The base of a triangular field is three times its height. If the cost of cultivating the feild at $36 per hectare is $486, find its base and height.

Please explain also​

The solution of the initial value problem y' = 2xy² ; y(1) = 1/2 is y(x) = -1/(x² - 3)

An initial value problem is a differential equation that contains the initial values of the variables of the differential equation.

Given the initial value problem

y' = 2xy² ; y(1) = 1/2

So, we solve the differential equation as follows

y' = 2xy²

dy/dx = 2xy²

Separing the variables, we have

dy/y² = 2xdx

Integrating both sides of the equation, we have

∫dy/y² = ∫2xdx

∫dy/y² = 2∫xdx

We know that ∫xⁿ = xⁿ⁺¹/(n + 1)

So, integrating the expressions, we have

y⁻²⁺¹/(-2 + 1) = 2x¹⁺¹/(1 + 1)

y⁻¹/(-1) = 2x²/2 + c

-y⁻¹ = x² + c

Given that y(1) = 1/2, substituting these into the equaqtion, we have

-y⁻¹ = x² + c

-(1/2)⁻¹ = 1² + c

-2 = 1 = c

c = -2 - 1

c = -3

So, -y⁻¹ = x² + c

-y⁻¹ = x² - 3

Dividing through by - 1, we have

y⁻¹ = -(x² - 3)

Taking the inverse of both sides, we have

y(x) = -1/(x² - 3)

So, y(x) = -1/(x² - 3)

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Answer:

No, it's not linear function.

Step-by-step explanation:

The x value repeatedly adds 3.

So far its a linear function.

If you look at the y value, it does NOT have a pattern, therefore that means it is NOT a linear function.

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

89 cents.

Step-by-step explanation:

hope this helps

Answer:

-6, 7

Step-by-step explanation:

Answer: B(-6,7)

Step-by-step explanation:

M(-5, 1)      A(-4,-5)       B(x,y)=?

\(\displaystyle\\M_x=\frac{x_A+x_B}{2} \\\\-5=\frac{-4+x_B}{2}\\\\\)

Multiply both parts of the equation by 2:

\(-5(2)=-4+x_B\\\\-10=-4+x_B\\\\-10+4=-4+x_B+4\\\\-6=x_B\\\\Thus,\ x_B=-6\)

\(\displaystyle\\\\\\1=\frac{-5+y_B}{2} \\\\\)

Multiply both parts of the equation by 2:

\(1(2)=-5+y_B\\\\2=-5+y_B\\\\2+5=-5+y_B+5\\\\7=y_B\\\\Thus,\ y_B=7\)

Answer:

Arc XY = 180- 43

= 137º

answer is C

Step-by-step explanation:

The correct answer is "No, because the sample members are not all magazine readers in the general population."

A sample chosen at random from a population is known as a random sample. This makes sure that everyone in the population has the same chance of getting into the sample.

The correct answer is "No, because the sample members are not all magazine readers in the general population."

This is because the sample of 25 respondents is likely to be too small and not representative of the entire population of readers. The sample may not accurately represent the opinions and interests of all readers, and there could be other factors that influence readership preferences that are not captured in the sample. Therefore, any conclusions drawn from this sample may not be true for all readers of the magazine. In order to draw more accurate conclusions about the entire population of readers, a larger and more representative sample would be needed.

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Answer: No, because the sample would probably include only readers with strong feelings about what they want to read about.

Step-by-step explanation:

The correct answer is "No, because the sample members are not all magazine readers in the general population."

A sample chosen at random from a population is known as a random sample. This makes sure that everyone in the population has the same chance of getting into the sample.

The correct answer is "No, because the sample members are not all magazine readers in the general population."

This is because the sample of 25 respondents is likely to be too small and not representative of the entire population of readers. The sample may not accurately represent the opinions and interests of all readers, and there could be other factors that influence readership preferences that are not captured in the sample. Therefore, any conclusions drawn from this sample may not be true for all readers of the magazine. In order to draw more accurate conclusions about the entire population of readers, a larger and more representative sample would be needed.

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Answer: No, because the sample would probably include only readers with strong feelings about what they want to read about.

Step-by-step explanation:

Answer: ASA, C

Step-by-step explanation:

I think it's ASA cuz since the lines indicate they are parallel, then you can find that the two interior angles are also congruent. Since two angles are the same with the side inbetween being the same, it's probably asa.

The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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Answer:

La altura del prisma es 2,4 m.

Step-by-step explanation:

Para calcular el volumen de un prisma rectangular, es necesario multiplicar sus tres dimensiones, esto es, longitud*ancho*altura. El volumen se expresa en unidades cúbicas.

Entonces:

volumen= longitud*ancho*altura

En este caso, los datos conocidos son:

Reemplazando:

24 m³= 2,5 m* 4 m* altura

Resolviendo:

\(altura=\frac{24 m^{3} }{2,5 m*4m}\)

\(altura=\frac{24 m^{3} }{10 m^{2} }\)

altura= 2,4 m

La altura del prisma es 2,4 m.

Answer:

7.5 litres

Step-by-step explanation:

Let the amount of orange juice ve 3x litres and amount of grapefruit juice be 1x. (As they are in ratio of 3:1.)

Now, according to the question,

So,

⇒ Amount of orange juice + Amount of grape fruit juice = 10 litres

⇒ 3x + x = 10

⇒ 4x = 10

⇒ x = 10 ÷ 4

⇒ x = 2.5

Now,

⇒ Amount of orange juice he used= 3x litres

⇒ Amount of orange juice he used= 3(2.5) litres

⇒ Amount of orange juice he used= 7.5 litres

∴ He used 7.5 litres of orange juice.

Given the functions:

Solve the equations means finding the values of x provided that f(x) = g(x)

so,

Make the square root alone on the right-side

Square both sides to eliminate the square root:

Simplifying the equation:

Solve the last equation to find the values of x

We can use the calculator to find the values of x

So,

Rounding to the nearest tenth

So, the answer will be x = {-1.7, 4.1 }

rAnswer:

50%

Step-by-step explanation:

7 nurses

3 doctors

4 offices

14 in total

7/14 or 50% is the probability

The probability that three nurses are selected is 7/14.

Probability refers to a possibility that deals with the occurrence of random events.

From the information, the total outcome if nurses are randomly selected is expressed as:

Total outcome = 7 + 4 + 3 = 14 outcomes

In order to get the probability that three nurses are selected, the expected outcome is 7;

P = 7/14

Hence the probability that three nurses are selected is 7/14.

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Answer:

You can not solve it because Side P does not exist

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

2x-4=10

   +10 +10

2x       14

2x/2   2/14

x = 7

The value of the function f(x) = -3x+4 is -3x+5

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given a function, f(x) = -3x+4

g(x) is described as f(x) +1

g(x) = -3x+4+1

g(x) = -3x+5

The graph of f(x) will move 1 unit farther when transformed into g(x).

Hence, The value of the function f(x) = -3x+4 is -3x+5

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Answer:

He can buy 160 crates of apples and 40 crates of pears. (160, 40).

Step-by-step explanation:

From the information given, you can write the following equations:

25x+25y=5000 (1)

6x+5.50y=1180 (2), where:

x is the number of crates of apples

y is the number of crates of pears

First, you can solve for x in (1):

25x=5000-25y

x=(5000/25)-(25y/25)

x=200-y (3)

Then, you can replace (3) in (2) and solve for y:

6(200-y)+5.50y=1180

1200-6y+5.50y=1180

1200-1180=6y-5.50y

20=0.5y

y=20/0.5

y=40

Finally, you can replace the value of y in (3) to find the value of x:

x=200-y

x=200-40

x=160

According to this, the answer is that he can buy 160 crates of apples and 40 crates of pears. (160, 40).

The standard form of the number  \((1.5*10^(13))^2\)  is  2.25×\(10^(26)\) .

What is standard form of a number ?

 An equation, an expression, or a set of integers can all be written in standard form using the standard form approach. It is possible to express a number in a way that adheres to certain standards by writing it in its standard form. Standard form refers to any number between 1.0 and 10.0 that may be expressed as a decimal number and multiplied by a power of 10. The term "standard form" in this context refers to the act of condensing a particularly big expanded form of a number.

Here given is ,

=> \((1.5*10^(13))^2\)

=> \(1.5^2\) × \(10^(13)^2\)

=> 2.25×\(10^(26)\)

Therefore standard form of the number is  2.25×\(10^(26)\).

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Answer:

4

Step-by-step explanation:

First let’s write out the info:

X        Y

5       10

2        ?

Five is to ten as two is to what? Well let’s find out.

Five times TWO is ten, so logically, we multiply two times two.

2x2=4

The answer is 4

I hope this helps! :D

pls give thx and brainliest if I’m right ;)

First step is to add x to both sides.

Second step is cube both sides.

Solving this equation for x initially yields three possible solutions.

Checking the solutions show that -2, 0 and 2 are valid solutions.

The percentage of students who scored between 529 and 681 on the exam is 47.7%.

The given information is;μ = 529σ = 76.Therefore, the students' scores in the Statistics course are Normally distributed with a mean of 529 and a standard deviation of 76.

The required percentage of students who scored between 529 and 681 on the exam is to be found out.Now, we need to find the Z-score for the upper bound and the lower bound of the interval.

The Z-score for the lower bound is;(529 - 529) / 76 = 0The Z-score for the upper bound is;(681 - 529) / 76 = 2The main answer:

The formula to find the percentage of values between two points for a normal distribution is;P (a < x < b) = Φ(b) − Φ.

Here, Φ(b) represents the area under the curve to the left of the upper bound, and Φ(a) represents the area under the curve to the left of the lower bound.

Therefore, we can write:P (529 < x < 681) = Φ(2) − Φ(0) = 0.9772 − 0.5 = 0.4772.The percentage of students who scored between 529 and 681 on the exam is 47.7%.

The percentage of students who scored between 529 and 681 on the exam is 47.7%

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Answer5.5:

Step-by-step explanation:

Divided 16.50 by 3

Answer:

5.50

Step-by-step explanation:

16.50 divided by 3 5.50

Based on the behavior of the terms and the comparison with the harmonic series, we conclude that the given series ∑ (7 - cos(3n))/(n^(2/3) - 2) is divergent.

First, let's consider the behavior of the individual terms in the series. The numerator, 7 - cos(3n), oscillates between values of -6 and 8 as n increases. The denominator, n^(2/3) - 2, grows without bound as n approaches infinity.

Since the numerator oscillates and the denominator grows, it suggests that the series does not converge absolutely. To confirm this, we can apply the Limit Comparison Test or the Comparison Test.

By comparing the series to a known convergent or divergent series, we can determine its convergence behavior. Let's compare it to the harmonic series, which is known to diverge. We can observe that as n approaches infinity, the denominator n^(2/3) - 2 grows at a faster rate than n, indicating that the series is also divergent.

Therefore, based on the behavior of the terms and the comparison with the harmonic series, we conclude that the given series ∑ (7 - cos(3n))/(n^(2/3) - 2) is divergent.

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The potential rational zeros for the polynomial function \(F(x) = 3x^4 - 9x^3 + x^2 - x + 1\) are: A. -1, 1, -3/1, 3/1, -9/1, 9/1.

To find the potential rational zeros of a polynomial function, we can use the Rational Root Theorem. According to the theorem, if a rational number p/q is a zero of a polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient.

In the given polynomial function \(F(x) = 3x^4 - 9x^3 + x^2 - x + 1,\) the leading coefficient is 3, and the constant term is 1. Therefore, the potential rational zeros can be obtained by taking the factors of 1 (the constant term) divided by the factors of 3 (the leading coefficient).

The factors of 1 are ±1, and the factors of 3 are ±1, ±3, and ±9. Combining these factors, we get the potential rational zeros as: -1, 1, -3/1, 3/1, -9/1, and 9/1.

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Answer:

the answer is a

Step-by-step explanation:

A function assigns values. The function that represents the graph is (1/4)^(x+2).

A function assigns the value of each element of one set to the other specific element of another set.

The function of the graph that will represent the graph given below is

\(y = (\dfrac{1}{4})^{(x+2)}\)

Thus, the function that represents the graph is (1/4)^(x+2).

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Answer:

#2 Alternate interior angles: 4 & 5 and 3 and 6

#4 :

m∠6 = 55°

m∠3 = 55°

m∠1 = 125°

Reasons: See below

Step-by-step explanation:

Angles 6 and 8 are supplementary angles since they are on the same straight line intersected by another straight line.

So m∠6 + m∠8 = 180
m∠6 + 125 = 180
m∠6 = 180-125= 55°

Angles 3 and 6 are alternate interior angles and equal to each other
m∠3 = m∠6 = 55°

Angles 1 and 3 are supplementary angles whose sum of measures should add up to 180°
m∠1 + m∠3 = 180
m∠1 + 55 = 180
m∠1 = 180-55 = 125°

Using relations in a right triangle, we have that:

1 - a) x = 54.28º.

1 - b) y = 57.794º.

1 - c) z = 31.056º.

2) The angle is of 62.8º.

3) The angle is of x = 53.017º.

4) The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

5) The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

The relations in a right triangle are given as follows:

For item 1a, we have that the sides, hence:

tan x = 8.9/6.4

x = arctan(8.9/6.4)

x = 54.28º.

For item 1b, we have the adjacent side and the hypotenuse, hence:

cos y = 9.7/18.2

y = cos^-1 (9.7/18.2)

y = 57.794º.

For item 1c, we have the opposite side and the hypotenuse, hence:

sin z = 6.5/12.6

z = sin^-1(6.5/12.6)

z = 31.056º.

For item 2, we have the sides, given at the graph at the end of the answer, hence:

tan x = 7.2/3.7

x = tan^-1(7.2/3.7)

x = 62.8º.

The angle is of 62.8º.

For item 3, first we find the hypotenuse of the bottom triangle, by the Pythagorean Theorem, as follows:

h² = 7.9² + 18.6²

h = sqrt(7.9² + 18.6²)

h = 20.21.

Then:

sin x = 20.21/25.3

x = sin^-1(20.21/25.3)

x = 53.017º.

For item 4, we have the adjacent side and the hypotenuse, hence:

cos(x) = 3/3.2

x = cos^-1 (3/3.2)

x = 20.364º.

The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

For item 5, we have the opposite side and the hypotenuse, hence:

sin y = 1.8/2.9

y = sin^-1 (1.8/2.9)

y = 38.37º.

The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

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Answer:

C

Step-by-step explanation:

Answer:

she receives 76 Dollars