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2 years ago

In ΔLMN, n = 510 cm, l = 820 cm and ∠M=20°. Find ∠L, to the nearest degree

Mathematics

1 answer:

Dafna11 [192]2 years ago

8 0

The angular measure L is : 47°

<h3>What are angles?</h3>

Angles are formed when two lines meet.

Analysis:

Firstly, we calculate for m using cosine rule.

$m^{2}$ = $510^{2}$ + $820^{2}$ -2(510)(820) cos 20

$m^{2}$ = 260100 + 672400 -83600(0.9396)

$m^{2}$ = 146618.56

m = $\sqrt{146618.56}$ = 382.9cm

using sine rule to find ∠L

382.9/sin20 = 820/sinL

sinL = 820sin20/382.9

sinL = 820(0.342)/382.9

sinL = 0.732

L = sin inverse of 0.732 = 47°

In conclusion, ∠L is 47°

Learn more about sine and cosine rule: brainly.com/question/4372174

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Locate the point in the complex plane and express the number in polar form.

EleoNora [17]

Answer:

We kindly invite you to see the result in the image attached below.

The number in polar form is $z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$ .

Step-by-step explanation:

A complex number is represented by elements of the form $a + i\,b$ , for all $a$ , $b$ $\in \mathbb{R}$ . The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.

Now we proceed to present the point on the graph: ( $a = 6$ , $b = 3$ ) We kindly invite you to see the result in the image attached below.

The polar form of the complex number is defined by:

$z = r\cdot e^{i\cdot \theta}$ (1)

Where:

$r$ - Magnitude of the complex number, dimensionless.

$\theta$ - Direction of the complex number, measured in radians.

The magnitude and the direction of the complex number are defined by the following formulas:

Magnitude

$r =\sqrt{a^{2}+b^{2}}$ (2)

Direction

$\theta = \tan^{-1} \frac{b}{a}$ (3)

If we know that $a = 6$ and $b = 3$ , then the polar form of the number is:

$r =\sqrt{6^{2}+3^{2}}$

$r = 3\sqrt{5}$

$\theta = \tan^{-1} \frac{6}{3}$

$\theta \approx 0.352\pi \, rad$

$z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$

The number in polar form is $z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}$ .

4 0

3 years ago

Suppose that the expected value of a measurement is 2.0 m. Which of the following sets of measurements is the MOST accurate? A.

zavuch27 [327]

Answer:

C is probably the answer

Step-by-step explanation:

1.9 Is approximately 2

2.3 Is approximately 2

2.2 is also approximated to 2

1.8 Is also approximately 2

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3 years ago

What are the vertex and x-intercepts of the graph of the function given below?

madreJ [45]

VERTEX
To determine the vertex (coordinate x) of parabola y = ax² + bx + c, use this following formula
x vertex = $-\dfrac{b}{2a}$

y = x² - 2x - 48
a = 1, b = -2, c = -48
plug in the numbers
x vertex = $-\dfrac{b}{2a}$
x vertex = $-\dfrac{(-2)}{2(1)}$
x vertex = $\dfrac{2}{2}$
x vertex = 1

To find y vertex, substitute the value of x vertex to the parabola equation
y = x² - 2x - 48
y = 1² - 2(1) - 48
y = 1 - 2 - 48
y = -49

The vertex is (1, -49)

X-INTERCEPT
x-intercept located in x axis, that means y = 0. Substitute y = 0 to the parabola equation
x² - 2x - 48 = y
x² - 2x - 48 = 0
(x - 8)(x + 6) = 0
x = 8 or x = -6
The x-intercepts are (8,0) and (-6,0)

The answer is first option

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4 years ago

Read 2 more answers

Find the equation of the line of the graph

leonid [27]

Answer:

So this is a negative slope remember this. We are going to use y = mx + b

m is the slope b is the y intercept. In this problem, the y intercept is 6.

The slope is -2;

Y = -2x + 6

Step-by-step explanation:

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3 years ago

Which set of transformations would generate the image of AABC with the coordinates

TEA [102]

Answer: I think it's a relflection over x-axis followed by a rotation of 180 degrees which is b

Step-by-step explanation:

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2 years ago