All categories

3 years ago

Need help with number 4

Mathematics

1 answer:

Reil [10]3 years ago

6 0

$\bf \begin{cases}
g(x)=2x\\
h(x)=x^2+4
\end{cases}\qquad 
\begin{array}{llll}
(h\circ g)(x)\implies h[~~g(x)~~]\\\\
(h\circ g)(-5)\implies h[~~g(-5)~~]
\end{array}\\\\
-------------------------------\\\\
g(-5)=2(-5)\implies g(-5)=-10
\\\\\\
h[~~g(-5)~~]\implies h[~~-10~~]\implies h(-10)=(-10)^2+4
\\\\\\
h(-10)=100+4\implies h(-10)=104$

You might be interested in

Solve the Questions following 81, 8-91, 4pda - Зроби 1. Xut 43 ,

posledela

Answer:

Solve the

Questions

following

81, 8-91, 4pda - Зроби

Xut 43

Step-by-step explanation:

Solve the

Questions

following

81, 8-91, 4pda - Зроби

Xut 43

4 0

3 years ago

Use De Moivre's theorem to write the complex number in trigonometric form: (cos(3pi/5) + i sin (3pi/5))^3

docker41 [41]

By De Moivre's theorem,

$\left(\cos\dfrac{3\pi}5+i\sin\dfrac{3\pi}5\right)^3=\boxed{\cos\dfrac{9\pi}5+i\sin\dfrac{9\pi}5}$

We can stop here ...

# # #

... but we can also express these trig ratios in terms of square roots. Let $x=\dfrac\pi5$ and let $c=\cos x$ . Then recall that

$\cos5x=c^5-10c^3\sin^2x+5c\sin^4x$

$\cos5x=c^5-10c^3(1-c^2)+5c(1-2c^2+c^4)$

$\cos5x=16c^5-20c^3+5c$

On the left, $5x=\pi$ so that

$16c^5-20c^3+5c+1=(c+1)(4c^2-2c-1)^2=0$

Since $c=\cos\dfrac\pi5\neq1$ , we're left with

$4c^2-2c-1=0\implies c=\dfrac{1+\sqrt5}4$

because we know to expect $\cos x>0$ . Then from the Pythagorean identity, and knowing to expect $\sin x>0$ , we get

$\sin x=\sqrt{1-c^2}=\sqrt{\dfrac58-\dfrac{\sqrt5}8}$

Both $\cos$ and $\sin$ are $2\pi$ -periodic, so that

$\cos\dfrac{9\pi}5=\cos\left(\dfrac{9\pi}5-2\pi\right)=\cos\left(-\dfrac\pi5\right)=\cos\dfrac\pi5$

and

$\sin\dfrac{9\pi}5=\sin\left(-\dfrac\pi5\right)=-\sin\dfrac\pi5$

so that the answer we left in trigonometric form above is equal to

$\cos\dfrac\pi5-i\sin\dfrac\pi5=\boxed{\dfrac{1+\sqrt5}4+i\sqrt{\dfrac58+\dfrac{\sqrt5}8}}$

7 0

3 years ago

-4 + 6g, for g = 4 i need in a sentence

laiz [17]

Answer:

-4+6*4 = 20

Step-by-step explanation:

If g is equal to 4 the answer is 20

8 0

3 years ago

Nestlé water pumps 1.2 million gallons per day out of G. Springs to put in bottles.

Delicious77 [7]

Answer:

3.2×10⁷ liters/week

Step-by-step explanation:

$\dfrac{1.2\cdot 10^6\,gal}{1\,day}\cdot\dfrac{7\,day}{1\,week}\cdot\dfrac{8\,pint}{1\,gal}\cdot\dfrac{1\,L}{2.11\,pint}=\dfrac{1.2\cdot 10^6\cdot 7\cdot 8\,L}{2.11\,week}\\\\\approx 3.2\cdot 10^7\,\dfrac{L}{week}$

5 0

3 years ago

Read 2 more answers

In the diagram above, which two red lines are skew?

inn [45]

D is the correct answer

5 0

3 years ago