find the exact length of the polar curve. r = θ2, 0 ≤ θ ≤ 7π/4

Answer:

here (edit I made a mistake)

Step-by-step explanation:

9) \(y=\frac{3}{5} x +5\)

10) y = x - 3

11)  \(y=-\frac{3}{5} x - 3\)

12) \(y=\frac{5}{4} x + 2\)

these are the slop int forms, my bad...

sorry

Answer:

9) -3/5x + y = 5

10) -x + y = -3

11) 3/5x + y = -3

12) -5/4x + y = 2

Step-by-step explanation:

Answer:

y=0.75x+2

Step-by-step explanation:

you can also do y=3/4x+2

Answer:

2.23

Step-by-step explanation:

tune able to find the area you should x one side by the other side to find the area 2.23 * 2.23 equals close to 5 square feet

The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

The formula for the volume of a cylinder is \(V = \pi r^2h,\) where V is the volume, r is the radius, and h is the height.

Let's assume that the cone and cylinder have a radius of 'r' and a height of 'h'.

The volume of the cylinder is given by \(= \pi r^2h.\)

The volume of the cone is given by V_cone = \((1/3)\pi r^2h.\)

Since the cone and cylinder have the same base and height, their radius and height are the same.

Therefore, we can simplify the volumes as V_cylinder = \(\pi r^2h\) and V_cone = \((1/3)\pi r^2h.\)

The ratio of the volume of the cone to the volume of the cylinder is then:

V_cone/V_cylinder = \(((1/3)\pi r^2h) / (\pi r^2h) = (1/3) / 1 = 1/3\)

So, the volume of the cone is one-third of the volume of the cylinder.

Alternatively, we can write this as the ratio of the volume of the cone to the volume of the cylinder being 1:2, since the volume of the cylinder is twice the volume of the cone.

Therefore,The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

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Answer:

So, /(100÷2) = 117/50 when reduced to the simplest form. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 234/100 is also equal to 2 17/50 when expressed as a mixed number.

Step-by-step explanation:

Answer:

2 17/50

Step-by-step explanation:

234%

= 234/100

= 2 34/100

= 2 17/50

Answer:

x=203/18

Step-by-step explanation:

convert the decimal into a fraction

203/50/x = 9/50 / 1/2

simply the complex fraction:

203/50x = 9/25

cross multiply

450x = 5075

divide both sides by 450:

x= 203/18

Answer:

X=11.2778

Step-by-step explanation:

4.06/X=0.18/0.5

cross multiply

0.18×X=4.06×0.5

0.18X=2.03

divide both sides by 0.18

0.18X/0.18=2.03/0.18

it becomes

X=2.03/0.18

X is therefore 11.2778

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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$390 represent 100%. To find what percentage $7.80 represent, we can use the next proportion:

Solving for x,

The sales tax rate is 2%

Answer:

Each term in pattern B is 9 less than the corresponding term in pattern A.

The value of expression cos (A - B)  is,

cos (A - B) = (4√2 - √5) / 9

We have to given that;

sin A = 1/3 where A terminates in Quadrant 1,

And , cos B = 2/3, where B terminates in Quadrant 4.

Since, We know that;

sin² A + cos² A = 1

(1/3)² + cos²A = 1

cos²A = 1 - 1/9

cos²A = 8/9

cos A = 2√2/3

And, We know that;

sin² B + cos² B = 1

(2/3)² + sin²B = 1

sin²B = 1 - 4/9

sin²B = 5/9

sin B = √5/3

Hence, We get;

cos (A - B) = cos A cos B + sin A sin B

Substitute all the values, we get;

cos (A - B) = 2√2/3 x 2/3  + 1/3 x √5/3

cos (A - B) = 4√2/9 - √5/9

cos (A - B) = (4√2 - √5) / 9

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The value of the line integral ∮c x dx + y dy / \((x^2 + y^2)\), where c is any Jordan curve whose interior does not contain the origin, traversed counterclockwise, is 0.

To evaluate the line integral ∮c x dx + y dy / \((x^2 + y^2)\), where c is any Jordan curve whose interior does not contain the origin, traversed counterclockwise, we can apply Green's theorem.

Green's theorem states that for a vector field F = P(x, y) i + Q(x, y) j, and a simple closed curve C with positively oriented boundary, the line integral of F along C is equal to the double integral of the curl of F over the region enclosed by C.

In this case, the vector field F = x i + y j, and the line integral becomes ∮c x dx + y dy / \((x^2 + y^2)\) = ∬R curl(F) dA.

The curl of F is given by curl(F) = (∂Q/∂x - ∂P/∂y) k = (1 - 1) k = 0.

Since the curl of F is zero, the line integral becomes ∬R 0 dA = 0.

Therefore, the value of the line integral ∮c x dx + y dy / \((x^2 + y^2)\), where c is any Jordan curve whose interior does not contain the origin, traversed counterclockwise, is 0.

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Answer:

\(\longrightarrow \boxed{\dfrac{ -b}{c}}\)

Step-by-step explanation:

Given that , α and ß are the zeroes of the polynomial ,

\(\longrightarrow f(x) = ax^2+bx + c \)

As , we know that ,

We need to find out the Value of ,

\(\longrightarrow \dfrac{1}{\alpha}+\dfrac{1}{\beta} \)

On simplifying ,

\(\longrightarrow \dfrac{ \alpha +\beta }{\alpha\beta} \)

Substitute ,

\(\longrightarrow \dfrac{\frac{-b}{a}}{\frac{c}{a}}\)

Cancel " a" in numerator and denominator ,

\(\longrightarrow \boxed{\dfrac{ -b}{c}}\)

Answer:

Please attach a screenshot of the question and I could answer it. Thank you!

Answer:

y = 14

Angle O is 41 degrees

Step-by-step explanation:

From the question, since we have an isosceles triangle, then the base angles are equal

This means that the angle at M is (4y-15) too

Mathematically, the sum of the angles in a triangle is 180 degrees

Thus;

7y + 4y-15 + 4y-15 = 180

15y-30 = 180

15y = 180+ 30

15y = 210

y = 210/15

y = 14

Angle O is 4y-15

= 4(14) -15 = 56-15 = 41 degrees

The probability that a randomly selected person from the group will have a systolic blood pressure below 112 is 0.0548.

To find the probability that a randomly selected person from the group will have a systolic blood pressure below 112, we need to standardize the variable using the z-score formula:

z = (x - μ) /σ

where x is the value, we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation.

For this problem, we have:

z = (112 - 120) / 5 = -1.6

Now, we need to find the probability that Z (the standardized variable) is less than -1.6. We can do this by using a standard normal distribution table.

Using a standard normal distribution table, we find that the probability of Z being less than -1.6 is approximately 0.0548.

Therefore, the probability that a randomly selected person from the group will have a systolic blood pressure below 112 is approximately 0.0548 or 5.48%.

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By using the formula for the distance between two points we will see that the distance between the two points is √80 is 8.9

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

The general formula for the distance between two points (a, b) and (c, d) is:

Distance = √[(a-d)²+(b - c)²]

In this case, we have the points (-4,1) and (4,5), replacing that in the above formula we get:

Distance = √[(-4-4)²+(1-5)²]

= √80

=8.9

Therefore the distance between the two points (-4,1) and (4,5) is 8.9

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Answer:

Step-by-step explanation:

AAS and SAS

The congruence theorems or postulates could be given as reasons why ABC= ADEF are SAS, AAS the correct options are A and F.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

\(\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\)

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

The diagram

Now,

Based on the information given in the diagram, we can use the following congruence theorems or postulates as reasons why ABC= ADEF:

SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

We can use SAS to show that ABC and ADEF are congruent, since AB = AD, BC = DE, and the included angle BAC = the included angle EDF.

AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

We can use AAS to show that ABC and ADEF are congruent, since the included angles BAC and EDF are congruent, angle ABC is congruent to angle ADE (since they are vertical angles), and side BC is congruent to side EF.

Therefore, by congruent triangles the answer will be SAS, AAS.

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Let y be the number of gallons she need to drive 418 miles

380 miles = 14 gallons

418 miles = x

cross-mutiply

380x =5852

Divide both-side by 380

x = 15.4 gallons

55oz converted into pounds is 3.4375 lbs.

Answer:

3.4375 lbs.

Yeah, not being the process... Sorry!

1. For the statement "The set of people who speak English, the set of people who speak Chinese" neither is a subset of the other.

2. For the statement "The set of fruits, the set of citrus fruits" the second set is a subset of the first.

3. For the statement "The set of planets, the set of planets with water" neither is a subset of the other.

4. For the statement "The set of even integers, the set of positive integers" first set is a subset of the second.

Let's analyze each pair of sets:

1. The set of people who speak English, the set of people who speak Chinese: Neither is a subset of the other.

Some people may speak both English and Chinese, while others may speak only one of the languages.

2. The set of fruits, the set of citrus fruits: The set of citrus fruits is a subset of the set of fruits.

All citrus fruits are a type of fruit, but not all fruits are citrus fruits. Therefore, the second set is a subset of the first.

3. The set of planets, the set of planets with water: Neither is a subset of the other.

There may be planets in the set of planets that do not have water, and there may be planets in the set of planets with water that are not part of the broader set of planets.

4. The set of even integers, the set of positive integers: The set of positive integers is not a subset of the set of even integers because the set of even integers includes both positive and negative numbers, while the set of positive integers includes only positive numbers.

However, the set of even integers is a subset of the set of positive integers because every even integer is also a positive integer.

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We have to find the value of  `(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)`

Let's find all trigonometric ratios:

We can say that:

\($$\tan \theta= \frac{opp}{adj}= \frac{-4}{3}$$$$\text\)

{Using the Pythagorean Theorem we can find the hypotenuse }

\($$$$\text{Hypotenuse = } \sqrt{(-4)^2+(3)^2}\)

\(= \sqrt{16+9}\)

= \(\sqrt{25}\)

=\(5$$$$\)

Substituting the values of sinθ, cosθ and tanθ in `

\(= \frac{\frac{3}{5} + \frac{-4}{5} - \frac{-4}{3}}{\frac{-4}{5} + \frac{5}{3} - \frac{-3}{4}}$$$$\)

\(=\frac{\frac{9}{15} + \frac{-12}{15} + \frac{20}{15}}{\frac{-16}{20} + \frac{25}{12} + \frac{3}{4}}$$$$\)

\(=\frac{\frac{17}{15}}{\frac{-14}{15}}$$$$\)

\(=-\frac{17}{14}$$\)

Therefore, \(`(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)\)` is equal to

`-17/14` when `tanθ=−43` (Quadrant II).

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Answer:

-203 is the answers for the question

Step-by-step explanation:

please give me brainlest

Answer:

-203

Step-by-step explanation:

=> -7 + 4 + (-200)

=> -(7 - 4) + (-200)

=> -3 + (-200)

=> -(3 + 200)

= -203

Answer:

All of the expressions

Step-by-step explanation:

A rational number is one that can be written as a ratio, or a number with a terminating decimal.

All of the expressions are whole numbers, so they are all rational.

Answer: x=8

Step-by-step explanation: these two polygons are similar. 96 divided by 8 equals 12. So 64 divided by 8 equals 8, which is the answer. I really hope this helps and I hope you have a great day!

Answer:

The function H(x) that represents how much you would pay if you use the mall coupon followed by applying the store discount of 25% would be: H(x) = (x-5)*0.25. This function takes the original cost of the jeans (x) and subtracts $5 from it (x-5) to account for the coupon, and then multiplies the result by 0.25 to account for the store discount.

The gradient of a function is a vector that points in the direction of the greatest rate of change of the function. The differential of a function is a linear approximation of the function near a point. The gradients and differentials of the three functions are as follows:

fi: (x, y) → x cos(y) defined on R²

Gradient: (cos(y), x sin(y))

Differential: dx * cos(y) + dy * x sin(y)

f2: (x, y, z) → 1 + x + xy + xyz defined on R³

Gradient: (1 + y, x + z, xy)

Differential: dx + dy + (x + z) * dx + xy * dy

f3: (x, y, z) → ² defined on {(x, y, z) € R³ | z ‡ 0}

Gradient: (0, 0, 2z)

Differential: 0 * dx + 0 * dy + 2z * dz

The gradient of a function is a vector that points in the direction of the greatest rate of change of the function. The differential of a function is a linear approximation of the function near a point.

In the first case, the gradient of fi is (cos(y), x sin(y)) because the greatest rate of change of fi is in the direction of (cos(y), x sin(y)). The differential of fi is dx * cos(y) + dy * x sin(y) because this is the linear approximation of fi near the point (x, y).

In the second case, the gradient of f2 is (1 + y, x + z, xy) because the greatest rate of change of f2 is in the direction of (1 + y, x + z, xy). The differential of f2 is dx + dy + (x + z) * dx + xy * dy because this is the linear approximation of f2 near the point (x, y, z).

In the third case, the gradient of f3 is (0, 0, 2z) because the greatest rate of change of f3 is in the direction of (0, 0, 2z). The differential of f3 is 0 * dx + 0 * dy + 2z * dz because this is the linear approximation of f3 near the point (x, y, z).

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Answer:

x = 5/3

y = -8/3

Step-by-step explanation:

To solve y = 2x - 6​ substitute the y for -x - 1 and solve for x.

-x - 1 = 2x - 6 Now you can solve this like a regular inequality. Start by subtracting 2x on both sides.

-3x - 1 = -6 Now add 1 to both sides

-3x = -5 Divide by -3 on both sides

x = 5/3 (the negatives cancel and become positive)

Because you have x, you can go back and properly solve for y. Substitute x for 5/3

y = 2(5/3) - 6 Simplify the right side to get your answer.

y = 10/3 - 6 In order to subtract 6, you first have to convert it to a fraction with a denominator of 3. To do this, put 6 over 1 (6/1) then find the least common denominator of 3 and 1, which is 3. Now multiply 1 by 3 and 6 by 3 to get 18/3

y = 10/3 - 18/3

y = -8/3

I hope this helped :)

Answer:

The answer is b. n=-3

Step-by-step explanation:

Answer: b. n = -3

Step-by-step explanation: