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1 year ago

State and prove De Moivre's theorem

Mathematics

1 answer:

Montano1993 [528]1 year ago

6 0

Answer:

assume the formula is true for n is equal to k prove that result is true for n is equal to k + 1 hence result proves since the thorum is true for n is equal to 1 and n k + 1 is unit through a and

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Write a equation of a hyperbola given the foci and the asymptotes

professor190 [17]

Solution:

The standard equation of a hyperbola is expressed as

$\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\text{ \lparen parallel to the x-axis\rparen} \\ \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ \lparen parallel to the y-axis\rparen} \end{gathered}$

Given that the hyperbola has its foci at (0,-15) and (0, 15), this implies that the hyperbola is parallel to the y-axis.

Thus, the equation will be expressed in the form:

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ ----equation 1}$

The asymptote of n hyperbola is expressed as

$y=\pm\frac{a}{b}(x-h)+k$

Given that the asymptotes are

$y=\frac{3}{4}x\text{ and y=-}\frac{3}{4}x$

This implies that

$a=3,\text{ and b=4}$

To evaluate the value of h and k,

$undefined$

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1 year ago

Identify each as an example of exponential growth or decay. What is the y-intercept? What is the end behavior? 1)y=10(0.45)^x 2)

jeyben [28]

The best answer is number 1

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3 years ago

Why can 2 obtuse angles make a right triangle please help

djverab [1.8K]

They can NOT. A right angle is 90°. An obtuse angle is greater than 90°. All the angles in a triangle must add up to exactly 180°. If two angles are greater than 90° then they will add up to greater than 180, beacuse 90 plus 90 equals 180. You cannot have a triangle with two obtuse angles because they will add up to greater than 180°.

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3 years ago

Can someone help me with this question?

belka [17]

Option 3 (1/4 x 60) since 59 is close to 60 and 25% can be rewritten as 1/4

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3 years ago

Question 3 (4 MARKS) Find the equation of the tangents to the curve of the function with rule y = x^2 at the points where x = a

Arte-miy333 [17]

Answer:

(0 , -a²)

Step-by-step explanation:

tangent at x = a and x = -a

y = x² (a , a²) and (-a , a²) must be on the curve and tangent to curve

gradient dy/dx = 2x

slope (m) at x = a is <u>2a</u> and slope (m') at x=-a is<u> -2a</u>

line1: (y - a²) / (x - a) = 2a

y - a² = 2a (x - a) y = 2ax - a² ... (1)

line2: (y - a²) / (x + a) = - 2a y = -2ax- a² ... (2)

(1) - (2): 4ax = 0 a≠0 x = 0

y = - a²

I wish I did it right, or ....

3 0

2 years ago