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2 years ago

9

The sum of the measures of three adjacent angles is 150°.The measures of the angles are in the ratio of 1 : 2 : 3. What is the m

easure in degrees of the largest angle?

1 answer:

taurus [48]2 years ago

5 0

Answer:

3=75 degrees

Step-by-step explanation:

1+2+3=6

1*150/6=25degrees

2*150/6=50 degrees

3*150/6=75 degrees

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Least common multiple for 16 and 24

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3 years ago

1/3×(9x + 3) = 3x = - 1 3

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Answer:

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3 years ago

Which equation can be used to solve for b?<br> B<br> 5 cm<br> 10 cm<br> 30°

kati45 [8]

The Question is Incomplete The complete question with figure is below.

Answer:

Therefore the equation to solve for b is

$\tan 30 = \dfrac{5}{b}$

Step-by-step explanation:

Given:

In Right Angle Triangle ABC

∠C = 90°

BC = 5 cm

AB = 10 cm

∠A = 30°

To Find:

b = ?

Solution:

In Right Angle Triangle ABC Tangent identity we have

$\tan A = \dfrac{\textrm{side opposite to angle A}}{\textrm{side adjacent to angle A}}$

Substituting the values we get

$\tan 30 = \dfrac{BC}{AC}\\\\\tan 30 = \dfrac{5}{b}$

Therefore the equation to solve for b is

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3 years ago

Calculus piecewise function.

Kipish [7]

Part A

The notation $\lim_{x \to 2^{+}}f(x)$ means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows $\lim_{x \to 2^{+}}f(x) = 2$

Then for the left hand limit $\lim_{x \to 2^{-}}f(x)$ , we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, $\lim_{x \to 2^{-}}f(x) = 1$

===============================================================

Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since $\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3$ , this means the limit $\lim_{x \to 4}f(x)$ does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

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