Tomas is finding the coordinates of point A. He knows that point A has an x-coordinate of 8. He starts to compute the value of the y-coordinate. Complete Tomas’s work to answer the question.



Which is the coordinate of point A?

Answer:

draw a rectangle with side lengths 8 and 5. the ratio of the side lengths will be 8:5.

To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.

The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.

Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.

The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:

\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)

Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:

\(\[dV = 3l^2 dl\]\)

Substituting this back into the previous equation, we get:

\(\[dv = 3l^2 dl\]\)

Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:

\(\[dl = \alpha l dt\]\)

Substituting this into the equation for dv, we have:

\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)

Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:

\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)

Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.

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Answer:

\(4\frac{1}{2}\)

Step-by-step explanation:

This question is basically saying: what is half of 7, or what is 7 divided by 2?

Based on this, it can be written both of the ways as:

»»  \(\frac{1}{2}\) of 7  OR  7 ÷ 2

So, just solve using either one and you’ll get 4.5 or \(4\frac{1}{2}\). But since the question wants the answer to be a mixed number, then choose \(4\frac{1}{2}\).

Hope this helps! :)

Answer:

XYZ= 100°

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Answer:

\(\huge\boxed{D) 14.76}\)

Useful information:

Circumference=pi*diameter

\(C=\pi*d\)

Step-by-step explanation:

In this example, the distance around the hat is equal to its circumference. To find the hat's circumference, you would simply multiply the diameter by the value of pi. This gives you 14.76.

1) Multiply pi by 4.7.

\(4.7*\pi =14.76 (2d.p)\)

Answer:

x=-6

Step-by-step explanation:

So you can write this as 10x-8x+2+10=0

Now you have to solve this equation for x

2x+12=0

2x=-12

x=-6

The z-score for which a total probability of 0.71 falls more than z standard deviations (in either direction) from the mean is -1.04 (rounded to two decimal places).

We need to find the z-score for which a total probability of 0.71 falls more than z standard deviations (in either direction) from the mean.

The given information can be represented as:

P(Z > z) + P(Z < -z) = 0.71

We know that the total probability for the standard normal distribution is equal to 1.

Therefore, we can rewrite the equation above as:

P(Z > z) + P(Z > z) = 0.71 ⇒ 2P(Z > z) = 0.71 ⇒ P(Z > z) = 0.355

Now, we need to find the z-score that corresponds to P(Z > z) = 0.355.

Using a standard normal distribution table, we can find the z-score that corresponds to this probability as follows:

z = -1.04 (rounded to two decimal places)

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

 43.3.

Step-by-step explanation:

· The area is approximately 43.3. The precise answer is 25 × √3. To get this answer, recall the formula for the area of an equilateral triangle of side a reads area = a2 …

The answer of this 70/cos 20° round to 1 decimal place  is 74.5

To solve the equation 70/cos 20° , firstly we need to find out the value of the cos 20°.

From the simple calculator we can find the value of cos 20° which is 0.9397.

Now we use this value to solve the above equation.

70/cos 20°;

70/0.9397;

74.491.

written that we  have to round of the value to first decimal place, so the answer will become 74.5

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Hey there!

“Two hundred five million, four hundred thousand six”

205,400,006

Because,

“two hundred five million” is

205,000,000

“Four hundred thousand” is

400,000

“Six” is simplify

6

The equation is:

205,000,000 + 400,000 + 0 + 0 + 6

Which converts to: 205,400,006

Answer: 205,400,006

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

what r the option and its regular 2

Answer:

y-axis

Explanation:

Quadrant I: ( + , + )

Quadrat II: ( - , + )

Quadrant III: ( - , - )

Quadrant IV: ( + , - )

x-axis = ( +/- , 0 )

y-axis = ( 0 , +/- )

Edit: You mentioned that x and y axis are options too therefore, the answer was changed.

Answer:

Straight along the horizontal axis

Step-by-step explanation:

Hope this helped :)

Answer:

b

Step-by-step explanation:

Answer: The answer is (2)

Just evaluate the functions with the values of the figure

1. Let's review the information provided to us to answer the question correctly:

Cost of the pizza = $ 0.10 * π * r², where r = radius of the pizza in inches

2. What does the constant 0.10 in the function represent?

Let's recall the formula of the area of a circle, in this case, the area of the pizza:

Area = π * r², therefore the constant 0.10 that is multiplying the area of the pizza, is the cost of the pizza in dollars per square inch and the total cost is the result of the multiplication of the area by 0.10. 18.30 inches

The Answer is 30 feet

Cause 3/4 of 40 is 30

The distance that she runs from one corner of the field to another is given as follows:

147.1 yards.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:

d² = 85² + 120²

d = sqrt(85² + 120²)

d = 147.1 yards.

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Answer:

12

Step-by-step explanation:

1/6  = 2/12     11/12 = 11/12

Answer:

12

Step-by-step explanation:

6 =3×2

12=3×2×2

Least common denominator = 3×2×2 = 12

The partial derivative of f(x, y) = \(5x^9 - y^5\) - 2 with respect to x (∂f/∂x) is 45\(x^8\), and the partial derivative with respect to y (∂f/∂y) is -5\(y^4\).

To find the partial derivative of a multivariable function with respect to a specific variable, we differentiate the function with respect to that variable while treating the other variables as constants.

Let's start by finding the partial derivative ∂f/∂x of f(x, y) = \(5x^9 - y^5\) - 2 with respect to x.

To differentiate \(x^9\) with respect to x, we apply the power rule, which states that the derivative of \(x^n\) with respect to x is n\(x^{n-1}\).

Therefore, the derivative of 5\(x^9\) with respect to x is 45\(x^8\).

Since \(y^5\) and the constant term -2 do not involve x, their derivatives with respect to x are zero.

Thus, ∂f/∂x = 45\(x^8\).

Next, let's find the partial derivative ∂f/∂y of f(x, y). In this case, since -\(y^5\) and -2 do not involve y, their derivatives with respect to y are zero.

Therefore, ∂f/∂y = -5\(y^4\).

In summary, the partial derivative of f(x, y) = 5\(x^9\) - \(y^5\) - 2 with respect to x is ∂f/∂x = 45\(x^8\), and the partial derivative with respect to y is ∂f/∂y = -5\(y^4\).

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The complete question is:

For the function f(x,y) = \(5x^9 - y^5\) - 2, find ∂f/∂x and ∂f/∂y.

To find the Maclaurin series for the function f(x) = ln(1+x)/(1-x), we can start by expressing ln(1+x) and 1/(1-x) as their respective Maclaurin series expansions.

The Maclaurin series expansion for ln(1+x) is:

ln(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...

The Maclaurin series expansion for 1/(1-x) is:

1/(1-x) = 1 + x + x^2 + x^3 + ...

Now, let's substitute these series expansions into f(x) = ln(1+x)/(1-x):

f(x) = (x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...) * (1 + x + x^2 + x^3 + ...)

Multiplying these series together, we can find the terms of the resulting series:

f(x) = (x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...) + (x^2 - (x^3)/2 + (x^4)/3 - ...) + (x^3 - (x^4)/2 + ...) + ...

Simplifying the terms, we get:

f(x) = x + (3/2)x^2 + (11/6)x^3 + (25/12)x^4 + ...

Now, we have the Maclaurin series for f(x). The radius of convergence R of this series can be determined by considering the convergence of the individual terms. In this case, each term is a polynomial in x, so the series converges for all x values. Therefore, the radius of convergence R is infinity.

To approximate ln(3) using the first four terms of the series, we substitute x = 2 into the series:

f(2) ≈ 2 + (3/2)(2^2) + (11/6)(2^3) + (25/12)(2^4)

Calculating the expression, we find:

f(2) ≈ 2 + 6 + 44/3 + 100/3 ≈ 44.333333

Therefore, using the first four terms of the series, the approximation for ln(3) is approximately 44.333333 (rounded to six decimal places).

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the answer is A 47

Step-by-step explanation:

48+24÷8-2²

48+3-2²

48+3-4

=47

hope it helps!

Answer: The value of sinB is b/c

Step-by-step explanation:since sinB =P/H

Here, P=perpendicular

         H=hypotenuse

so here, P=b and H=c

sinB=b/c

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Answer:

h = 6

Step-by-step explanation:

Step 1: Distribute

7h + 15.75 = 57.75

Step 2: Subtract 15.75 on both sides

7h = 42

Step 3: Divide both sides by 7

h = 6

Answer:

15:22.5:52.5

Step-by-step explanation:

The first step is to calculate the sum

2+3+7

= 12

2/12 ×90

1/6×90

= 15

3/12×90

1/4×90

= 22.5

7/12×90

= 52.5

Hence the answer is

15:22.5:52.5

Answer:

15/8

Hope it helps

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Thank you

Answer:

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The times spent in training is an illustration of proportions

The times spent in training is 80 hours

The given parameters are:

Time spent = 6 hours

Time spent as a percentage = 7.5%

Let the total time spent in training be x.

The scenario is represented by the following equation

Time spent = Time spent as a percentage  * Total Time

So, we have:

6 = 7.5% * x

Express percentage as decimal

6 = 0.075 * x

Divide both sides by 0.075

80 = x

Rewrite as:

x = 80

Hence, the times spent in training is 80 hours

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