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Artyom0805 [142]
3 years ago
8

Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

Mathematics
1 answer:
katrin2010 [14]3 years ago
6 0

Answer:

9

Step-by-step explanation:

Pythagorean Theorem

a²+b²=c²

(c² is the hypotenuse)

a² + 40² = 41²

a² + 1,600 = 1,681

subtract 1681-1600 in order to isolate a², which is the missing leg we are trying to find

a² = 81 in order to find our answer, we isolate a by squaring both sides

√a² = √81

a = 9

Our answer is 9.

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Assume that T is a linear transformation. Find the standard matrix of T. T: R^3 right arrow R^2 , T(e 1) =(1,2), and T(e2 ) =( -
irina [24]

Answer:

A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

Step-by-step explanation:

Given

T:R^3->R^2

T(e_1) = (1,2)

T(e_2) = (-4,6)

T(e_3) = (2,-6)

Required

Find the standard matrix

The standard matrix (A) is given by

Ax = T(x)

Where

T(x) = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]

Ax = T(x) becomes

Ax = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]

The x on both sides cancel out; and, we're left with:

A = [T(e_1)\ T(e_2)\ T(e_3)]

Recall that:

T(e_1) = (1,2)

T(e_2) = (-4,6)

T(e_3) = (2,-6)

In matrix:

(a,b) is represented as: \left[\begin{array}{c}a\\b\end{array}\right]

So:

T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right]

T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right]

T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right]

Substitute the above expressions in A = [T(e_1)\ T(e_2)\ T(e_3)]

A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

Hence, the standard of the matrix A is:

A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]

6 0
3 years ago
Brianna has 0.15 liter of a liquid. She will use 0.4 of this liquid. How many liters will she use?
alukav5142 [94]

Answer: 0.0375

Step-by-step explanation:

0.15 divided by 4 = 0.0375

4 0
3 years ago
PLS HELPP ITS URGENT
WITCHER [35]

Answer:

Step-by-step explanation:

The angles between the parallel sides add up to 180 degrees.

So 180-70 = 110 degrees.

8 0
2 years ago
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Problem 5.A miner is trapped inside a mine and has access to 3 doors. The first door leads to a tunneland can take him to safety
Likurg_2 [28]

Answer:

Expected time is 15 hours for him to get to safety.

Step-by-step explanation:

We define X as the time that this miner would get to safety.

We define Y as the door he chooses initially.

P(Y= 1) = P(Y=2)=P(Y=3) = 1/3

We have E[X|Y=1] = 3

E[X|Y] = 5 hours + E[X}

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Then we have

E[X] = 1/3(3 + 5 + E[X] + 7 + E[X])

We cross multiply

3*E[X] = (15 + 2E[x])

3E[X] - 2E[X] = 15

E[X] = 15

So the time it would take to get him to safety is 15 hours

5 0
3 years ago
a population of rabbits triple every month. the population starts with two rabbits. how many are there after three months?
Lera25 [3.4K]
2 x 3 = 6
6 x 3 = 18
18 x 3 = 54 

The answer is 54

6 0
3 years ago
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