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3 years ago

Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?

Mathematics

2 answers:

Nuetrik [128]3 years ago

5 0

Hello There!

It would be 16.

Hope This Helps You!
Good Luck :)

- Hannah ❤

Naya [18.7K]3 years ago

4 0

(x + 4) (x +4) can be your answer

hope this helps

that will equal x²+ 8x + 16

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A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 22 mi/h. Find the speed and direc

Minchanka [31]

Answer: The speed is 22.2 mi/hr and woman is 8° north relative to the surface of the water.

Step-by-step explanation:

Since we have given that

Speed at which woman walks due west = 3 mi/hr

Speed at which ship moving due north = 22 mi/hr

Now it forms "Pythagorus theorem":

So, it becomes,

$H^2=B^2+P^2\\\\H^2=3^2+22^2\\\\H^2=9+484\\\\H^2=493\\\\H=\sqrt{493}\\H=22.20\ mi/hr$

And the direction of the woman relative to the surface of the water is given by

$\theta=\sin^{-1}x(\dfrac{3}{22.2})=7.76\approx 8^\circ$

Hence, the speed is 22.2 mi/hr and woman is 8° north relative to the surface of the water.

5 0

3 years ago

1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

iogann1982 [59]

$y=\displaystyle\sum_{n=0}^\infty a_nx^n$

then

$y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n$

The ODE in terms of these series is

$\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0$

$\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}$

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

$\boxed{y(x)=a_0e^{-2x}}$

7 0

3 years ago

1/3 + 5/6 + 5/12 What is the answer

SOVA2 [1]

1/3 + 5/6 + 5/12

1.583333333333333

3 0

3 years ago

Read 2 more answers

Rhett is solving the quadratic equation 0= x2 – 2x – 3 using the quadratic formula. Show the correct substitution of the values

Grace [21]

I hope this helps you

5 0

3 years ago

Help please it's math

qwelly [4]

A) is the correct answer

5 0

3 years ago