A side of the triangle below has been extended to form an exterior angle of 163°. Find the value of x

In which number is the digit 8 ten times larger than it is in the number 18?

ollegr [7]

Answer:

387 contains 80 and 8 x 10 = 80

8 0

1 year ago

Which expression is a fourth root of -1+isqrt3?

aleksklad [387]

Answer:

Step-by-step explanation:

$\sf n^{th}$ roots of a complex number is given by DeMoivre's formula.

$\sf \boxed{\bf r^{\frac{1}{n}}\left[Cos \dfrac{\theta + 2\pi k}{n}+i \ Sin \ \dfrac{\theta+2\pi k}{n}\right]}$

Here, k lies between 0 and (n -1) ; n is the exponent.

$\sf -1 + i\sqrt{3}$

a = -1 and b = √3

$\sf \boxed{r=\sqrt{a^2+b^2}} \ and \ \boxed{\theta = Tan^{-1} \ \dfrac{b}{a}}$

$\sf r = \sqrt{(-1)^2 + 3^2}\\\\ = \sqrt{1+9}\\\\=\sqrt{10}$

$\sf \theta = tan^{-1} \ \dfrac{\sqrt{3}}{-1}\\\\ = tan^{-1} \ (-\sqrt{3})$

$\sf = \dfrac{-\pi }{3}$

n = 4

For k = 0,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{\dfrac{-\pi}{3} +0}{4}+iSin \ \dfrac{\dfrac{-\pi}{3}+0}{4}\right] \\\\\\z= \sqrt[4]{10} \left[Cos \ \dfrac{ -\pi }{12}+iSin \ \dfrac{-\pi}{12}\right]\\\\\\z = \sqrt[4]{10}\left[-Cos \ \dfrac{\pi}{12}-i \ Sin \ \dfrac{\pi}{12}\right]$

For k =1,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{5\pi}{12}+i \ Sin \ \dfrac{5\pi}{12}\right]$

For k =2,

$z = \sqrt[4]{10}\left[Cos \ \dfrac{11\pi}{12}+i \ Sin \ \dfrac{11\pi}{12}\right]$

For k = 3,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{17\pi}{12}+i \ Sin \ \dfrac{17\pi}{12}\right]$

For k = 4,

$\sf z =\sqrt[4]{10}\left[Cos \ \dfrac{23\pi}{12}+i \ Sin \ \dfrac{23\pi}{12}\right]$

4 0

1 year ago

A ballplayer catches a ball 3.4s after throwing it vertically upward. with what speed did he throw it, and what height did it re

Daniel [21]

From the equation of motion, we know,

$s=ut+\frac{1}{2}at^{2}$

Where s= displacement

u= initial velocity

a= gravitational force

t= time

Displacement is 0 since the ball comes back to the same point from where it was thrown.

A = $-9.8m/s^{2}$ since the ball is thrown upwards.

Plug the known values into the equation.

=> $0=u\left ( 3.4 \right )+\frac{1}{2}\left ( -9.81 \right )(3.4^{2})$

Solving for u gives :

u= 16.67 m/ sec ....... equation (1)

At maximum height, final velocity i.e v is 0

Time take to reach the top = $\frac{3.4}{2} = 1.7 sec$

$v^{2}=u^{2}+2as$

=> $0=(16.67)^{2}+2(-9.81)(s)$

Solving for s we get

s= 14.16 m

4 0

3 years ago

the function y = 3.75 + 1.5(x-1) can be used to determine the cost in dollars for a taxi ride of x miles. what is the rate of ch

Nesterboy [21]

Cost for travelling 1 mile = 3.75
cost 2 miles = 5.25
cost 3 miles = 6.75
cost 4 miles = 8.25

rate of change = 1.5 dollars per mile

8 0

3 years ago

Read 2 more answers

Solve Quadratic Equations by Factoring:

mr_godi [17]

Answer:

x = 0 or 1
x = ±i/4
x = -5 (twice)

Step-by-step explanation:

Factoring is aided by having the equations in standard form. The first step in each case is to put the equations in that form. The zero product property tells you that a product is zero when a factor is zero. The solutions are the values of x that make the factors zero.

1. x^2 -x = 0

x(x -1) = 0 . . . . . x = 0 or 1

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2. 16x^2 +1 = 0

This is the "difference of squares" ...

(4x)^2 - (i)^2 = 0

(4x -i)(4x +i) = 0 . . . . . x = -i/4 or i/4 (zeros are complex)

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3. x^2 +10x +25 = 0

(x +5)(x +5) = 0 . . . . . x = -5 with multiplicity 2

5 0

2 years ago