3. Consider the vector field F(x, y) = (2xy, x²- sin y). Evaluate
∫▒c F ds where C is the curve c(t) = (t2/3, sin()), 0 ≤ t≤ 1. (Hint: Apply Green's theorem to a suitable region.)

Answer:

( 6,6) is outside

Step-by-step explanation:

(x - 2)^2 + (y - 1)^2 = 25

This is of the form

(x - h)^2 + (y - k)^2 = r^2

where ( h,k) is the center and r is the radius

(x - 2)^2 + (y - 1)^2 = 5^2

The center is at ( 2,1) and the radius is 5

P(0,5), Q(2,2) R(5,-2), and S(6,6)

Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)

( 6,6) is outside the circle

Answer:B

Step-by-step explanation:

Took the test

Answer:

Step-by-step explanation:

the way it is written, the answer is

5x^2 - 6x + 2 + 19x - 7

5x^2 + 13x - 5    is the answer.

However I suspect you mean

5x^2 - 6x + 2 + 9x^2 + 10x - 7

14x^2 + 3x - 5    is the answer if the revision I've made is correct.

The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

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Answer:

-3

Step-by-step explanation:

Variables are letters which are used to represent particular unknown quantities in equations.

Now the variable in this question is x.

When we talk about coefficient , we mean the number before the variable in question.

We can see that the variable is written as -3x

-3 is the value before the variable so we can agree that -3 is its coefficient

Answer:

its -3, i took the test

Have a great day!!

Step-by-step explanation:

The center line of the  x - chart  is simply the average of the sample means.

Therefore, we can use 0.50 as an estimate of the center line.

The center line of the x-chart  is simply the average of the sample means. Since we don't have any sample means yet, we can't calculate the center line directly.

However, we can use the specification limits to estimate the center line. If the bolts are properly adjusted, we would expect the average bolt length to be in the middle of the specification range, which is 0.50 inches. Therefore, we can use 0.50 as an estimate of the center line.

Keep in mind that this is just an  estimate, and the actual center line may be higher or lower depending on the data. Once we start collecting data and calculating sample means, we can use those values to calculate the true center line.

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The discriminant is -68. Since the discriminant is negative the roots of the quadratic equation are imaginary values, hence they have no real values.

A quadratic equation's number of roots can be calculated using the discriminant. A discriminant might be zero, negative, or positive. The kind of roots can be identified by knowing the value of a determinant as follows:

The quadratic equation has two actual and distinct solutions if the discriminant value is positive.

The quadratic equation has just one solution or two real and equal solutions if the discriminant value is zero.

There are no actual solutions to the quadratic equation if the discriminant value is negative.

The discriminant is given as:

D = b² - 4ac

In the given equation:

b = -2, a = -3, and c = -6.

D = (-2)² - 4(-3)(-6)

D = 4 - 72

D = -68

The discriminant is -68.

Since the discriminant is negative the roots of the quadratic equation are imaginary values.

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Answer:

-68 and the nonreall is 2

Step-by-step explanation:

A right triangle ABC is formed when we join three points around a lake. Length of the side AC = 6 miles. Length of the side BC = 2 miles. We have to find Length of side AB.Using Pythagorean theorem for Right triangle ABC , Right angled at B→AB² + BC²= AC²→ AB² + 2²= 6²→ AB² = 36 - 4→ AB²= 32→ AB = √ 32→→AB = 5.66 (approx)Option (B) AB = 5.66 is Right choice.

Answer:

AB+ BC^2= AC

AB^2+ 2^2= 6^2

AB^2 = 36 - 4

AB^2= 32

AB = sqrt 32

AB = 5.66 (approx)

Option (B) AB = 5.66 is Right choice.

Answer:

B

Step-by-step explanation:

It shows how in 3 seconds it went 12 feet so I divided it by 3 and got four.

The matrix A does not eigenvector v corresponding to the given eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

v is an eigenvector of A calculate corresponding eigenvalue,

A × v = λ × v

where A is the given matrix.

v is the given vector.

λ is the corresponding eigenvalue.

× denotes matrix multiplication.

Let's first calculate A × v we have,

A × v

= [-11 60] × [ 1 3λ]

= [-11-33λ    60+ 180λ]

Check A× v is equal to λ × v ,

λ × v =

λ × [ 1 3λ]

= [λ  3λ^2]

Set these two vectors equal to each other and get the following system of equations ,

-11-33λ = λ  __(1)

60+ 180λ = 3λ^2  ___(2)

From equation (1) we get,

⇒34λ = -11

⇒ λ = -11/34

Substituting this value of λ into the second equation, we have,

60+ 180λ = 3λ^2

⇒ 60 + 180(-11/34) = 3(-11/34)^2

⇒ (2040 -1980)/ 34 = 3(-11/34)^2

⇒ 60/34 = 3( 11/34)^2

⇒ 60 × 34 = 3 × 11 × 11

⇒20× 34 = 11 × 11

Which is not true.

so the value of λ does not satisfies both equations.

Therefore, v is not an eigenvector of A with corresponding eigenvalue λ.

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The above question is incomplete, the complete question is:

Check whether v is an eigen vector of A  if yes find the corresponding eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

Answer:

x = 154/13

Step-by-step explanation:

You are given the measures of all three angles in a triangle

so according to the Triangle Sum Theorem:

∠MNO + ∠OMN + ∠NOP = 180

1. Substitute the measures of the angles into the equation:

(3x + 11) + (2x + 20) + (8x - 5) = 180

2. Combine like terms:

(3x + 2x + 8x) + (11 + 20 -5) = 180

13x + 26 = 180

3. Isolate x by subtratcing 26 from both sides

13x + 26 -26 = 180 -26

13x  = 154

4. Solve for x by dividing both sides by 13

13x/13 = 154/13

x = 154/13

Answer:

=

Hope that helps!

Step-by-step explanation:

The shaded areas therefore cover a total area of 86.84 cm2.

Let's calculate the whole trapezoid's area. You multiply by the height after adding the top and bottom sides and dividing the result by two.

To get the length of the top side, we sum the values that make up that side.

6.4+5.2+9.6=21.2

The underside is 5.2.

The top and bottom sides are added.

21.2+5.2=26.4

We multiply by 2.

26.4/2=13.2

We increase by the height, which is 6.2 as we can see.

13.2×9.1=120.12

Next, we locate the rectangle's unlit portion.

6.4×5.2 = 33.28

To get the total area of the two shaded triangles, we deduct this from the trapezoid's overall area.

120.12 - 33.28 = 86.84

The shaded areas therefore cover a total area of 86.84 cm2.

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The expression is (3+4=5) Or (3+4≥5). The expression is false. The expression as (3+4=7) or(3+4>5). The number 7 is true.

Given that,

The expression is (3+4=5) Or (3+4≥5).

We have find the value and the expression is true or false.

The expression is false

3+4=5

7=5

The number 7 is not equal to 5.

Now

3+4≥5

7≥5

The number 7 is not equal to 5 but it is greater then 5.

So, we can write the expression as (3+4=7) or(3+4>5)

Therefore, The number 7 is not equal to 5 or The number 7 is not equal to 5 but it is greater then 5. The expression as (3+4=7) or(3+4>5).

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Brett's claim that AABC is congruent or similar to ADEF is false

Congruence of Triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all  three corresponding angles are equal.

From the given information, we can see that both AABC and ADEF are right triangles because they have one angle that is 90 degrees.  

However, we cannot conclude that AABC and ADEF are congruent (that is, identical in size and shape) because there is not enough information to determine their side lengths and the remaining angles.

Also, we  cannot conclude that AABC and ADEF are similar (ie have the same shape but possibly different sizes) because we only know one pair of corresponding angles (ie right angles) and one pair of corresponding sides (ie AC and DF), which  not enough to show similarity.  Therefore, Brett's claim that AABC is congruent or similar to ADEF is false, and we cannot conclude that AABC-ADEF (ie the difference between these two triangles) is a triangle with well-defined sides and angles.

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The staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags

To determine the number of bags of each color that the staff should order, we need to use the information from the sample of 120 students and make an inference about the entire population of 800 students.

If we assume that the sample of 120 students is representative of the entire population, we can use the proportions from the sample to estimate the number of bags of each color that the staff should order.

Let's use the following proportions from the sample:

40% of the students prefer blue bags (0.40 x 120 = 48)

45% of the students prefer black bags (0.45 x 120 = 54)

15% of the students prefer gray bags (0.15 x 120 = 18)

Therefore, based on this sample, the staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags.

However, it's important to note that this is just an estimate based on a sample, and there may be some variability or uncertainty in the actual preferences of the entire population.

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The isotopes of gallium-69 are Ga71 and Ga67.

Ga71 is an isotope of gallium-69 because it has the same number of protons (31) but a different number of neutrons (40) compared to the standard isotope of gallium-69 (31 protons and 38 neutrons).

Ga67 is another isotope of gallium-69 because it also has 31 protons but a different number of neutrons (36) compared to the standard isotope of gallium-69.

These isotopes have different mass numbers due to the varying number of neutrons, while still retaining the same number of protons. Isotopes of an element have the same atomic number (number of protons) but different mass numbers.

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Answer:

7 weeks

Step-by-step explanation:

b​=95+(10+9​)w

Combine like terms

b​=95+(19​)w

Let b = 220

220 = 95 + 19w

Subtract 95 from each side

220-95 = 19w

125 = 19w

Divide each side by 19

125/19 = w

6.578947368

Round up

After 7 week

Answer:

Step-by-step explanation:

This is a 30°-60°-90° triangle, so the sides are in the ratio 1:√3:2

The side opposite the 90° angle is 16, so the side opposite the 30° angle is 8, and the side opposite the 60° angle is 8√3.

x = 8√3

y = 8

Given:

Let's evaluate and find the quotient.

We have:

SInce it is not a repeating decimal, we are asked to leave to answer as it is.

A repeating decimal is a decimal with digits or group of digits that repeats endlessly.

The decimal 5.937

ANSWER:

5.9375

Answer:

- "stars that shine" --> alliteration

- "never-ending line" --> hyperbole

- "dances with the daffodils" --> personification

Step-by-step explanation:

- "stars that shine" --> alliteration since both stars and shine start with the 's' sound

- "never-ending line" --> hyperbole since never ending is an exaggeration

- "dances with the daffodils" --> personification since your heart (from the prev line) dances, hence personifies your heart as a human being that dances, or could also be interpreted as the daffodils dancing with you heart, also showing personification.

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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Answer:

0 or 2

Step-by-step explanation:

The number of distinct imaginary roots possible are 2.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

If f(x) is a third degree polynomial then by corollary to the fundamental theorem of algebra , it must have 3 roots.

It as complex roots occurs in pairs, thus there must be even number of complex roots.

So, there is 2 complex distinct complex roots are possible in third degree polynomial.

Corollary to the fundamental theorem states that every polynomial of  degree n>0 has exactly n zeroes.

Therefore, the number of distinct imaginary roots possible are 2.

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The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:

porportional

Step-by-step explanation:

Step-by-step explanation:

Marla drove 567

Gudio drove 560

The trip was 679

Answer:

1239

Step-by-step explanation:

Juanita: x

Guido: 5x

Marla: 5x+7

We know Juanita drove 112 miles. This means that x=112.

Juanita: 112

Guido: 5*112=560

Marla: 560+7= 567

Now we can add up the number of miles each friend drove to get the total distance of the trip.

112+560+567=1239