PLEASE HELP ME‼️(SEE IMAGE)
Solve the system of equations using determinants.
3x + 5y = 27
2x - y = -8
Find the values of determinants D, Dx and Dy
D=?
Dx=?
Dy=?
Answers
Answer:
D = -13, Dx = 13, and Dy = -78
Step-by-step explanation:
To solve the system of equations using determinants, we need to first set up the coefficient matrix and the constant matrix. The coefficient matrix is formed by the coefficients of the variables, and the constant matrix is formed by the constants on the right-hand side of the equations.
The coefficient matrix for this system is:
```
3 5
2 -1
```
The constant matrix is:
```
27
-8
```
We can now use these matrices to find the values of D, Dx, and Dy.
D is the determinant of the coefficient matrix:
```
| 3 5 |
| 2 -1 |
D = (3 * -1) - (5 * 2)
D = -3 - 10
D = -13
```
Dx is found by replacing the x-coefficients in the coefficient matrix with the constants from the constant matrix:
```
| 27 5 |
| -8 -1 |
Dx = (27 * -1) - (5 * -8)
Dx = -27 + 40
Dx = 13
```
Dy is found by replacing the y-coefficients in the coefficient matrix with the constants from the constant matrix:
```
| 3 27 |
| 2 -8 |
Dy = (3 * -8) - (27 * 2)
Dy = -24 - 54
Dy = -78
```
Therefore, D = -13, Dx = 13, and Dy = -78.
To find x and y, we can use Cramer's rule:
```
x = Dx / D
y = Dy / D
x = 13 / (-13)
x = -1
y = (-78) / (-13)
y = 6
```
So the solution to this system of equations is x = -1 and y = 6.
Related Questions
True or False:
The Ratios form a proportion:
5/8
42.5/68
Answers
The Ratios form a proportion: 5/8 and 42.5/68.
Yes, they form a ratio
Two fractions A/B and C/D form a ratio when A/B = C/D.
In this case, we want to know if 5/8 = 42.5/68 is true.
Suppose two fractions are equal. We will use the cross multiplication operation to get the following:
Therefore,
5/8 = 42.
⇒ 5/68
⇒ 5*68 = 8*42.5
⇒ 340 = 340
is rated at 340 on the left and right sides. This makes the last equation true, so the first equation must also be true. The two fractions therefore form a ratio.
another example
Suppose we want to know if 1/2 and 1/3 are equal.
They are not equal. Now assuming they are equal we will show that the contradiction occurs
⇒ 1/2 = 1/3 (assuming this is true)
⇒ 1*3 = 2*1 (cross multiplication)
⇒ 3 = 2 (this is where the difference occurs)
We have discrepancies because the left and right sides do not match. This inconsistency has the domino effect of making the original equation false as well brings us back to our two original fractions 5/8 and 42.5/68
Now,
We can use a calculator to convert each value to decimal form
5/8 = 0.625
and,
42.5/68 = 0.625
both give the same decimal value of 0.625, so that must mean that the two fractions must be equal and proportional.
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You want to be able to withdraw $20,000 each year for 15 years. Your account earns 8% interest.
a) How much do you need in your account at the beginning?
$
b) How much total money will you pull out of the account?
$
c) How much of that money is interest?
$
Answers
Answer:
a.the amount needed in the account at the beginning is $1,564,826.
b.the total amount of money pulled out of the account is $300,000.
c.The negative result means that the interest earned is not enough to cover the withdrawals, and there is actually a loss of $1,264,826.
A woman borrowed 20000 for four weeks and agrees to pay 25000 at the end of the four weeks, calculate each installment
Answers
write the polynomial in standard form
-3m^(2)n^(2)+8mn^(3)+m^(3)n
Answers
The standard form of the polynomial is [tex]$$m^3n-3m^2n^2+8mn^3$$[/tex] we arrange the terms in descending order of the exponent of the variable.
To write a polynomial in standard form, we need to arrange the terms in descending order of the exponent of the variable. In this case, the variable is [tex]$m$[/tex]. The highest exponent of [tex]$m$[/tex] in the given polynomial is 3, so we start with the term[tex]$m^3n$[/tex]. Then, we look at the terms with the next highest exponent of [tex]$m$[/tex], which is 2, and arrange them in descending order of the exponent of [tex]$n$[/tex]. Finally, we look at the remaining terms with exponent of [tex]$m$[/tex] less than 2, and arrange them in descending order of the exponent of[tex]$n$[/tex]. The resulting polynomial is in standard form.
The given polynomial is:
[tex]$$-3m^2n^2+8mn^3+m^3n$$[/tex]
To write it in standard form, we arrange the terms in descending order of the exponent of [tex]$m$[/tex]:
[tex]$$m^3n-3m^2n^2+8mn^3$$[/tex]
This is the standard form of the polynomial.
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Main Street and Washington Avenue meet at a right angle. A large park begins at this corner. Joe's school lies at the opposite corner of the park. Usually, Joe walks 3.6 miles along Main Street and then 1.5 miles up Washington Avenue to get to school. Today he walked in a straight path across the park and returned home along the same path. What is the difference in distance between the two round trips?
Complete the explanation and enter your answers rounded to the nearest tenth of a mile.
Answers
The difference in distance between the two round trips 2.4 miles.
The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.
The x-coordinate, often known as the abscissa, is a point's separation from the y-axis.
Now, total joe walked the distance is
[tex]\sqrt{3.6^{2}+1.5^{2} }[/tex]=3.9 miles
and on the daily basis he usually walks
3.6+1.5=5.1 miles
So, the difference in the distance in first trip
5.1-3.9=1.2 miles
and thus the difference in the distance in two round trips will be
1.2×2=2.4 miles.
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Show that the lines x2-4xy+y2=0 and x+y=1 form an equilateral triangle
Answers
Answer:
Step-by-step explanation:
hello here is qn solution
Suppose A and B are angles in standard position with sin(A)= and sin(B)=-1/3. Find
the exact value of cos(A + B) if A is in Q2 and B is in Q3.
Answers
The exact value of cos(A + B) is 2√2/3 - ()/3.
What is the Pythagorean identity?
The Pythagorean identity tells us that no matter what the value of θ is, sin²θ+cos²θ is equal to 1. This follows from the Pythagorean theorem, which is why it's called the Pythagorean identity.
Since sin(A) is positive and A is in quadrant 2, we know that cos(A) is negative. Using the Pythagorean identity, we can find cos(A):
cos²(A) + sin²(A) = 1
cos²(A) + = 1
cos²(A) = 1 -
cos(A) = -√(1 - )
Similarly, since sin(B) is negative and B is in quadrant 3, we know that cos(B) is negative. Using the Pythagorean identity, we can find cos(B):
cos²(B) + sin²(B) = 1
cos²(B) + 1/9 = 1
cos²(B) = 8/9
cos(B) = -√(8/9) = -2√(2)/3
Now we can use the sum formula for cosine to find cos(A+B):
cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
= (-√(1 - ))(-2√(2)/3) - ()(-1/3)
= 2√(2)/3 +
Therefore, the exact value of cos(A+B) is 2√(2)/3 + .
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How do you find the area?
Answers
The area of triangle is 47.89 in². So correct option is B) None of the other answers are correct.
Describe triangle ?There are different ways to classify triangles based on their sides and angles. Based on sides, a triangle can be:
Equilateral: all three sides are equal in length.
Isosceles: two sides are equal in length.
Scalene: all three sides are of different lengths.
Based on angles, a triangle can be:
Acute: all three angles are acute (less than 90 degrees).
Right: one angle is a right angle (exactly 90 degrees).
Obtuse: one angle is obtuse (greater than 90 degrees).
A triangle also has several properties, such as the sum of its interior angles is always 180 degrees, and the longest side of a triangle is opposite to the largest angle. The area of a triangle can be calculated using various formulas depending on the information provided, such as the base and height, the lengths of the sides, or the angles and sides.
To find the area of the triangle, we can use the formula A = (1/2)bh, where b is the base and h is the height of the triangle.
First, we need to find the height of the triangle. We can use trigonometry and the given angle to find the height.
sin(110°) = h/PK
h = PKsin(110°) = 9sin(110°) ≈ 8.11 in
Next, we can use the formula for the area of a triangle to find the area:
A = (1/2)(PH)(h) = (1/2)(11.8)(8.11) ≈ 47.89 in²
Therefore, the closest answer choice is B) None of the other answers are correct.
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Molly took care of her neighbors’ house for 8 days while they were out of town. Her neighbors paid her a daily rate for housesitting plus an extra $20 for mowing the lawn on Saturday. Molly earned a total of $140.
Which equation can you use to find X molly’s daily rate for housesitting
Answers
[tex]\text{The equation is} \ 8x+20=140[/tex]
[tex]\text{Solve for x to get}[/tex]
[tex]8x=120[/tex]
[tex]x=15[/tex]
[tex]\bold{Milly's \ daily \ rate \ for \ house-sitting \ is \ 15 \ dollars.}[/tex]
What is the equation of the line that passes through the point (−4,5) and has an undefined slope?
Answers
y = -4 is the equation of the line through the point (-4,-6) with an undefined slope.
If the slope of a line is undefined, then the line must be vertical, meaning that it is parallel to the y-axis.
A line's standard equation is written as y = mx+b, where
the slope is m,
and the y-intercept is b.
Since the line passes through the point (-4, 5), we know that the x-coordinate of any point on the line must be -4. As a result, the line's equation is:
x = -4
This is because, for any value of y, the x-coordinate will always be -4, which gives us a vertical line passing through the point (-4, 5).
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heather has divided 6300.00 between two investments, one paying 9% the other paying 5% how much did she invest in both if her return on the investment is 427.00
Answers
In linear equation, 2800 did she invest in both if her return.
What is the most effective way to explain linear equations?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).
In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
assuming that the two investments are X & Y
X + Y = 6300
X = 6300 - Y (1)
9/100X + 4/100 Y = 427 (2)
replacing X from (1) into (2)
9/100(6300-Y) + 5/100 Y = 427
567 - 9/100Y + 5/100Y = 427
(-9+5)/100Y = 427 - 567
4/100Y = - 140
Y = 100* 140/4 = 3500
From (1) we can get X
X = 6300 - 3500 = 2800
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How do describe what each rule does to Mugs original hat
Hat 5 (x + 2,3y)
Hat 6 (2x,3y)
Hat 7 (-2x, -2y)
Answers
the result of applying Hat 5 to the original hat is a hat that is shifted to the right and stretched vertically, the result of applying Hat 6 to the original hat is a hat that is stretched horizontally and result of applying Hat 7 to the original hat is a hat that is reflected across both axes.
Each of the three rules provided represents a transformation of Mug's original hat, which is not described in the question. However, assuming that the original hat is a standard hat with no specific features, we can describe the effect of each rule on a generic hat.
The first rule, Hat 5, transforms the original hat by adding 2 to the x-coordinate and leaving the y-coordinate unchanged. This means that the hat is shifted 2 units to the right along the x-axis. Additionally, the transformation multiplies the y-coordinate by 3, which stretches the hat vertically. Therefore, the result of applying Hat 5 to the original hat is a hat that is shifted to the right and stretched vertically.
The second rule, Hat 6, multiplies the x-coordinate by 2, which stretches the hat horizontally, and leaves the y-coordinate unchanged. This means that the hat is transformed into a wider shape. Therefore, the result of applying Hat 6 to the original hat is a hat that is stretched horizontally.
The third rule, Hat 7, multiplies both the x- and y-coordinates by -2, which reflects the hat across both the x- and y-axes. This means that the hat is transformed into an upside-down and backwards version of itself. Therefore, the result of applying Hat 7 to the original hat is a hat that is reflected across both axes.
In summary, the three rules provided each represent a specific transformation of Mug's original hat. Hat 5 shifts the hat to the right and stretches it vertically, Hat 6 stretches the hat horizontally, and Hat 7 reflects the hat across both axes.
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Which expression is not a polynomial?
Answers
Answer:
last choice
Step-by-step explanation:
Based on this definition, the last choice is NOT a polynomial: for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
(x³ + 1) / x = 1/x(x³ + 1)
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 6.5 inches and b = 5.5 inches, what is c? If necessary, round to the nearest tenth.
Answers
Step-by-step explanation:
Use Pythagorean theorem for right triangles
c^2 = a^2 + b^2
c^2 = 6.5^2 + 5.5 ^2
c^2 = 72.5
c = sqrt (72.5) = 8.5 units
A trader sells x pencils at 90 each, y pens at
#120 each and 5 erasers at Nx each. How much
money does the trader get altogether?
Answers
The expressiοn that we can use tο find the tοtal revenue is 90x + 120y - 5n
What is an Algebraic expressiοns?An algebraic expressiοn is a cοmbinatiοn οf numbers, variables, and mathematical οperatiοns, such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Algebraic expressiοns can be used tο represent a wide range οf mathematical relatiοnships
Given that
A trader sells x pencils at 90 each,
Then selling price οf 'x' pencils = 90x
The trader sοld y pens at 120
Then the selling price οf y pens = 120y
5 erasers are sοld at N
Cοst οf 5 erasers = 5 × N = 5N
Hence, the tοtal revenue = 90x + 120y - 5n
Therefοre,
The expressiοn that we can use tο find the tοtal revenue is 90x + 120y - 5n.
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HELPPPPP ME PLEASE, I NEED HELP
Answers
The area of the trapezium is 84 square meters.
The formula for a trapezium's area must be used to resolve this issue:
Area is equal to (the sum of parallel sides) x (the distance between them) / 2.
In this instance, the parallel sides are 12 metres and 9 metres long, with an 8 metre gap between them. This allows us to enter these values into the formula:
Area =(12 + 9) x 8 / 2
Area = 21 x 8 / 2
Area = 168 / 2
84 square metres of area
As a result, the trapezium has a surface area of 84 square metres.
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Find the nth term of this number sequence 2 , 4 , 6 , 8
Answers
Answer:
it's an AP series and it's nth term is
a+(n-1)d
where a = ist term
n = number of term
d = difference of 2nd and 1st term
You roll two dice.
What is the probability you will roll a 4, then roll a number less than 3?
1/36
1/6
1/18
1/9
Answers
the probability roll a 4 will be 1/18.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Consider first the likelihood of rolling a 4 on a typical six-sided die. A 4 will come up 1/6 of the time on the dice.
The likelihood of rolling a number less than 3 on a typical six-sided die is the subject of the next section. The probability of rolling a number less than 3 is 2/6, or 1/3, because there are only two possible outcomes for a six-sided die.
When calculating the likelihood of rolling a 4, then a number less than 3, we multiply the likelihood of rolling a 4 by the likelihood of rolling a number less than 3:
(1/6) * (1/3) = 1/18
Hence the probability will be 1/18.
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how to solve for area1/5 + 4/8= _________________+ 20/40
Answers
Answer:
8/40 or 1/5
Step-by-step explanation:
Solve 1/5 + 4/8
Convert to same denominator
8/40 + 20/40 =28/40
28/40 = _____ + 20/40
28/40 - 20/40 = x
X = 8/40 = 1/5
Based on historical data, an insurance company estimates that a particular customer has a 2.7% likelihood of having an accident in the next year, with the average insurance payout being $3300.
If the company charges this customer an annual premium of $210, what is the company's expected value of this insurance policy?
Answers
Answer:
Expected value = $115.83
You are standing 50 feet away from the base of a building. While lying on your belly, and with your handy dandy clinometer, you measure the angle from yourself to the top of the building to be 30 degrees. How high is the building? Show work
Answers
The height of the building of the given trigonometric function is approximately 28.87 feet.
What is trigonometric function?
In mathematics , trigonometric functions which is also called circular functions or angle functions are those which are real functions that relate the angle of a right triangle to the ratios of two side lengths.
We here use the trigonometric function tan to solve the problem.
tan angle =(opposite side)/(adjacent side)
tan 30° = (height of the building )/ 50
(1/√3)= (height of the building)/50
height of the building= (50/√3)
= (50√3)/3
√3=1.732
=28.87 feet
Hence, the height of the building is approximately 28.87 feet.
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Solve for x round to newest tenth urgent show proofs
Answers
The value of x is 15.5
What are similar triangles?Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.
To find the value of x, we use Pythagoras theorem to find the other side of the small triangle. represent it by y
y= √18² + 15²
y =√ 324 + 225
y = √ 549
y = 23.43
using similar triangle theorem;
15+x/23.43 = 23.43/18
= 18(15+x) = 23.43×23.43
18(15+x) = 549
15+x = 30.5
x = 30.5-15
x = 15.5
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A teacher was measuring his students. The tallest student measured 5.2 feet. The shortest student measured 4.5 feet. Which measurement is between the heights of the two students?
Answers
To contrast the measurements we convert them with inches. For this, we really want to realize that there are 12 inches in a foot and 3 feet in a yard. So there are 3×12=36 inches in a yard.
Sarah's height is now in inches. Jake's height is 414 feet. This is the same as 4+14 feet. Since there are 12 inches in a foot, there are 4×12=48 inches in 4 feet, and 3 inches in a 14 foot. So Jake's height in inches is 48+3=51 inches.
For Andy, we have seen that there are 36 inches in a yard, so there are 18 inches in half a yard, so in inches, Andy's height is 36+18=54.
At long last, Emily is 4 feet and 4 inches tall. There are 4×12=48 inches in 4 feet, so Emily is 48+4=52 inches tall.
The table shows every one of the heights in inches, in decreasing order.
Student Height in Inches
Andy 54
Emily 52
Jake 51
Sarah 50
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the complete question is:
Mr. Liu asked the students in his fourth-grade class to measure their heights. Here are some of the heights they recorded:
Student Height
Sarah 50 inches
Jake 414 feet
Andy 112 yards
Emily 4 feet and 4 inches
List the four students from tallest to shortest.
Base of trash can is 32square inches and volume of 288 cubic inches will Hassan trash can fit under his sink which is a clearance height of 8 inches .
Answers
As sink has a clearance height of only 8 inches while the height of trash can is 9 inches, Hassan trash can couldn't fit under his sink.
How to determine the height?To determine if Hassan's trash can will fit under his sink, we need to calculate the height of the trash can based on its given base area and volume.
The trash can must be cylindrical thus volume = πr²h
Here, πr² is the base and h is height
πr² given 32² in
And volume = 288³ in
So,
height = volume / base area
height = 288 / 32
height = 9
So the height of the trash can is 9 inches.
However, As sink has a clearance height of only 8 inches while the height of trash can is 9 inches, Hassan trash can couldn't fit under his sink.
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The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 195 cm², what is
the length of the diagonal?
Answers
Consequently, the diagonal is roughly 24.43 centimetres long.
What is a rectangle made of?An enclosed 2-D object called a rectangle has four sides, four edges, and four right angles (90°). A rectangle has identical and parallel opposing edges. A rectangular has two dimensions—length and width—because it is a two-dimensional form. The rectangle's larger side is its length, and its shorter side is its breadth.
Let's start by using algebra to find the dimensions of the rectangle.
Let L be the length of the rectangle in cm, and let W be the width of the rectangle in cm. We know that:
W = 2L - 9 (the width is 9 less than twice the length)
The area of the rectangle is given as 195 cm²:
A = L× W = L × (2L - 9) = 195
Expanding the expression for the area, we get:
2L² - 9L - 195 = 0
We can solve for L using the quadratic formula:
L = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = -9, and c = -195.
Plugging in these values, we get:
L = (-(-9) ± √((-9)² - 4(2)(-195))) / (22)
= (9 ± √(9² + 42×195)) / 4
= (9 ± √(1521)) / 4
= (9 ± 39) / 4
So L = 12.75 or L = -3.75. We can ignore the negative value, since length cannot be negative. Therefore, the length of the rectangle is 12.75 cm.
To find the diagonal of the rectangle, we can use the Pythagorean theorem. Let D be the length of the diagonal in cm. Then:
D² = L²+ W² (Pythagorean theorem)
We already know that L = 12.75 cm, and we can find W using the equation we derived earlier:
W = 2L - 9 = 2(12.75) - 9 = 16.5 cm
Plugging in these values, we get:
D² = 12.75² + 16.5²
D² = 324.5625 + 272.25
D² = 596.8125
D = √(596.8125)
D ≈ 24.43
Therefore, the length of the diagonal is approximately 24.43 cm.
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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 48 ounces and a standard deviation of 3 ounces. Use the 68-95-99.7 Rule and a sketch of the normal distribution in order to answer these questions. a) 95% of the widget weights lie between and b) What percentage of the widget weights lie between 39 and 54 ounces? % c) What percentage of the widget weights lie above 45 ?
Answers
After calculating we found that: a) 95% of widget weights lie between 42 and 54 ounces.b) 97.35% of widget weights lie between 39 and 54 ounces and c) 0.3% of widget weights lie above 45 ounces.
a) Since the distribution is bell-shaped and the mean is 48 ounces with a standard deviation of 3 ounces, we can use the 68-95-99.7 Rule to determine that 68% of the widget weights lie within one standard deviation of the mean, 95% lie within two standard deviations of the mean, and 99.7% lie within three standard deviations of the mean. Thus, we know that 95% of the widget weights lie between:
48 - 2(3) = 42 ounces and 48 + 2(3) = 54 ounces.
b) To find the percentage of widget weights that lie between 39 and 54 ounces, we need to determine how many standard deviations away from the mean these values are.
39 ounces is 9 ounces below the mean, so it is (9/3) = 3 standard deviations below the mean.
54 ounces is 6 ounces above the mean, so it is (6/3) = 2 standard deviations above the mean.
Using the 68-95-99.7 Rule, we know that 99.7% of the widget weights lie within three standard deviations of the mean. Since 39 ounces is three standard deviations below the mean, we can conclude that 0.15% (or 0.003 x 100) of the widget weights lie below 39 ounces.
Likewise, since 54 ounces is two standard deviations above the mean, we know that 2.5% of the widget weights lie above 54 ounces. Thus, the percentage of widget weights that lie between 39 and 54 ounces is:
100% - 0.15% - 2.5% = 97.35%
c) We need to find the percentage of widget weights that lie above 45 ounces. Since 45 ounces is three standard deviations below the mean, we know that 99.7% of the widget weights lie above 45 ounces. Therefore, the percentage of widget weights that lie above 45 ounces is:
100% - 99.7% = 0.3%.
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Can you please help me i didnt understand the question and find the answer.
Thank you for your help.
Answers
The correct response is C. 2.05 cm to 2.15 cm. The possible range for the length of the segment is 2.05 cm to 2.15 cm.
The length of a segment is the separation between any two points on a line. The length of a horizontal line is just the difference between the x-coordinates of the two points when dealing with horizontal lines. Similar to this, one of the y-coordinates can be subtracted from the other to determine the length of a vertical line. By the way, you are actually applying the Pythagorean Theorem to a hypothetical right triangle, with the hypotenuse being the line connecting the two lines. A segment is an area that is enclosed by a circle's chord and its intercepted arc. A minor segment is one that has an intercepted arc that is smaller than a semicircle.
2.05 cm to 2.15 cm
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Solving proportions can anyone help?
Answers
Using proportions, we can get the value of the unknown variables as:
1. m = 4/3
2. b = 16/5
3. x = 40/9
4. x = 20
5. x = 11/3
6. k = 28/3
Define proportions?A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general.
According to the definition of proportion, two ratios are in proportion when they are equal. It is an equation or a statement that shows that two ratios or fractions are equal.
Here in the question,
We have:
2/6 = m/4
Cross multiplying the values,
m = 2× 4/6
m = 4/3
Now,
4/5 = b/4
b = 4×4/5
=16/5
8/9 = x/5
x = 8×5/9
=40/9
10/x = 2/4
x = 10×4/2
x = 20
(x-2)/5 = 2/6
⇒ 6(x-2) = 2×5
⇒ 6x -12 = 10
⇒ 6x = 22
⇒ x = 22/6
⇒ x =11/3
6/5 = 10/(k-1)
⇒ 6(k-1) = 10 × 5
⇒ 6k - 6 = 50
⇒ 6k = 56
⇒ k = 56/6
⇒ k = 28/3
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If the x-axis is placed at a height of 100 meters, the outer edge of a cooling tower can be modeled by the hyperbola ^2/900 - y^2/1600 = 1, measured in meters. If the tower is 150 meters tall, find
the width of the cooling tower at the top.
Answers
The width of the cooling tower at the top is approximately 127.2 meters.
What is hyperbola?
A hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.
First, we need to find the x-value at the top of the tower, where y = 150 meters.
We can plug this value into the equation of the hyperbola and solve for x:
x²/900 - (150)²/1600 = 1
x²/900 - 5625/1600 = 1
x²/900 = 5625/1600 + 1
x²/900 = 7225/1600
x² = 900 * (7225/1600)
x² = 4050.625
x ≈ 63.6
So the x-value at the top of the tower is approximately 63.6 meters.
Next, we need to find the width of the tower at the top, which is the distance between the two points on the hyperbola with y = 150 meters. To find these points, we can plug y = 150 into the equation of the hyperbola and solve for x:
x²/900 - (150)^2/1600 = 1
x²/900 - 5625/1600 = 1
x²/900 = 5625/1600 + 1
x²/900 = 7225/1600
x² = 900 * (7225/1600)
x ≈ ± 63.6
So the two x-values at y = 150 meters are approximately 63.6 meters and -63.6 meters.
The width of the cooling tower at the top is the distance between these two points, which is:
width = 2 * 63.6 ≈ 127.2 meters
Therefore, the width of the cooling tower at the top is approximately 127.2 meters.
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write the absolute value of
a) -8
b) +4
c) 6
d) 0
e) -5
f) +2½
g) 5.6
h)-3/2
Answers
Step-by-step explanation:
The absolute value of a number is its distance from zero on the number line. It is always a non-negative value.
a) The absolute value of -8 is 8. | -8 | = 8
b) The absolute value of +4 is 4. | 4 | = 4
c) The absolute value of 6 is 6. | 6 | = 6
d) The absolute value of 0 is 0. | 0 | = 0
e) The absolute value of -5 is 5. | -5 | = 5 f) The absolute value of +2½ is 2.5. | 2½ | = 2.5
g) The absolute value of 5.6 is 5.6. | 5.6 | = 5.6 h) The absolute value of -3/2 is 3/2. | -3/2 | = 3/2.
(Note that when working with fractions, the absolute value of a fraction is always positive, regardless of whether the fraction itself is positive or negative.)
