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Sav [38]
3 years ago
13

A group of 33 people attended a ball game. there were twice as many children as adults in the group. set up a system of equation

s that represents the numbres of adults and children who attended the game and solve the system to find the nymber of adults and the number of children
Mathematics
1 answer:
taurus [48]3 years ago
8 0
Gjoydxvbkurulnjuvxrhbv
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Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.
fenix001 [56]

Answer:

The angle between vector \vec{u} = 5\, \vec{i} - 8\, \vec{j} and \vec{v} = 5\, \vec{i} + \, \vec{j} is approximately 1.21 radians, which is equivalent to approximately 69.3^\circ.

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

  • their dot products, and
  • the product of their lengths.

To be precise, if \theta denotes the angle between \vec{u} and \vec{v} (assume that 0^\circ \le \theta < 180^\circ or equivalently 0 \le \theta < \pi,) then:

\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}.

<h3>Dot product of the two vectors</h3>

The first component of \vec{u} is 5 and the first component of \vec{v} is also

The second component of \vec{u} is (-8) while the second component of \vec{v} is 1. The product of these two second components is (-8) \times 1= (-8).

The dot product of \vec{u} and \vec{v} will thus be:

\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}.

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both \vec{u} and \vec{v}:

  • \| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}.
  • \| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}.

<h3>Angle between the two vectors</h3>

Let \theta represent the angle between \vec{u} and \vec{v}. Apply the formula\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} to find the cosine of this angle:

\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}.

Since \theta is the angle between two vectors, its value should be between 0\; \rm radians and \pi \; \rm radians (0^\circ and 180^\circ.) That is: 0 \le \theta < \pi and 0^\circ \le \theta < 180^\circ. Apply the arccosine function (the inverse of the cosine function) to find the value of \theta:

\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ .

3 0
2 years ago
Help ASSAP . Find the perimeter I will give you 20 points and brainlyist.
Tpy6a [65]

Answer:

I think it may be 120 cm

Step-by-step explanation:

A F is 13 using pythagorean theorem on triangle CED and applying the hypotenuse length to A F.

ABC is similar to triangle CED and is dilated by a factor of 3  so the base is 36.

using pythagorean theorem on triangle ABC gets the hypotenuse length of 39 which can be applied to FE

add all the values together

39 + 13 + 15 + 36 +12 +5 = 120

5 0
3 years ago
Which fraction does point P represent on the number line below?
yarga [219]
The answer is C because it is at the first of four intervals between 0 and 1           
8 0
2 years ago
Read 2 more answers
What is -3/11 divided by -5/6
Masja [62]

Answer:

0.00909090909

Step-by-step explanation:

8 0
3 years ago
Someone please help me, use a variable to represent the situation, and solve the equation using inverse operations.
Scorpion4ik [409]

Answer:

36 in

Step-by-step explanation:

T= toucan

M= macaw

T= 2/3M

T= 24

24= 2/3M

72=2M

36= M

4 0
2 years ago
Read 2 more answers
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