The function represents a <em>cosine</em> graph with axis at y = - 1, period of 6, and amplitude of 2.5.
<h3>How to analyze sinusoidal functions</h3>
In this question we have a <em>sinusoidal</em> function, of which we are supposed to find the following variables based on given picture:
- Equation of the axis - Horizontal that represents the mean of the bounds of the function.
- Period - Horizontal distance needed between two maxima or two minima.
- Amplitude - Mean of the difference of the bounds of the function.
- Type of sinusoidal function - The function represents either a sine or a cosine if and only if trigonometric function is continuous and bounded between - 1 and 1.
Then, we have the following results:
- Equation of the axis: y = - 1
- Period: 6
- Amplitude: 2.5
- The graph may be represented by a cosine with no <em>angular</em> phase and a sine with <em>angular</em> phase, based on the following trigonometric expression:
cos θ = sin (θ + π/2)
To learn more on sinusoidal functions: brainly.com/question/12060967
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Answer:
(A) Set A is linearly independent and spans
. Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors
, we are to decide which of the given statements is true:
In Matrix
, the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans
. Thus it is basis for
.
Answer:
Explanation:
<u>1) Write the changes in the temperature of the city over the 4 days in an easy way to read.</u>
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<u>2) Write the expression to show the average daily change in temperature.</u>
The average of a set of data is calculated with the expression:
- Average = (sum of the data) / amount of data
Hence, you need to add the four change of temperature data and divide by 4.
The expression is:
- Average = [ 1.34 °C + (- 5 / 7 °C) + ( - 0.75 °C) + 4/9 ° C ] / 4
<u>3) Write the steps to solve the expression:</u>
You can choose between adding fractions or adding the decimal forms of the numbers.
If you choose adding decimals, keep the complete decimals in your calculator, to avoid the accumulation of errors due to rounding. Round only the final result.
These are the steps.
<u>a. Find the decimal forms of the fractions:</u>
<u>b. Add the four data:</u>
- 1.34°C + (- 0.71428 °C) + (-0.75 °C) + 0.44444 °C ≈ 0.32019 °C
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<u>c. Divide the sum by the number of data (4)</u>
- 0.32019 °C / 4 ≈ 0.080004 °C
<u>4. Round to the nearest hundredth</u>
The place of the hundreth is the second after the decimal point, which is 8 in this case:
(8/9)^2 is 64/81. Exponent is 2. Hope this help