I believe your answer is 513200000
Hope this helps!
Median of 10, 55, 34, 21
First we arrange number in ascending or descending
10, 21, 34, 55 in ascending.
Median is the middle number and this is between 21 and 34.
We find the average:
(21 + 34) /2 = 55/2 = 27.5
Median is 27.5.
Answer:
<h2>x = 9, y = -72/5</h2>
Step-by-step explanation:
Given the 2 by 2 matrix ![A = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D)
, we are to find the value of x and y for the expression A² = A to be true.
First we need to find A² by multiplying the same matrix together
![A^2 = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right] \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\\\ \ we \ normally \ multiply \ the \ rows \ of \ the \ first \ matrix \ with \ the \ column \ of \ the \ second \\\\A^2 = \left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right]\\\\Since \ A^2 = A,\ hence;\\\\\left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right] = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\](https://tex.z-dn.net/?f=A%5E2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%20%5C%20we%20%5C%20normally%20%5C%20multiply%20%5C%20the%20%5C%20rows%20%5C%20of%20%5C%20the%20%5C%20first%20%5C%20matrix%20%5C%20with%20%5C%20the%20%5C%20column%20%5C%20of%20%5C%20the%20%5C%20second%20%5C%5C%5C%5CA%5E2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%5E2%2B5y%265x-40%5C%5Cxy-8y%265y%2B64%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CSince%20%5C%20A%5E2%20%3D%20A%2C%5C%20hence%3B%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%5E2%2B5y%265x-40%5C%5Cxy-8y%265y%2B64%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7B-cc%7Dx%265%5C%5Cy%26-8%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C)
Equating the first row and second column of both matrices together, we will have;
5x-40 = 5
add 40 to both sides of the equation
5x-40+40 = 5+40
5x = 45
x = 45/5
x = 9
Similarly, we will equate the second row and second column of both matrices to have;
5y+64 = -8
Subtract 64 from both sdies
5y+64-64 = -8-64
5y = -72
y = -72/5
<em>Hence the value of x is 9 and y is -72/5</em>
Answer:
i think is 167
Step-by-step explanation:
Answer:
6. 36°
7. 33.1 cm
Step-by-step explanation:
6. The tangent function relates the sides of a right triangle to the acute angles. Here, the angle west of south that is the direction of the ship from harbour is related to the distances by ...
tan(angle) = (18 km)/(25 km)
Then the angle can be found using the inverse tangent function:
angle = arctan(18/25) ≈ 35.75°
The direction back to the harbour is this same angle east of north. Since bearing angles are measured clockwise from north, the desired bearing is 36°.
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7. The cosine function relates the hypotenuse of a right triangle to the side adjacent to the angle of interest. Here, we have ...
cos(72°) = (diameter of glass)/(straw length to glass rim)
straw length to glass rim = (diameter of glass)/cos(72°) ≈ (9 cm)/0.309017
straw length to glass rim ≈ 29.1 cm
The straw extends 4 cm above the rim of the glass, so is 4 cm longer than this calculated value. The straw is about 33.1 cm long.
