients, a polynomial is a type of mathematical expression.
Given that x+3 is a factor of polynomial 2x³ + 9x² + 7x - 6. So that
2x³ + 9x² + 7x - 6
⇒ 2x³ + 6x² + + 3x² + 7x - 6
⇒ 2x²(x+3) + 3x² + 7x - 6
⇒ 2x²(x+3) + 3x² + 9x - 2x - 6
⇒ 2x²(x+3) + 3x(x+3) - 2(x+3)
⇒ (x+3)(2x² + 3x - 2)
⇒ (x+3)(2x² + 4x - x - 2)
⇒ (x+3)[2x(x+2) -1(x+2)]
⇒ (x+3)(x+2)(2x-1)
Hence, Factors of given expression are (x+3)(x+2)(2x-1)
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determine whether the statement is true or false. lim x→1 x2 4x − 5 x2 3x − 4 = lim x→1 x2 4x − 5 lim x→1 x2 3x − 4
The statement is false because the limit of the denominator is equal to zero.
In this case, the limit of the denominator (lim x→1 x2 3x − 4) is equal to zero, so this statement is false.
The limit of the quotient of two functions is equal to the quotient of their limits only when the limit of the denominator is not equal to zero.
In this case, the limit of the denominator (lim x→1 x2 3x − 4) is equal to zero, so this statement is false.
The statement is false because the limit of the denominator is equal to zero.
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find the length and breadth of the rectangle whose area is 6x^2-29x+30. Also find its perimeter.
Answer: l = (2x-3) ; b = (2x-10) ; Perimeter = (10x - 26)
Step-by-step explanation:
l * b = area
area = 6x^2 - 29x + 30
l * b = 6x^2 - 29x + 30
Split the middle term of 6x^2 - 29x + 30
6x^2 - 20x - 9x + 30
2x(3x-10) -3(3x-10)
(2x-3) (3x-10)
l = (2x-3)
b = (3x-10)
Perimeter of a Rectangle = 2(l+b)
= 2 ((2x-3) + (3x-10))
= 2( 2x-3 + 3x-10 )
= 2 (5x -13)
= (10x - 26)cm
For each of the following situations, identify the measure of central tendency (mean, median, or mode) that would provide the best description of the "average" or most representative score. Please explain your choice: a. A researcher asks each individual in a sample of 50 adults to name his/her favorite season (summer, fall, winter, spring). b. An insurance company would like to determine how long people remain hospitalized after a routine appendectomy. The data from a large sample indicate that most people are released after 2 or 3 days but a few develop infections and stay in the hospital for weeks c. A teacher measures scores on a standardized reading test for a sample of children from a middle-class, suburban elementary school.
The measure of central tendency best suited for the given situation are mode (a), median (b) and mean (c) respectively.
a. The measure of central tendency best suited for this situation is the mode, because it would provide the most representative score of the favorite season. The mode is the most commonly occurring value in a set of data, so it would be useful for determining the most popular season among the sample of 50 adults.
b. The measure of central tendency best suited for this situation is the median, because it would provide the most representative score of the length of stay in the hospital after a routine appendectomy. The median is the middle value in a set of data when the values are arranged in numerical order, and it is not affected by very high or very low values (as the mean is). Therefore, it would be the most useful for determining the average length of stay in the hospital for this particular sample.
c. The measure of central tendency best suited for this situation is the mean, because it would provide the most representative score of the standardized reading test scores. The mean is the average of all the values in a data set, so it would be useful for determining the average score of the sample of children from the middle-class, suburban elementary school.
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Peyton is a waitress at a restaurant. Each day she works, Peyton will make a guaranteed wage of $30, however the additional amount that Peyton earns from tips depends on the number of tables she waits on that day. From past experience, Peyton noticed that she will get about $9 in tips for each table she waits on. How much would Peyton expect to earn in a day on which she waits on 16 tables? How much would Peyton expect to make in a day when waiting on
Answer:
Around $174
Step-by-step explanation:
Correct me if I'm wrong
9x16=144
144+30=174
Mandy rode her bicycle 1/2 of a mile from her house to the park. Then she rode 1/8 of a mile from the park to the library. How many miles did Mandy ride in all?
Answer:
0.625 miles
Step-by-step explanation:
1/2 of a mile is 880 yards and 1/8 of a mile is 220. 880+220=1100. 1100 yards is 0.625 miles.
If the point P( 9/10, y) is on the unit circle in quadrant IV, then y
=
A unit circle has a radius of 1, so r = 1. The point P(9/10, y) in the IV quadrant will have a positive x-value and a negative y-value.
How to solve the problem?Using the Pythagorean theorem we know that, x² + y² = r², in a Cartesian coordinate system. We can solve for y by rearranging the formula, r² - x2 = y², or y = ±√(r² - x²).
y = ±√(r² - x²)
y = ±√([1]² - [9/10]²)
Simplify the expression we have
y = ±√(1 - 81/100)
y = ±√(1-0.81)
y = ±√0.19, we choose the negative for quadrant IV.
y = -√0.19
y = -0.4359
Sin -0.4359 = 26 degrees in the IV quadrant, = 360-26 =334 degrees
CosA = 0.4359 in the Iv quadrant is positive we chose the positive figure 64 degrees
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A total cost of attending a state university is 19,700 for this year
a student grandparents will pay of this half
an athletic scholarship will pay another 5,000
Which amount is closest to the minimum that the student will need to save every month in order to pay off the remaining cost at the end of 12 months
Step-by-step explanation:
Half is paid by grandparents :
[tex] \frac{19700}{2} = 9850[/tex]
Therefore, amount paid by scholarship and grandparents:
[tex]9850 + 5000 = 14850[/tex]
Find the amount needed to pay :
[tex]19700 - 14850 = 4850[/tex]
then the student need to save per month :
[tex]4850 \div 12 = 404.167[/tex]
Therefore the closest minimum is 405 per month
The member of the art club are making keychain that require 18 bead apiece. The art club advier brought a bag with 250 bead for them to ue. If there are 70 bead left in the end, how many keychain were made?
The member of the art club are making keychain that require 18 bead apiece and the art club adviser brought a bag with 250 bead for them to use, if there are 70 bead left in the end, then 5 keychain were made.
The member of the art club are making keychain that require 18 bead apiece.
The art club adviser brought a bag with 250 bead for them to use.
Let the member of the art club are make x keychain.
So the number of beads used in making x keychains = 18x
The left beads are 70.
So the total beads = 18x + 70
But they have total 250 beads.
So the equation should be:
18x + 70 = 150
Subtract 70 on both side, we get
18x = 80
Divide by 18 on both side, we get
x = 5
So the member of the art club were made 5 keychains.
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11. Consider the right triangle below in which a = 4 and b = 8. (3 points)
a. What is the value of c written in simplified radical from?
b. What is the value of c rounded to the nearest hundredth?
The value of c is given as follows:
a) Radical form: [tex]c = \sqrt{80}[/tex]
b) Rounded to the nearest hundredth: 8.94.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For this problem, we have that:
a and b are the sides.c is the hypotenuse.Applying the Pythagorean Theorem, the value of c is obtained as follows:
c² = a² + b²
c² = 4² + 8²
c² = 80
[tex]c = \sqrt{80}[/tex]
c = 8.94 -> nearest hundredth = two decimal digits.
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a sphere has a radius of 6.69 meters. what is the cross-sectional area that passes through its center?
The cross-sectional area of a sphere that passes through its center is a circle with a diameter equal to the diameter of the sphere. In this case, the diameter of the sphere is 6.69 meters * 2 = 13.38 meters.
The formula for the area of a circle is: A = π * r^2, where r is the radius.
Therefore, the cross-sectional area of the sphere that passes through its center is: A = π * (13.38/2)^2 = π * (6.69)^2 = 136.57 square meters.
A sphere is a three-dimensional shape that has a uniform, rounded surface that is symmetrical in all directions. When you cut a sphere through its center, you get a cross-sectional area that is a circle.
This is because a sphere can be thought of as a set of circular cross-sections that are concentric with each other and with the center of the sphere.
The cross-sectional area of the sphere that passes through its center is called the central cross-section of the sphere. It has the same diameter as the sphere itself and its area can be calculated using the formula for the area of a circle: A = π * r^2, where r is the radius of the circle.
In this case, the sphere has a radius of 6.69 meters, which means that its diameter is 6.69 * 2 = 13.38 meters.
The radius of the central cross-section of the sphere is half of the diameter, which is 6.69 meters. Therefore, the area of the central cross-section of the sphere is: A = π * (6.69)^2 = 136.57 square meters.
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2+2=60,30+30=4 how say me?
The value of the additions are
2 + 2 = 4 30 + 30 = 60What is addition operation?The addition operation is a mathematical operation that combines two or more numbers to produce a new number.
It is symbolized by the "+" sign and can be thought of as finding the total of two or more values.
In the problem, we have two numbers, 2 and 2, 30 and 30
the addition operation would give us 2 + 2 = 2, and 30 + 30 = 60
meaning that the sum of 2 and 2 is 4. and the sum of 30 and 30 is 60
Addition is one of the basic arithmetic operations and is essential for solving many mathematical problems.
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it is easier to get a precise estimate of the binomial parameter when π is near 0 or 1 than when it is near 1/2. explain why.
yes ,it is easier to get a precise estimate of the binomial parameter when π is near 0 or 1 than when it is near 1/2
in binomial distributions, we have parameters for the probability of success or failure (either of the two conditions that the variable may take), and for the number of trials, which turn out to be easier to estimate for extreme values.
Due to the estimator's decreasing standard error, it is simpler to estimate a binomial parameter when it is closer to 0 or 1 than when it is 0.50. Since the latter has p(1 - p) in its numerator, a value close to 0 or 1 reduces the standard error to almost zero. It is simpler to estimate a binomial parameter correctly when the standard error of the estimate is exceptionally low. It is more challenging to estimate when the parameter is 0.50, which reflects the highest amount of inaccuracy. As either event is equally likely, a value of 0.50 can be thought of as introducing greater ambiguity. When it's far away from 1 or 0, it appears to be much more likely that one of the answers is correct.
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Describe a transformation that maps the blue figure, ABC, to the red figure, A'B'C'.
One possible transformation is a , followed by a
One possible transformation is a Rotation, followed by a Translation.
What is transformation?There are rigid and non-rigid transformations (where the preimage's size or shape is left unaltered) (where the size is changed but the shape remains the same). These are the fundamental principles that this idea abides by. It is a simple method for transforming 2D shapes.
By separating between planar transformations and spaces, the transformation can be grouped according to the dimensions of the operand sets. They can be categorised based on their characteristics as well.
An object's image will resemble its pre-image when its size is changed, whether for larger or smaller objects. Dimensions are proportionally equal for the similar figures.
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Complete question:
Robin saves $500 at a yearly simple interest rate of 4% what is the total amount of money she had after 20 years
Expected Total Amount = $900
The simple interest formula, I = PRT (P×R×T)
where, P = principal amount
R = rate of interest
T = time period (years)
so, I = PRT
I = 500×0.04×20
I = 400
By adding the interest (400) to the principal amount (500) , hence she will have $900 in 20 years.
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The length of a rectangle is 4 ft longer than its width.
If the perimeter of the rectangle is 36 ft, find its area.
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
A factory makes 3.5 silk flowers every second.
Each flower uses 60.3 cm of silk.
How many metres of silk are used in one minute?
The amount of silk used in one minute by the factory was 126
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
A factory makes 3.5 silk flowers every second.
60 second = 1 minute
Amount of silk made in one minute = 3.5 silk flowers every second * 60 seconds = 210 silk flowers
Each flower uses 60.3 cm of silk.
Hence, for 210 silk flowers:
Amount of silk used = 210 silk flowers * 60 cm of silk = 12600 cm of silk
100 cm = 1 m
12600 cm = 12600 cm * 1 m per 100 cm = 126 m
The amount of silk used was 126
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After a dicount of 25 percent the aving on a pair of roller blade wa $12. 0. What wa the ale price?
The sales price is $36.
We have been told that the discount on the pair of rollerblades is 25%. It has also been told that the discounted price is $12.0. Now, first, we need to find the original price of the rollerblades. Let the original price of the rollerblades be = $x.
Now - x/100 * 25 = $12
- x/100 = 12/25
- 25x = 1200
- x = $48
Now, in order to find the sale price, we need to -
= Original price - Discounted price
= $48 - $12
= $36
Hence, the price of the rollerblades after putting in a 25% discount is $36.
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The local newspaper has letters to the editor from 60 people. If this number represents 8% of all of the newspaper's readers, how many readers does the newspaper have?
There are the newspaper has 750 readers.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.
If the number of letters to the editor is 60, and it represents 8% of all of the newspaper's readers, we can find the total number of readers by dividing the number of letters by the percentage as a decimal:
60 / 0.08 = 750
So the newspaper has 750 readers.
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The total number of readers the newspaper have is 750.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The local newspaper has letters to the editor from 60 people and it is 8% of the total readers.
let, The total number of readers be 'x'.
Therefore, 60 is 8% of 'x' which can be numerically expressed as,
(8/100)×x = 60.
0.08x = 60.
x = 60/0.08.
x = 750.
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Make x the subject, y= 1/2x + 6
Work Shown:
y = (1/2)x + 6
y-6 = (1/2)x
2(y-6) = x
x = 2(y - 6)
x = 2y - 12
Which values are in the solution set of the compound inequality? Select two options. 4(x + 3) ≤ 0 or x+1>3 –6 –3 0 3 8
The set of solutions are [-6,-3,3,8,10] for the inequality
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequalities are 4(x + 3) ≤ 0 or x+1>3
we know that, In this system of inequalities, for a value to be the solution of the system, it is enough that it satisfies at least one of the two inequalities.
x=-6
Substitute the value of x=-6 in the inequality 1
4(-6+3)≤ 0
-12≤ 0
The value of x=-6 is a solution of the compound inequality-----> It is not necessary to check the second inequality, because the first one satisfies
Substitute the value of x=-3 in the inequality 1
0≤ 0
The value of x=-3 is a solution of the compound inequality
Substitute the value of x=3 in the inequality 1
The value of x=3 is a solution of the compound inequality
The value of x=8 is a solution of the compound inequality
The value of x=10 is a solution of the compound inequality
Hence, the set of solutions are [-6,-3,3,8,10] for the inequality
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Select the correct answer
Which area should have the lowest temperatures?
OA. 1
OB. 2
0 с. 3
OD. 4
ڈے
Answer:
Option A: 1
Step-by-step explanation:
The higher the altitude, the lower the temperature.
The highest point is the peak which corresponds to Area 1
So area 1 has the lowest temperatures
Option A
Answer:
1
Step-by-step explanation:
The higher the atmosphere the lower the temperature which is why you often have snow on top of mountains and clouds form up so high
Simplify: 6(x + 5) =
Answer:
You want to multiply the 6 to the numbers inside the parythesis:
6 * x = 6x
6 * 5 = 30
6x + 30
Step-by-step explanation:
Hope it helps! =D
Answer:
6x + 30
Step-by-step explanation:
1. 6(x + 5)
2. 6x+30
a ramp begins at the end of a sidewalk and rises 15 feet verticall feet over a horizzontal distance of 150 feet. find the legnth of the ramp to the nearest thenth of a foor.
Rounding to the nearest tenth of a foot, the ramp length is 150.7 feet.
To find the length of the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ramp) is equal to the sum of the squares of the other two sides (the rise and the run).
We have the rise (15 feet) and the run (150 feet), so we can use the formula: ramp length = √(rise^2 + run^2)
Plugging in the values, we have: ramp length = √(15^2 + 150^2) = √(225 + 22500) = √22725 = 150.7 feet
Therefore, rounding to the nearest tenth of a foot, the ramp length is 150.7 feet.
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I added a picture below
For each of the equations;
a) Two solutions
b) Two solutions
c) Two solutions
d) Two solutions
How many solutions does the equation have?In mathematics, the number of solutions that the equation would have has a lot to do with the kind of equation that we are dealing with. If the equation that we are dealing with is a linear equation then it would have only one solution.
In the same way, if what we have is a quadratic equation of a system of linear equations that have two variables then we are going to have two solutions for the equation.
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