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2 years ago

If f(x) = 2-x1/2 and if g(x) = x2-9, what is the domain of g(x) / f(x)

Mathematics

1 answer:

Yuliya22 [10]2 years ago

4 0

G(x)/f(x)= (x²-9)/(2-√x)

the domain is (0, ∞).

because 0 makes function undefined and the function is positive.

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Michael invests USD 20 000 at 9.6% p.a. compounded monthly.

alexandr1967 [171]

Given :

A = 25000

P = 20000

r % = 9.6 % = 0.096

n = 12

To Find :

The time taken say t.

Solution :

We know, compound interest is given by :

$A=P(1+\dfrac{r}{n})^{n.t}$

Taking log both sides :

$A=P(1+\dfrac{r}{n})^{n.t}\\\\log\ \dfrac{A}{P}= n.t\times log( 1+\dfrac{r}{n})\\\\t =\dfrac{1}{n}\times \dfrac{log\ \dfrac{A}{P}}{log(1+\dfrac{r}{n})}\\\\\\t=\dfrac{1}{12}\times \dfrac{log\ \dfrac{25000}{20000}}{log(1+\dfrac{0.096}{12})}\\\\\\t=2.33\ years$

Hence, this is the required solution.

5 0

2 years ago

Jerome went on a hike. He climbed three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles per hour?

OlgaM077 [116]

You could do this with fractions. I'll do decimals later.

d = 3/4 mile
t = 2/3 hour
r = ????

r = 3/4 // 2/3 Invert and multiply the denominator
r = 3/4 * 3/2 = 9/8 = 1 1/8

If your calculator handles fractions, you can use it to do this. If not you can change this to a decimal.
d = 3/4 = 0.75 miles
t = 2/3 hour = 0.666666666 hours.
r = ???

d = r*t
r = d/t
r = 0.75 / 0.66666667
r = 1.125 miles / hour
which gives you exactly the same answer 1.125 = 1 1/8

3 0

2 years ago

Read 2 more answers

Solve for m:<br> -3(1 – 5m) = — 38 + 8m

Solnce55 [7]

Answer:

m = - 5

Step-by-step Explanation:

$-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}$

3 0

1 year ago

Read 2 more answers

The height of a baseball thrown from the catcher to first base is modeled by the function h(t) = –0.09t2 + 0.72t + 6, where h is

Black_prince [1.1K]

The height of a baseball thrown from the catcher to first base is modeled by the function $h(t) = -0.09t^2 + 0.72t + 6$ , where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds

To find out height of the ball at 10 seconds, we plug in 10 for t

$h(t) = -0.09t^2 + 0.72t + 6$

$h(10) = -0.09(10)^2 + 0.72(10) + 6$

h(10)=4.2 feet

the height of the ball at 10 seconds= 4.2 feet

3 0

1 year ago

"If you switch to the late shift, you will receive a 10% wage increase." Great! I make $12.00 per hour now, and that extra 10% w

maxonik [38]

Answer:

$13.20/hr

Step-by-step explanation:

A 10% wage increase would amount to 0.10($12) = $1.20. Adding this increase to the starting rate $12/hr results in $13.20/ hr.

A faster way in which to do this is shown below:

Wages after a 10% increase = (1.10)($12/hr) = $13.20/hr

7 0

1 year ago