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3 years ago

Item 1

Mathematics

2 answers:

sdas [7]3 years ago

6 0

Answer:

OPTION B

Step-by-step explanation:

AS 1KG=1000GRAMS

SEE IMAGE FOR PROOF .

nirvana33 [79]3 years ago

4 0

1000 grams. 1 kilogram is equivalent to 1000 grams

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Mark the statement either true (in all cases) or false (for at least one example). If false, construct a specific example to sho

LUCKY_DIMON [66]

Answer with Step-by-step explanation:

We are given that $v_1,v_2,..,v_4$ are in $R^4$ and $v_1,v_2,v_3$ is linearly dependent then {v_1,v_2,v_3,v_4}[/tex] is also linearly dependent.

We have to find that given statement is true or false.

Dependent vectors:Dependent vectors are those vectors in which atleast one vector is a linear combination of other given vectors.

Or If we have vectors $x_1,x_2,....x_n$

Then their linear combination

$a_1x_1+a_2x_2+.....+a_nx_n=0$

There exist at least one scalar which is not zero.

If $v_1,v_2,v_3$ are dependent vectors then

$a_1v_1+a_2v_2+a_3v_3=0$ for scalars $a_1,a_2,a_3$

Then , by definition of dependent vectors

There exist a vector which is not equal to zero

If vector $v_3$ is a linear combination of $v_1\;and \;v_2$ , So at least one of vectors in the set is a linear combination of others and the set is linearly dependent.

Hence, by definition of dependent vectors

{ $v_1,v_2,v_3,v_4$ } is linearly dependent.

Option B is true.

8 0

3 years ago

What is the value of y?

romanna [79]

Answer:

Step-by-step explanation:

y+y+60=180

2y =120

therefore,y=60

7 0

3 years ago

Read 2 more answers

What two numbers have a difference of 5 and a product of 3.36

iris [78.8K]

X-y=5
xy=3.36
add y to both sides on first
x=5+y
sub that in other eqation
(5+y)y=3.36
expand
y^2+5y=3.36
minus 3.36 both sides
y^2+5y-3.36=0
use quadratic formula

for
ay^2+by+c=0
$y= \frac{-b+/- \sqrt{b^2-4ac} }{2a}$
for 1y^2+5y-3.36
$y= \frac{-5+/- \sqrt{5^2-4(1)(-3.36)} }{2(1)}$
$y= \frac{-5+/- \sqrt{25+13.44} }{2}$
$y= \frac{-5+/- \sqrt{38.44} }{2}$
$y= \frac{-5+/- 6.2}{2}$
y=-2.5+/-3.1
y=5.6 or 0.6
sub back

x=y+5
so
x=10.6 or 5.6

the numbers are either 10.6 and 5.6 or 0.6 and 5.6
wait,but 10.6 and 5.6 don't multiply to get 3.36 so that is an extrainiesous answer

answer is 0.6 and 5.6

7 0

3 years ago

Suppose the temperature outside is dropping 3 degrees each hour. How much will the temperature change in 8 hours

tester [92]

8 × 3 = 24 so it drops 24 degrees

8 0

3 years ago

ASAP!!! Use the pythagorean theorem to prove that the point (√2/2, √2/2) lies on the unit circle. I need setup, explination, ans

docker41 [41]

Answer:

In brief, apply the pythagorean theorem to show that the distance between the point $(\sqrt{2}/2,\sqrt{2}/2)$ and the origin is $1$ .

Step-by-step explanation:

The pythagorean theorem can give the distance between two points on a plane if their coordinates are known.

A point is on a circle if its distance from the center of the circle is the same as the radius of the circle.

On a cartesian plane, the unit circle is a circle

centered at the origin $(0,0)$
with radius $1$ .

Therefore, to show that the point $(\sqrt{2}/2,\sqrt{2}/2)$ is on the unit circle, show that the distance between $(\sqrt{2}/2,\sqrt{2}/2)$ and $(0,0)$ equals to $1$ .

What's the distance between $(\sqrt{2}/2,\sqrt{2}/2)$ and $(0,0)$ ?

$\displaystyle \sqrt{\left(\frac{\sqrt{2}}{2}-0}\right)^{2} + \left(\frac{\sqrt{2}}{2}-0\right)^{2}} = \sqrt{\frac{1}{2} + \frac{1}{2}}= \sqrt{1}= 1$ .

By the pythagorean theorem, the distance between $(\sqrt{2}/2,\sqrt{2}/2)$ and the center of the unit circle, $(0,0)$ , is the same as the radius of the unit circle, $1$ . As a result, the point $(\sqrt{2}/2,\sqrt{2}/2)$ is on the unit circle.

3 0

3 years ago