What is the arc measure of a 90 degree angle

The partial derivatives we found earlier: dw = (-3sin(3x + 5y - 7z))dx + (-5sin(3x + 5y - 7z))dy + (7sin(3x + 5y - 7z))dz

To write the differential dw in terms of the differentials dx, dy, and dz, we'll first find the partial derivatives of w with respect to x, y, and z. Given w = f(x, y, z) = cos(3x + 5y - 7z):

∂w/∂x = -3sin(3x + 5y - 7z)
∂w/∂y = -5sin(3x + 5y - 7z)
∂w/∂z = 7sin(3x + 5y - 7z)

Now, we can write dw as the sum of the products of the partial derivatives and the corresponding differentials:

dw = (∂w/∂x)dx + (∂w/∂y)dy + (∂w/∂z)dz

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Let's start with the smallest prime number 2

60/2 = 30

Divide that result over 2

30/2 = 15

We can't divide this by 2 because 15/2 = 7.5 isn't a whole number

Let's move onto 3

15/3 = 5

The result is a prime number, so we stop.

The values we divided as denominators were: {2, 2, 3}

We add the result 5 to the set to completely list all of the prime factors of 60

The prime factorization would be

which is the same as saying

The horizon's distance for a typical human being (2 m height) for earth is 5 km, for mars it is 3.7 km, for moon its 2.6 km, and for Diemos it is 0.15 km (all calculations approx).

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

\(|AC|^2 = |AB|^2 + |BC|^2\)

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

The complete question is:

" For a typical human height of 2 meters, what is the horizon distance on A) Earth (R=6378 km); B) Mars ( 3,374 km); C) The Moon ( 1,738 km); Mars' moon Diemos ( 6 km) "

Radius touching the line which passes touching the circle (tangent) is perpendicular(to 90°) to it.

Consider the diagram attached below:

The distance D is the distance of horizon from the eyesight of viewer.

The value of h is the height of the observer.

For the triangle ABC, the length of the hypotenuse is: h + R

Other two sides which are mutually perpendicular are of length R and D.

Thus, by using Pythagoras theorem, we get:

\(R^2 + D^2 = (h+R)^2\\D = \sqrt{h^2 + R^2 + 2hR -R^2}\\\\D = \sqrt{h^2 + 2hR}\\\)

(positive root as D is representing length, a non-negative quantity).

We're given h = 2, so we get:

\(D = \sqrt{4+4R} = 2\sqrt{1+R} \: \rm m\)

6378 km = 6378000 m

\(D = 2\sqrt{6379001} \approx 5051 \: \rm m \approx 5 \: km\)

3374 km = 3374000 m

\(D = 2\sqrt{3374001} \approx 3674 \: \rm m \approx 3.7 \: km\)

C) The Moon ( 1,738 km);

1738 km = 1738000 m

\(D = 2\sqrt{1738001} \approx 2637 \: \rm m \approx 2.6 \: km\)

D)Mars' moon Diemos ( 6 km)

6 km = 6000 m

\(D = 2\sqrt{6001} = 154.93 \: \rm m \approx 0.15 \: km\)

Thus, the horizon's distance for a typical human being (2 m height) for earth is 5 km, for mars it is 3.7 km, for moon its 2.6 km, and for Diemos it is 0.15 km (all calculations approx).

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The answer is

\(y = - \frac{1}{5} x - 1.2\)

or you can replace -1/5 with -0.2

follow the procedures in the attachment please.

Answer:

$32,055.75

Step-by-step explanation:

51.95 x 12341 = 641,114.95 (the total amount of money made by the books)

641,114.95 x 0.05 = 32,055.7475

(0.05 is the 5% royalty, since percents are out of 100 you use decimal points to find them)

$32,055.75 (final answer rounded)

Answer:

f(x)=5

Step-by-step explanation:

3(4)-7

12-7

5

Hope This Helps!

Answer:

Y=-6

Y= -1.1

Y=-43

Step-by-step explanation:

Answer:

y=6,x=0

Step-by-step explanation:

here's an attachment with how to solve

Answer:

he would be 14

Step-by-step explanation:

Answer:Bob is 8 years old

Step-by-step explanation:

Andrew is 6 years, Phil is 8 years, add those together, subtract that by 22

The value of x is expressed as x = -5 ± 12. 9

From the information given, we have the quadratic equation given as;

x² + 5x - 84 = 0

Given the quadratic general formula as;

ax + bx + c

We have the variables as;

a = 1

b = 5

c = -4

Then, using the formula, we get;

x = -b± √b²-4ac

Substitute the values

x = -(5) ± \(\sqrt{\frac{-(5) - 4(1)(-84)}{2(1)} }\)

Multiply the values, we get

x = -5± √331/2

Divide the values, we get;

x = -5 ± √165.5

Find the square root of the value

x = -5 ± 12. 9

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Answer:

if f(10) was shown if the graph, f(n) would be -20

Answer:

Yes, she is correct.

Step-by-step explanation:

\(3x+5=64\\\\3x+5-5=64-5\\\\3x=59\\\\\frac{3x}{3}=\frac{59}{3}\\\\ \frac{59}{3}=19\frac{2}{3}\\\\19\frac{2}{3}=19.666...\\\\ \text{Therefore}:\\x=\boxed{19.666...}\)

The digit of 6 is repeating.

Answer:

Step-by-step explanation:

The formula for finding the nth term of an arithmetic sequence is expressed as shown;

\(Tn = a+(n-1)d\)

a is the first term of the sequence

n is the number of terms

d is the common difference

If T₁₂ = 70 and T₃₀ = 124

T₁₂  = a+(12-1)d = 70

T₁₂  = a+11d = 70... (1)

Similarly;

T₃₀ = a + (30-1)d = 124

T₃₀ = a +29d = 124...(2)

Solving equation 1 and 2 simultaneously to get a and d.

Subtracting 2 from 1 we have;

29d - 11d = 124-70

18d = 54

d = 54/18

d = 3

Substituting d = 3 into equation 1 to get a we have;

a + 11(3) = 70

a + 33 = 70

a = 70-33

a = 37

The explicit rule for the nth term of the sequence can be gotten by substituting the value of a and d into the formula Tn = a+(n-1)d

Tn = 37+(n-1)*3

Tn = 37+3n-3

Tn = 34+3n

Answer:

I believe it is y=1/4x.

Step-by-step explanation:

the answer is in the above image

A quadratic functiοn f whose zeroes are 2 and 5 is f(x) = x² - 7x + 10.

A quadratic functiοn is a secοnd-degree pοlynοmial functiοn οf the fοrm:

f(x) = ax² + bx + c

where a, b, and c are cοnstants, and a is nοt equal tο 0. The graph οf a quadratic functiοn is a parabοla, which can οpen upwards οr dοwnwards depending οn the sign οf the leading cοefficient a.

The term ax² is the quadratic term, bx is the linear term, and c is the cοnstant term. The cοefficient a determines the shape οf the parabοla, while the cοnstants b and c determine its pοsitiοn and οrientatiοn.

Quadratic functiοns can have οne, twο, οr zerο real rοοts (alsο knοwn as sοlutiοns οr zerοs), which cοrrespοnd tο the x-intercepts οf the parabοla. The number and nature οf the rοοts depend οn the value οf the discriminant, which is given by b² - 4ac.

If the zeroes are x = 2 and x  = 5 then the solutions must be:

(x - 2)(x - 5)

Multiply them and make a quadratic function

⇒ (x - 2)(x - 5)

⇒ (x²  - 5x)- (2x - 5)

⇒ x² -5x - 2x + 5

⇒ x² -5x - 2x + 5

⇒ x² - 7x + 5

Comparing this to the form of the quadratic function f(x) = ax² + bx + c, we see that a = 1, b = -7, and c = 10. Therefore, the quadratic function with zeros at 2 and 5 is:

f(x) = x²- 7x + 10

So, the correct option is f(x) = x² - 7x + 10.

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Answer:

3

Step-by-step explanation:

You would do 3/5 =6 then do 13/7 = 18/6=3

The surface area of a right circular cone is computed as follows:

where r is the radius and s is the slant height of the cone.

Substituting with r = 3 mm and s = 4 mm, we get:

The system of linear equations has at least one solution is consistent , whereas a system of linear equations that has no solution is inconsistent

What is a system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system (see linearization).

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To find the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days, we use the simple interest formula as follows:

Simple Interest = (P × R × T)/100Where:P = Principal or amount borrowedR = Rate of interest per annumT = Time in years or fraction of a year110 days ÷ 360 days = 0.3056 (time as a fraction of a year)The rate of interest, 10(1/3)% is equal to 10 + (1/3) percent = 10.33% per annum in decimal form = 0.1033Substituting the values we have into the formula,Simple Interest = (P × R × T)/100= (3,290 × 0.1033 × 0.3056)/100= $100.68 (rounded to the nearest cent)

Therefore, the interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68.

A credit union loan is a type of personal loan that can be used for a variety of purposes. One of the most common reasons people take out credit union loans is to purchase big-ticket items like a new computer system. When you take out a loan, you must pay back the amount borrowed plus the interest charged by the lender. The interest rate is usually expressed as a percentage of the amount borrowed and is charged for a specific period of time known as the loan term. Simple interest is a method of calculating interest that is charged only on the principal amount borrowed.

It does not take into account the interest that has already been paid. Simple interest is calculated by multiplying the principal amount borrowed by the interest rate and the length of the loan term. The answer is more than 100 words.The interest of Chris Owens’ credit union loan of $3,290 at 10(1/3)% interest for 110 days is $100.68. Therefore, he would pay $3,290 + $100.68 = $3,390.68 in total to the credit union over the loan term. It is important to note that when rounding dollar amounts to the nearest cent, amounts that end in .50 or higher are rounded up to the next highest cent, while amounts that end in .49 or lower are rounded down to the next lowest cent. In this case, $100.6847 would be rounded up to $100.68. In conclusion, the interest charged on a loan can significantly increase the total amount that must be repaid, making it important for borrowers to understand how interest is calculated and the terms of their loan.

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The dimensions are;

Length = 7 meters

Width = 5 meters

The area of a rectangle is expressed as;

Area = length × width

From the information given, we have that;

Length = 2w - 3

Area = 65

Substitute the values

65 = (2w - 3)w

expand the bracket

65 = 2w² - 3w

solve the quadratic equation;

2w² + 13w - 10w - 65

Factorize the terms

w(2w + 13) - 5(2w + 13)

w = 5

Substitute the value

Length = 2w - 3 = 2(5) - 3 = 7

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Answer:

Slope: 4

Y-interecept: -2

Step-by-step explanation:

To find the slope, use rise over run. Go up from the y-intercept and over until you hit another exact point.

To find the y-intercept, just find the point that is on the y-axis.

The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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To find the domain and range, the function we simply solve the equation y=f(x) to determine the values of the independent variable x and obtain the domain.

Domain: In simple words, the domain is the set of values of x for which function f(x) is defined,  and also the set of values of x for which we can calculate the value of f(x)

Range: The range of function can define as the set of values of f(x) for the value of its domain

For finding the domain of any function f(x) ..find the value of all x for which function f(x) is defined

For finding the value of the range of function f(x), calculate the value of f(x) for all values of x in the set of domains of f(x)

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The correct option is  B) increase.

To decrease sample error, a pollster must increase the number of respondents. The larger the sample size, the more representative it is likely to be of the target population, leading to a lower margin of error.

When conducting surveys or polls, it is essential to obtain responses from a diverse and random group of individuals. By increasing the number of respondents, the pollster can capture a broader range of perspectives, which helps to reduce sampling bias and increase the accuracy of the results.

For example, let's say a pollster wants to understand the political preferences of voters in a particular city. If they only survey 50 people, the sample may not accurately reflect the larger population, and the margin of error could be high. However, if they survey 500 or even 1000 people, the results are more likely to provide a reliable estimate of the overall population's preferences.

Therefore, to decrease sample error, pollsters should increase the number of respondents in their surveys or polls. This approach helps to ensure a more accurate representation of the population's views and minimize the potential for misleading or biased results.

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False.

Data reduction techniques can be applied to both rows (observations) and columns (variables) in a given dataset. Data reduction techniques like Principal Component Analysis (PCA) and Factor Analysis are applied to variables in order to reduce the number of variables and extract relevant information from them. These techniques aim to identify underlying factors or components that explain the variance in the data and represent them in a lower-dimensional space. Similarly, techniques like clustering and outlier detection can be applied to observations in order to group similar observations together or identify outliers.

Therefore, data reduction can be applied to both rows and columns, depending on the analysis goals and data characteristics.

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Answer:

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