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4 years ago

Determine by inspection whether the vectors are linearly independent. Justify your answer.

Mathematics

1 answer:

jekas [21]4 years ago

7 0

Answer:

B. The set is linearly independent because at least one of the vectors is a multiple of another vector.

Step-by-step explanation:

A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.

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Lisa has a recipe that needs 3 fourths of a teaspoon of butter for every 3 cups of milk. If Lisa increases the amount of milk to

vfiekz [6]

1.25 teaspoon of butter per 5 cups of milk
3/4 tsp butter = 3 cups milk
5/4 tsp butter = 5 cups milk

6 0

4 years ago

Question Help

klasskru [66]

Answer:

16 times

Step-by-step explanation:

$\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.

$\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h$

Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.

<h3>Proof</h3>

Given:

radius = 6
height = 9

Substituting the given values into the formula:

$\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units$

If the radius is quadrupled:

radius = 6 × 4 = 24
height = 9

Substituting the new given values into the formula:

$\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units$

To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:

$\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16$

So the volume of the larger cone is 16 times greater than the volume of the smaller cone.

4 0

2 years ago

Read 2 more answers

These triangles are congruent. What value is x?

Lynna [10]

Answer:

8 cm

Step-by-step explanation:

Congruent means same. so x is 8

3 0

3 years ago

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The set of independent variables of a function is the ____.

Anon25 [30]

independent variables is that whose variation does not depend on other
The set of independent variables of a function is the
Domain
which is defined as set of input values of independent variables
so correct option i conclude is A
hope it helps

6 0

4 years ago

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Help asap first gets brainliest if ur right!!!

Olin [163]

Answer:

Step-by-step explanation:

angle AD = 90

FD= 90- 77 = 13

x = 13

I hope im right!

6 0

3 years ago