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1 year ago

What is the angle between the given vector and the positive direction of the x-axis?

Mathematics

1 answer:

jeka57 [31]1 year ago

6 0

The angle is 75.52 degrees

If there is a vector with the form a i + b j, the cosine of the angle between the given vector and the positive direction of the x - axis is calculated as:

cos θ = $a/\sqrt{a^{2}+b^{2} }$

So, given the vector i+ $\sqrt{15 j$ , the cosine of the angle between the vector and the x-axis is:

cos θ = 0.25

Therefore, the angle θ between the given vector and the positive direction of the x-axis is:

θ = cos-1(0.25) = 75.52

For more information about angles, visit

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Evaluate 4 - 2(a2 – b2)2 when a = 3 and b = 2.

Anton [14]

Answer:

-46

Step-by-step explanation:

4 - 2(a^2 – b^2)^2 =

= 4 - 2(3^2 – 2^2)^2

= 4 - 2(9 - 4)^2

= 4 - 2(5)^2

= 4 - 2(25)

= 4 - 50

= -46

6 0

3 years ago

Read 2 more answers

Find -12(-23). A. 230 B. -35 C.-276 D. 276

ad-work [718]

if u multiply a negative and a negative sign you will get a positive so the answer will be 276

4 0

2 years ago

What is 8.478 in expanded form?

nataly862011 [7]

8+0.4+0.07+0.008 you basically separate the numbers starting with the largest working down to the smallest.

i hope i helped

7 0

2 years ago

Read 2 more answers

PLEASE HELP FOR TEST will mark brainiest !!

sdas [7]

Answer:

552.920307 yd^2 or 552.92 yd^2 for sigfigs

Step-by-step explanation:

basically you take the area of the entire circle and subtract the interior circle to leave the ring and that’s your answer

so the area formula of a circle is π r^2

the radius (r) is just half the diameter so the entire diameter is 48 so the radius is 24 - π(24)^2 = 1809.557368^2

then the interior circle’s diameter is 40 so the radius is 20 - π(20)^2 = 1256.637061^2

so now it’s just subtraction:

1809.557368 yd^2 - 1256.637061 yd^2 =
552.920307 yd^2 or 552.92 yd^2 for sigfigs

hope this helps :)

6 0

2 years ago

Read 2 more answers

Five years from now, the sum of the ages of a women and her daughter will be 40 years. The difference in their present age is 24

CaHeK987 [17]

Answer:

Her daughter is 3 years old now.

Step-by-step explanation:

Given:

Five years from now, the sum of the ages of a women and her daughter will be 40 years.

The difference in their present age is 24 years.

Now, to find how old is her daughter now.

Let the age of daughter be $x\ years$ .

And the age of mother be $y\ years$ .

According to question:

$(x+5)+(y+5)=40$

⇒ $x+y+10=40$

Subtracting both sides by 10 we get:

⇒ $x+y=30$

⇒ $x=30-y$ ............( 1 )

Now, as given in question:

The difference in their present ages is 24 years.

$x-y=24$

Putting the equation ( 1 ) in the place of $x$ we get:

⇒ $(30-y)-y=24$

⇒ $30-2y=24$

Moving variable on one side and the numbers on the other:

⇒ $30+24=2y$

⇒ $54=2y$

Dividing both sides by 2 we get:

⇒ $27=y$

So, the age of the mother is 27 years.

Now, putting the value of $y$ in equation( 1 ) we get:

$x=30-27$

⇒ $x=3$

The age of daughter is 3 years.

Therefore, her daughter is 3 years old now.

4 0

2 years ago