If the r-value, or correlation coefficient, of a data set is 0.841, what is the

Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture

ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

x^2 = 1

x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

f(-1) = (-1)^3 = -1

So, using the points (1,1) and (-1,-1) in our parallel line, we have:

first line using (1,1) : 1 = 3*1 + b

b = -2

second line using (-1,-1) : -1 = -3*1 + b

b = 2

The value of b is the y-intercept of the line, so the line with smaller y-intercept is y = 3x - 2, and the line with larger y-intercept is y = 3x + 2

8 0

2 years ago

Factor y=x^4 +6x^2-7

sasho [114]

(x^2-1)(x^2+7) should be your answer

4 0

3 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Find the solution s

irina [24]

Answer:

34.55/6.28=0

Step-by-step explanation:

7 0

3 years ago

Which table shows a proportional relationship between x and y?

Semenov [28]

Answer:

B

Step-by-step explanation:

A proportional relationship is a relationship which crosses through the origin (0,0) and which has a proportional constant. We can determine this either by finding (0,0) where x=0 and y=0 in the table or by dividing y/x. None of the tables contain (0,0) so we will divide y by x. We are looking for a table which when each y is divided by its x we have the same constant appearing.

Table A

$\frac{12}{3} \neq \frac{15}{6} \neq \frac{18}{8} \neq \frac{20}{10}$

These fractions are not equal. This is not proportional.

Table B

$\frac{0.5}{1}=\frac{1}{2} =\frac{3.5}{7} =\frac{4}{8}$

These fractions are equal and each shows the numerator to be half of the denominator. This is proportional.

Table C

$\frac{1}{3}\neq \frac{2.5}{7.5} \neq \frac{4}{15} \neq \frac{6}{20}$

These fractions are not equal. This is not proportional.

Table D

$\frac{7}{2} \neq \frac{9}{3}\neq \frac{11}{4} \neq \frac{13}{5}$

These fractions are not equal. This is not proportional.

3 0

3 years ago

How many minutes did he/she play in all

Lerok [7]

Add the 3 fractions together.
Mixed fractions: 5 3/4 + 2 2/3 + 10 1/6
Convert to improper fractions and then add. Or simply use a calculator.

Total = 223/12 = 18 7/12

5 0

3 years ago

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