1.) What is the measure of ∠K, to the nearest degree?

Mathematics

2 answers:

IRISSAK [1]3 years ago

6 0

Answer:

Hello! The correct answer to the first question is 66 degrees.

lora16 [44]3 years ago

5 0

We know that
the law of sines establish
a/sin A=b/sin B

problem N 1

50/sin K=53/sin 76-------> 50*sin 76=53*sin K-----> sin K=50*sin 76/53
sin K=0.9154
K=arc sin (0.9154)--------> K=66.25°------> K=66°

the answer problem N 1 is the option
<span>c.) 66°
</span>
Problem N 2

30/sin R=35/sin 69------> sin R=30*sin 69/35-----> sin R=0.8002
R=arc sin(0.8002)-------> R=53.15°-----> R=53°

the answer problem N 2 is the option
<span>b.) 53°</span>

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Two lines that have the same y intercept and different slopes intersect at exactly one point.

jek_recluse [69]

Answer:

False. They will be parallel to each other

6 0

3 years ago

Read 2 more answers

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'

vodka [1.7K]

Answer:

a) $v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9$

$a(t) = x''(t) = v'(t) =6t-12$

b) $0$

c) $a(t) = x''(t) = v'(t) =6t-12$

When the acceleration is 0 we have:

$6t-12=0, t =2$

And if we replace t=2 in the velocity function we got:

$v(t) = 3(2)^2 -12(2) +9=-3$

Step-by-step explanation:

For this case we have defined the following function for the position of the particle:

$x(t) = t^3 -6t^2 +9t -5 , 0\leq t\leq 10$

Part a

From definition we know that the velocity is the first derivate of the position respect to time and the accelerations is the second derivate of the position respect the time so we have this:

$v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9$

$a(t) = x''(t) = v'(t) =6t-12$

Part b

For this case we need to analyze the velocity function and where is increasing. The velocity function is given by:

$v(t) = 3t^2 -12t +9$

We can factorize this function as $v(t)= 3 (t^2- 4t +3)=3(t-3)(t-1)$

So from this we can see that we have two values where the function is equal to 0, t=3 and t=1, since our original interval is $0\leq t\leq 10$ we need to analyze the following intervals: