A trend line is a line that indicates the tendency of a graph; in other words, is the line that shows the apparently direction of a group of points on a graph. There are various types of trend lines; let’s check them:
Linear
Linear trend lines are used when the points on your graph follow a straight line pattern, which means that something is increasing or decreasing at a fixed rate (the slope of the straight line).
Logarithmic
Logarithmic trend lines are curved lines used when the rate of change increases very quickly and then settles down.
Polynomial
Polynomial trend lines are curved lines used when the data oscillates (change in direction from increasing to decreasing or vice versa).
Power
Power trend lines are curved lines used when you have a positive set of data that increases at a specific rate.
Exponential
Exponential trend lines are curved lines used when you have a set of data that increase or decreases at increasingly or decreasingly higher rates.
Moving averages
Moving averages are used when your data that varies a lot. They can be straight lines, curved lines or a combination of both.
As you can see, all trend lines are either straight lines or curved lines; therefore, the correct answer is a. curved lines or straight lines
Answer:
Step-by-step explanation:
To write a percent for a decimal, move the decimal point two places to the right. Add the percent sign.
First, divide by 100.
40/100=0.4
Therefore, the correct answer is 0.4.
Answer:
The required quadratic function is .
Step-by-step explanation:
The standard form of the parabola is
Where the focus is (h, k + p) and the directrix is y = k - p.
The directrix of y = 2 and a focus of (3, −4).
On comparing both sides we get
...... (1)
...... (2)
Add equation (1) and (2).
Substitute k=-1 in equation (1).
Therefore the equation of parabola is
It can be rewritten as
Therefore the required quadratic function is .
Answer:
8/15 (fraction) or 0.5333333333333...
Step-by-step explanation:
Answer:
4/15
Step-by-step explanation:
115×41=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
1×415×1=415
This fraction cannot be reduced.
Therefore:
115×41=415
Apply the fractions formula for multiplication, to
115×41
and solve
1×415×1
=415
(a) A + B: The result is -4i - 6j, with a magnitude of 2√13 and a direction angle of arctan(3/2).
(b) A - B: The result is -2i + 6j, with a magnitude of 2√10 and a direction angle of arctan(-3).
The given vectors are:
B = -i - 4j
A = -3i - 2j
(a) A + B:
To add two vectors,
Simply add their corresponding components.
So, A + B = (-3i - 2j) + (-i - 4j)
Combining the i-components, we get:
-3i - i = -4i.
And combining the j-components, we get:
-2j - 4j = -6j.
Therefore, A + B = -4i - 6j.
To find the magnitude of A + B,
Use the Pythagorean theorem:
|A + B| = ,
Where x is the magnitude of the i-component and y is the magnitude of the j-component.
In this case,
x = -4 and y = -6,
So: |A + B| =
|A + B| = 2√13
To find the direction angle of A + B,
Use the arctan function:
θ = arctan(y / x),
Where y is the j-component and x is the i-component.
In this case,
x = -4 and y = -6,
so: θ = arctan(-6 / -4)
θ = arctan(3/2)
Therefore, the magnitude of A + B is 2√13 and the direction angle is arctan(3/2).
(b) A - B:
To subtract two vectors,
Subtract their corresponding components.
So, A - B = (-3i - 2j) - (-i - 4j).
Combining the i-components, we get:
-3i + i = -2i.
And combining the j-components, we get:
-2j - (-4j) = 2j + 4j = 6j.
Therefore, A - B = -2i + 6j.
To find the magnitude of A - B,
Use the Pythagorean theorem:
,
Where x is the magnitude of the i-component and y is the magnitude of the j-component.
In this case,
x = -2 and y = 6,
so:
|A - B| = 2√10
To find the direction angle of A - B,
Use the arctan function:
θ = arctan(y / x),
Where y is the j-component and x is the i-component.
In this case, x = -2 and y = 6,
so:
θ = arctan(6 / -2)
θ = arctan(-3)
Therefore,
The magnitude of A - B is 2√10 and the direction angle is arctan(-3).
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The complete question is:
For vectors B =−i −4j and A =−3i −2j ,
Calculate (a) A + B and its magnitude and direction angle, and (b) A − B and its magnitude and direction angle.
The resulting vectors after adding and subtracting vectors A and B are A + B = -4i - 6j with a magnitude of 7.21 and A - B = -2i + 2j with a magnitude of 2.83. The direction angle for the vectors are calculated using arctan of the absolute value of the components' ratios.
For vectors B = -i - 4j and A = -3i - 2j, you first need to add and subtract these vectors component-wise to get the resulting vectors. Addition gives A + B = -i + (-3i) + -4j + (-2j) = -4i - 6j, whereas subtraction gives A - B = -3i - (-i) + -2j - (-4j) = -2i + 2j.
The magnitude of a vector is calculated by the Pythagorean theorem: (magnitude of A+B) = sqrt((-4)^2 + (-6)^2) = 7.21 and (magnitude of A-B) = sqrt((-2)^2 + 2^2) = 2.83.
The direction angle is found using arctan(|Ay / Ax|), but adjustment must be made depending on the quadrant of the resulting vector. In conclusion, (a) A + B = -4i - 6j, |A + B| = 7.21, angle = arctan(6/4), and (b) A - B = -2i + 2j, |A - B|= 2.83, angle = arctan(2/2).
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