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3 years ago

Find the angle between u=(8, -2) and v=(9,3) Round to the nearest tenth of a degree.

Mathematics

2 answers:

Kryger [21]3 years ago

5 0

Answer:

the angle between u=(8, -2) and v=(9,3) is 32.5°

Step-by-step explanation:

u=(8,-2)=(u1,u2)→u1=8, u2=-2

v=(9,3)=(v1,v2)→v1=9, v2=3

We can find the angle between two vectors using the formula of dot product:

u . v =║u║║v║cos α (1)

And the dot product is:

u . v = u1 v1 + u2 v2

u . v = (8)(9)+(-2)(3)

u . v = 72-6

u . v = 66

║u║=√(u1²+u2²)

║u║=√((8)²+(-2)²)

║u║=√(64+4)

║u║=√(68)

║u║=√((4)(17))

║u║=√(4)√(17)

║u║=2√(17)

║v║=√(v1²+v2²)

║v║=√((9)²+(3)²)

║v║=√(81+9)

║v║=√(90)

║v║=√((9)(10))

║v║=√(9)√(10)

║v║=3√(10)

Replacing the known values in the formula of dot product (1):

u . v =║u║║v║cos α

66 = 2√(17) 3√(10) cos α

Multiplying:

66 = 6√((17)(10)) cos α

66 = 6√(170) cos α

Solving first for cos α: Dividing both sides of the equation by 6√(170):

$\frac{66}{6\sqrt{170} }=\frac{6\sqrt{170}cos \alpha}{6\sqrt{170} }$

$\frac{66}{6\sqrt{170}}=cos\alpha$

Simplifying: Dividing the numerator and denominator on the left side of the equation by 6:

(66/6)/(6√170/6)=cosα→11/√170=cosα→cosα=11/√170

cosα=11/13.03840481→cosα=0.84366149

$\alpha=cos^{-1}0.84366149\\\alpha=32.47119205^{\°}\\ \alpha=32.5^{\°}$

Hatshy [7]3 years ago

3 0

Answer:

The answer is 32.5 degrees.

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OlgaM077 [116]

Answer:

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Step-by-step explanation:

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$\frac{x-1}{(x-1)(x-2)}=\frac{1}{x-2}\\\\\frac{x-2}{(x-2)(x-3)} =\frac{1}{x-3}\\\\\frac{x-5}{(x-3)(x-5)} =\frac{1}{x-3}$

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3 0

3 years ago

Use the image to match the arc/angle measure.

IrinaK [193]

Answer:

The following measurements are:

$m\angle{STR}=23^\circ$ (Option #4)

$m{QT}=142^\circ$ (Option #7)

$mST=134^\circ$ (Option #5)

$mRQ=38^\circ$ (Option #2)

Step-by-step explanation:

To begin, we can find the measure of $\angle{STR}$ by applying the inscribed angle theorem: an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

Since the intercepted arc (RS) is 46 degrees, we have:

$46=2\theta\\23=\theta$

Next, we can find the measure of arc QT using the same theorem. So,

$QT=2(71)\\QT=142$

Notice that the chord RT is actually a diameter. From the theorem about the inscribed angle including a diameter, we know that the intercepted arc will have a measure of $180^\circ$ . Since the arc ST is part of the arc RST, and we know RS is $46^\circ$ , we can set up and solve this equation: