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dolphi86 [110]
3 years ago
14

40 POINTS + BRAINLIEST! PLEASE SHOW ALL WORK

Mathematics
1 answer:
Elina [12.6K]3 years ago
7 0
Hey there,

Your correct answer would be in the attachment below.

Hope this helps you!

~Jurgen

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The numerator and the denominator of a fraction are thirteen and fifty, respectively. When a certain number is added to this num
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(13 + x)/(50 - x ) = (2/1)
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Question 15 (5 points)<br> Find the angle between u = &lt;7, -2&gt; and v= (-1,2&gt;.
Tema [17]

Answer:

Approximately 2.3127 radians, which is approximately 132.51^{\circ}.

Step-by-step explanation:

Dot product between the two vectors:

\begin{aligned}& u\cdot v \\ =\; & 7 \times (-1) + (-2) \times 2 \\ =\; & (-11) \end{aligned}.

Magnitude of the two vectors:

\begin{aligned} \| u \| &= \sqrt{{7}^{2} + {(-2)}^{2}} \\ &= \sqrt{53} \end{aligned}.

\begin{aligned} \| v \| &= \sqrt{{(-1)}^{2} + {2}^{2}} \\ &= \sqrt{5} \end{aligned}.

Let \theta denote the angle between these two vectors. By the property of dot products:

\begin{aligned} \cos(\theta) &= \frac{u \cdot v}{\|u\| \, \| v \|} \\ &= \frac{(-11)}{(\sqrt{53})\, (\sqrt{5})} \\ &= \frac{(-11)}{\sqrt{265}}\end{aligned}.

Apply the inverse cosine function {\rm arccos} to find the value of this angle:

\begin{aligned} \theta &= \arccos\left(\frac{u \cdot v}{\| u \| \, \| v \|}\right) \\ &= \arccos\left(\frac{(-11)}{\sqrt{265}}\right) \\ & \approx \text{$2.3127$ radians} \\ &= 2.3127 \times \frac{180^{\circ}}{\pi} \\ &\approx 132.51^{\circ}\end{aligned}.

8 0
3 years ago
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