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Natasha2012 [34]
3 years ago
5

Hiya! can anyone help me with these? it would be greatly appreciated!

Mathematics
2 answers:
kolezko [41]3 years ago
5 0

Answer:

K would be -6 and w would be 9

Len [333]3 years ago
4 0

Answer:

k = -6

w = ±9

f = -7

Determinant = -136

Step-by-step explanation:

\left[\begin{array}{cc}-12&-w^{2}\\2f&3\end{array}\right] =\left[\begin{array}{cc}2k&-81\\-14&3\end{array}\right]

Each cell in the left matrix equals the corresponding cell in the right matrix:

-12 = 2k → k = -6

-w² = -81 → w = ±9

2f = -14 → f = -7

\left|\begin{array}{ccc}-4&5&6\\0&4&4\\-2&-5&4\end{array}\right|

To find the determinant of a 3x3 matrix, you can use something called "Laplace expansion".

Start with the first column in the top row (-4).  If you block out the row and column containing that cell, you get a 2x2 matrix:

\left|\begin{array}{ccc}*&*&*\\ *&4&4\\ *&-5&4\end{array}\right|

Multiply the -4 by the determinant of that 2x2 matrix:

-4\left|\begin{array}{cc}4&4\\-5&4\end{array}\right|

Repeat for the other two cells in the top row.

5\left|\begin{array}{cc}0&4\\-2&4\end{array}\right|

6\left|\begin{array}{cc}0&4\\-2&-5\end{array}\right|

Add them together, alternating the signs (first column positive, second column negative, third column positive).

-4\left|\begin{array}{cc}4&4\\-5&4\end{array}\right|-5\left|\begin{array}{cc}0&4\\-2&4\end{array}\right|+6\left|\begin{array}{cc}0&4\\-2&-5\end{array}\right|

To find the determinants of the 2x2 matrices, multiply the top left and bottom right, then subtract the top right times the bottom left.-4((4\times4)-(4\times-5))-5((0\times4)-(4\times-2))+6((0\times-5)-(4\times-2))

Simplify:

-4(16-(-20))-5(0-(-8))+6(0-(-8))\\-4(36)-5(8)+6(8)\\-144-40+48\\-136

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Find the output, k, when the input, t, is –7.<br> k = 10t -19
kupik [55]

Answer:

k = - 89

Step-by-step explanation:

To calculate the output, substitute t = - 7 into the equation for output, that is

k = 10(- 7) - 19 = - 70 - 19 = - 89

7 0
3 years ago
Find the area of a trapezium whose parallel sides are 25 cm ,13 cm and other sides are 15 cm and 15 cm
cupoosta [38]
The answer is area= 285 cm
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A spherical cantaloupe is cut in half. The visible cross-section has an area of 5252 in2. The volume of the cantaloupe is _____
artcher [175]

Answer:

V = 286319.465 cm3

Step-by-step explanation:

First, you have to find the radius to be able to find the volume of a sphere.

The equation for the area of a circle is pi r^2 so you have to so some algebra.

5252 = pi r ^2

5252/pi = r^2

1671.76352 = r^2

sqrt(1671.76352) = r

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then you do the equation for the volume of a circle which is 4/3 pi r^3

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V = 286319.465 cm3

6 0
2 years ago
2) Find the missing measure. Show your work.<br> X =<br> 130°
Veronika [31]

Answer:

The missing angle I believe is 25%.

Step-by-step explanation:

180-130=50

Divide 50 by 2 and it equals 25. 25 degrees for each angles.

5 0
3 years ago
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Summer spent $55.60 on clothes before sales tax. If sales tax is 7.5%, what did Summer spend with tax included?  *Add Explanatio
vampirchik [111]
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3 years ago
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