Find the equation of the line that goes through the points (0, 6) and (12, 2).
y = 12x + 2
y = -1/3 x + 2
y = -1/3 x + 6
y = -3x + 6

Answer:

\(\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)(1+\sec^2(x-y)(8+x^2))}\)

Step-by-step explanation:

So we have the equation:

\(\tan(x-y)=\frac{y}{8+x^2}\)

And we want to find dy/dx.

So, let's take the derivative of both sides:

\(\frac{d}{dx}[\tan(x-y)]=\frac{d}{dx}[\frac{y}{8+x^2}]\)

Let's do each side individually.

Left Side:

We have:

\(\frac{d}{dx}[\tan(x-y)]\)

We can use the chain rule, where:

\((u(v(x))'=u'(v(x))\cdot v'(x)\)

Let u(x) be tan(x). Then v(x) is (x-y). Remember that d/dx(tan(x)) is sec²(x). So:

\(=\sec^2(x-y)\cdot (\frac{d}{dx}[x-y])\)

Differentiate x like normally. Implicitly differentiate for y. This yields:

\(=\sec^2(x-y)(1-y')\)

Distribute:

\(=\sec^2(x-y)-y'\sec^2(x-y)\)

And that is our left side.

Right Side:

We have:

\(\frac{d}{dx}[\frac{y}{8+x^2}]\)

We can use the quotient rule, where:

\(\frac{d}{dx}[f/g]=\frac{f'g-fg'}{g^2}\)

f is y. g is (8+x²). So:

\(=\frac{\frac{d}{dx}[y](8+x^2)-(y)\frac{d}{dx}(8+x^2)}{(8+x^2)^2}\)

Differentiate:

\(=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}\)

And that is our right side.

So, our entire equation is:

\(\sec^2(x-y)-y'\sec^2(x-y)=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}\)

To find dy/dx, we have to solve for y'. Let's multiply both sides by the denominator on the right. So:

\(((8+x^2)^2)\sec^2(x-y)-y'\sec^2(x-y)=\frac{y'(8+x^2)-2xy}{(8+x^2)^2}((8+x^2)^2)\)

The right side cancels. Let's distribute the left:

\(\sec^2(x-y)(8+x^2)^2-y'\sec^2(x-y)(8+x^2)^2=y'(8+x^2)-2xy\)

Now, let's move all the y'-terms to one side. Add our second term from our left equation to the right. So:

\(\sec^2(x-y)(8+x^2)^2=y'(8+x^2)-2xy+y'\sec^2(x-y)(8+x^2)^2\)

Move -2xy to the left. So:

\(\sec^2(x-y)(8+x^2)^2+2xy=y'(8+x^2)+y'\sec^2(x-y)(8+x^2)^2\)

Factor out a y' from the right:

\(\sec^2(x-y)(8+x^2)^2+2xy=y'((8+x^2)+\sec^2(x-y)(8+x^2)^2)\)

Divide. Therefore, dy/dx is:

\(\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)+\sec^2(x-y)(8+x^2)^2}\)

We can factor out a (8+x²) from the denominator. So:

\(\frac{dy}{dx}=y'=\frac{\sec^2(x-y)(8+x^2)^2+2xy}{(8+x^2)(1+\sec^2(x-y)(8+x^2))}\)

And we're done!

Answer:

  2/15

Step-by-step explanation:

You want to know the fraction that is 2/3 of 1/5.

In this context, "of" means "times."

  2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15

2/15 of the pets are alley cats.

Answer:

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Step-by-step explanation:

Points:

Slope-intercept form:

Slope is:

denominator of the fraction is zero, we can't divide by zero, so this line has no slope

----------

It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Answer:

D.

Step-by-step explanation:

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

edge 2020

We can see here that with the information given, one can prove that this quadrilateral is a parallelogram. Thus, it is yes>

A polygon with four sides and four vertices (corners) is called a quadrilateral. Its internal angles add up to 360 degrees.

Squares, rectangles, parallelograms, trapezoids, and rhombuses are all examples of quadrilaterals.

We can see that looking at the quadrilateral, we can deduce that it is parallelogram. This is because the opposites sides are equal. Also, their opposite angles are equal.

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Answer:

D

Step-by-step explanation:

The sequence an = (-1)ⁿ * 5ⁿ alternates between positive and negative terms and grows without bound as n increases, so it does not converge and the limit does not exist (DNE).

The sequence is defined as an = (-1)ⁿ * 5ⁿ.

When n is odd, (-1)ⁿ is equal to -1, so an = -5ⁿ.

When n is even, (-1)ⁿ is equal to 1, so an = 5ⁿ.

Therefore, the sequence alternates between positive and negative terms, and the absolute value of the terms grows without bound as n increases.

This means that the sequence does not converge.

Hence, the limit of the sequence as n approaches infinity does not exist (DNE).

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Answer:

A number minus the product of

4

and its reciprocal is less than zero. Find the numbers which satisfy this condition.

AAny number less than

−

2

or between

0

and

2

BAny number between

−

2

and

2

CAny number less than

2

DAny number between

0

and

2

Solution

Let the number be x

Then

x

−

(

4

×

1

x

)

≤

0

⇒

x

≤

4

x

⇒

x

2

≤

4

⇒

|

x

|

≤

2

⇒

−

2

≤

x

≤

2

Step-by-step explanation:

The numbers which satisfy this condition is less than 1. it will be 0, - 1, -2, 0, -3, -4, -5, -6, -7..................

let

the number  = x

The reciprocal of 36 = 1 / 36

Therefore, a number minus the product of 36 and it's reciprocal can be express below

Then when it is less than zero, it can be express as follows

The number(x) which satisfy this condition (x - 1 < 0) is less than 1. This means the numbers are 0 to negative infinity.

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The sales tax percentage is approximately 10%.

To find the sales tax percentage, we can use the following formula:

Sales Tax = Final Cost - Original Cost

Let's assume the sales tax percentage is represented by "x".

Given that the original cost of the snowboard is $650 and the final cost (including sales tax) is $715, we can set up the equation as follows:

Sales Tax = $715 - $650

Sales Tax = $65

Using the formula for calculating the sales tax percentage:

Sales Tax Percentage = (Sales Tax / Original Cost) * 100

Sales Tax Percentage = ($65 / $650) * 100

Sales Tax Percentage ≈ 10%

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The orthogonal vector w to vectors u and v is given by w = 2i - j - 2k.

To find the orthogonal vector w to vectors u and v, we can use the cross product.

The cross product of two vectors u and v is given by the determinant of the matrix formed by the unit vectors i, j, and k in the first row and the components of the vectors u and v in the second and third rows, respectively.

Given vectors u = i + 2j and v = i + k, we can find the cross product w = u × v as follows:

w = | i  j  k  |
     | 1  2  0  |
     | 1  0  1  |

Calculating the determinant, we get:

w = i(2*1 - 0*0) - j(1*1 - 0*1) + k(1*0 - 1*2)
w = 2i - j - 2k

So, the orthogonal vector w to vectors u and v is given by w = 2i - j - 2k.

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Answer:

1st answer choice

no because there is no whole number that when multiplied by itself gives 125

Step-by-step explanation:

125 is a perfect cube

5 times 5 times 5 = 125

Answer:

Option A

Step-by-step explanation:

125 is NOT a perfect square, because there is no whole number that multiplies by itself to give 125.

To check the perfectness of a square, take the square root:

\(\sqrt{125} =\) 11.1803399

The above number is NOT a whole number

∴125 is NOT a perfect square

To find the length of the curve defined by y = 4x^3 + 15x from the point (-3,-153) to the point (4,316), you'd have to compute the integral of √[1 + (f'(x))^2] dx, where f(x) = 4x^3 + 15x.

First, we need to find f'(x) by taking the derivative of f(x):
f'(x) = 12x^2 + 15

Next, we can plug f'(x) into the integral formula:
∫[-3,4] √[1 + (12x^2 + 15)^2] dx

This integral can be solved using trigonometric substitution. Let u = 12x^2 + 15, then du/dx = 24x and dx = du/24x. Substituting these values, we get:
∫[-3,4] √[1 + (12x^2 + 15)^2] dx
= ∫[177,693] √[1 + u^2]/24x du
= (1/72)∫[177,693] √[1 + u^2]/(u/2) du
= (1/72)∫[177/15,693/15] √[1 + (u/15)^2]/(u/30) du (substituting u/15 = tanθ)
= (1/36)∫[arctan(177/15),arctan(693/15)] secθ dθ
= (1/36)ln|sec(arctan(693/15)) + tan(arctan(693/15))| - (1/36)ln|sec(arctan(177/15)) + tan(arctan(177/15))|
≈ 18.24

Therefore, the length of the curve from (-3,-153) to (4,316) after integral is approximately 18.24 units.

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Answer:

(0.5, -0.5)

EXPLANATION:

CHECK THE IMAGE UP FOR THE ANSWER

The statistical model is not good, and this is true for a negatively skewed curve.

It is a statistical term implies that a curve is skewed at the left side.

In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.

In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.

In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.

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Answer:

The angle for each slice is 45 degrees.

Step-by-step explanation:

In order to calculate the angle of each slice, we first need to calculate the total area of the pizza, because we will use that to find the area of each slice and as a result it's angle. To calculate the area of the pizza we must use:

pizza area = pi*r²

r = d / 2 = 14 /2 = 7 inches

pizza area = pi*(7)² = 153.86 square inches

Since the pizza was divided in 8 pieces, the area of each piece is given by the area of the pizza divided by the number of slices. We have:

slice area = pizza area  / 8 = 153.86 / 8 =19.2325 square inches

Each slice is a circle sector, therefore it's area is given by:

slice area = (angle*pi*r²)/360

Therefore we can solve for angle:

19.2325 = (angle*pi*7²)/360

angle*pi*49 = 6923.7

angle = 6923.7 / pi*49 = 45 degrees

The angle for each slice is 45 degrees.

Answer:

Step-by-step explanation:

6+3x=27

-6 for both sides

3x=21, divide both by 3

x=7

so 2x would be 14 as 2*7 equals 14

If the value of the variable x is 7. Then the value of the expression 2x will be 14.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The equation is given below.

6 + 3x = 27

Simplify the equation, then we have

6 + 3x = 27

3x = 27 - 6

3x = 21

x = 21 / 3

x = 7

Then the value of the expression 2x will be given as,

2x = 2 (7) = 14

If the value of the variable x is 7. Then the value of the expression 2x will be 14.

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Answer:

3000

Step-by-step explanation:

Answer:

the answer is 3000

Step-by-step explanation:

5000 -2000=3000

It would take Mr. Hows 7.5 hours to grade the tests if he worked alone.

Let's assume Ms. Disher's grading rate is represented by "D" (tests per hour) and Mr. Hows' grading rate is represented by "H" (tests per hour).

We are given the following information:

Ms. Disher's grading rate:

D = 1 set of tests / 5 hours

D = 1/5 sets of tests per hour

Ms. Disher and Mr. Hows' combined grading rate:

(D + H) = 1 set of tests / 3 hours

(D + H) = 1/3 sets of tests per hour

To find Mr. Hows' grading rate, we can subtract Ms. Disher's grading rate from their combined grading rate:

H = (D + H) - D

H = 1/3 - 1/5

H = (5 - 3) / (3 × 5)

H = 2 / 15 sets of tests per hour

To determine how long it would take Mr. Hows to grade the tests alone, we can use his grading rate:

1 set of tests / (2/15 sets of tests per hour) = 15/2 hours

15/2 hours = 7.5 hours

Therefore, it would take Mr. Hows 7.5 hours to grade the tests if he worked alone.

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The mean retirement age in the census report is 68.3 years.

The given information states that the population mean retirement age is 68.3 years, and a random sample of retirement age has a sample mean of 65.8 years. We can use this information to estimate the population mean with a certain level of confidence.

However, the question asks us to find the mean of 68.3 years, which is simply the given population mean. Therefore, we can state that the mean of 68.3 years remains the same, as it is not affected by the sample mean or any other sample statistic.

In other words, the population mean of 68.3 years is a fixed value, and it does not change based on the sample mean or any other sample statistic. Therefore, we can simply state that the mean retirement age is 68.3 years, which is the given information provided in the question.

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Answer:

The inside of a saucepan has a cylindrical shape so the capacity of  a saucepan is: \(V=\pi .(\frac{20}{2})^{2}.13=4084(cm^{3})=4.084(l)\)

Step-by-step explanation:

The exterior angle to ∠X is 104.25°

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.

from the above definition , if ∠Y = 62.45° and ∠Z = 41.8°

It means from exterior angle theorem that

exterior ∠X = ∠Y + ∠Z

exterior ∠X  = 62.45° + 41.8°

exterior ∠X  = 104.25°

In conclusion the exterior angle X is 104.25°

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The source of the force in the gas sample is; The force is composed of the sum of the collisions only between the gas molecules and the container

We are given that;

Pressure = Force /Area

Now, for any gas sample, force is defined as basically the force exerted by the gas molecules when they strike the surface and bounce back inside the container where they are located.

Now, from the definition above we can conclude that the source of the force in the gas sample will be The force is composed of the sum of the collisions only between the gas molecules and the container

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1) the exact value of cos(2x) is \(1 - 2y^2\). 2) sin(x/2) = √((1 + √6/3)/2).

1) If sin(x) = y in the first quadrant, then we can find the value of cos(2x) using the double-angle identity for cosine. The double-angle identity states that \(cos(2x) = 1 - 2sin^2(x).\)

Since sin(x) = y, we can substitute it into the formula to get\(cos(2x) = 1 - 2y^2.\)

Therefore, the exact value of \(cos(2x) is 1 - 2y^2.\)

2) Since cos(x) = -√6/3 in the second quadrant, we can use the Pythagorean identity\(sin^2(x) + cos^2(x) = 1\) to find the value of sin(x). Since cos(x) = -√6/3, we have \(sin^2(x) = 1 - cos^2(x) = 1 - (-√6/3)^2 = 1 - 6/9 = 1 - 2/3 = 1/3.\)

Taking the square root of both sides, we get sin(x) = ±√(1/3).

However, since x is in the second quadrant, sin(x) is positive.

Therefore, sin(x) = √(1/3).

To find sin(x/2), we can use the half-angle identity for sine:

sin(x/2) = ±√((1 - cos(x))/2) = ±√((1 - (-√6/3))/2) = ±√((1 + √6/3)/2).

Since x is in the second quadrant, sin(x/2) is positive. Therefore, sin(x/2) = √((1 + √6/3)/2).

3) The expression sin(x)cos(y) - cos(x) is incomplete.

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To calculate the lowest score Stephen can get on the fifth test and still maintain an average score of 90 points, we need to find the score that brings the average up to 90. The lowest score he can get on the fifth test is 96 points.

To maintain an average score of 90 points, Stephen's total points from all five tests should be (5 * 90) = 450.

Given that Stephen has already earned scores of 88, 94, 89, and 85 on the first four tests, we can calculate the total of these scores:

Total of the first four tests = 88 + 94 + 89 + 85 = 356.

To find the lowest score Stephen can get on the fifth test while maintaining an average score of 90, we subtract the total of the first four tests from the desired total points:

Desired total points - Total of the first four tests = 450 - 356 = 94.

Therefore, the lowest score Stephen can get on the fifth test and still have an average score of 90 is 94 points.

Among the given answer options (a-94, b-95, c-96, d-97), the correct answer is c-96.

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Answer:

We can start by using the slope formula to find the equation of the line:

slope = (change in y) / (change in x)

We know the slope is 4, so we can plug in the coordinates (-10, 15) and (x/2, 7) to solve for x:

4 = (15 - 7) / (-10 - x/2)

Multiplying both sides by (-10 - x/2) gives:

-40 - 2x = 8

Solving for x, we get:

x = -24

Therefore, the missing x-value for the coordinate point is -24.

Step-by-step explanation:

The correct answer is option A) Set W is all the unique three-digit numbers using the digits 1, 3, and 5.

The given set of numbers is {1, 2, 3, 4, 5}. Set V contains all the

3-digit numbers are formed using the above digits only once.

Since no other elements other than those given in the sets cannot be used, we cannot use 0, 6, or 7.

Since set X contains 6, Y contains 0 and Z contains 7, they cannot be subsets of V. Hence we can rule out these sets.

The only choice left is A. This set, set W, involves 1,3, and 5 which is the right subset of digits to use.

Hence, option A) Set W is all the unique three-digit numbers using the digits 1, 3, and 5, contains the correct set of digits, and is the subset of the set V.

The correct question is:

Set V is all the unique three-digit numbers using the digits 1, 2, 3, 4, and 5. Which set would be considered a subset of set V?

A) Set W is all the unique three-digit numbers using the digits 1, 3, and 5.

B) Set X is all the unique three-digit numbers using the digits 2, 4, and 6.

C) Set Y is all the unique three-digit numbers using the digits 0, 2, and 4.

D) Set Z is all the unique three-digit numbers using the digits 3, 5, and 7.

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Answer:

The middle graph

Step-by-step explanation:

x > -4 simply means that the value of x must be greater than -4. In the first and third graphs, there is at least one indicated point with a value of -4 or less. However, in the second graph, all of the indicated points have values greater than -4

The **compression constant** of the human hand is typically around **500 N/mm**.

The compression constant refers to the amount of force per unit area that can be applied to compress or deform a material. In the case of the human hand, it represents the capacity of the hand to withstand compressive forces. The compression constant of 500 N/mm indicates that for every millimeter of the hand's surface area, it can withstand up to 500 newtons of compressive force.

The human hand is a complex structure composed of bones, ligaments, tendons, muscles, and soft tissues. It possesses remarkable strength and flexibility, allowing us to perform various tasks requiring grip, dexterity, and manipulation. The compression constant of 500 N/mm highlights the hand's ability to endure compressive forces exerted during activities like gripping objects, applying pressure, or absorbing impacts.

It's important to note that the compression constant can vary among individuals due to factors such as hand size, bone density, muscle strength, and overall hand health. Additionally, the compression capacity of the hand may change in certain conditions, such as injuries or degenerative diseases affecting the hand's structures. However, the average compression constant for a healthy human hand is around 500 N/mm, showcasing its impressive ability to withstand compressive forces.

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