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2 years ago

What is the inverse of f(x)=5x-4

Mathematics

1 answer:

sergejj [24]2 years ago

5 0

It'll be 4/5 + x/5.

Switch the x to a y so:

x=5y-4

Add 4 to both sides

x+4=5y

Divide by 5 to get y by itself

(x+4)/5=y

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A rock climber's elevation above sea level changed −8212 feet in 214 minutes as she descended. What was the climber's average ch

stich3 [128]

Elevation per minute

elevationchange=-8212
timechange=214

elevation per minute=-8212/214=
-8132/214-80/214=
-38-40/107=
-38 and 40/107

answer is -38 and 40/107 ft per minute

6 0

3 years ago

Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer

AfilCa [17]

Answer:

$\theta = \cos^{-1} (\pm \frac{1}{2} )$

Step-by-step explanation:

The function is $g(\theta) = 8\cdot \theta - 2\cdot \tan \theta$ , whose first derivative is:

$g'(\theta) = 8 - 2\cdot \sec^{2}\theta$

Let equalize the derivative to zero:

$8 - 2\cdot \sec^{2}\theta=0$

$\sec^{2}\theta = 4$

$1 = 4\cdot \cos^{2}\theta$

$\cos \theta = \pm\sqrt {\frac{1}{4} }$

$\cos \theta = \pm \frac{1}{2}$

The solutions are given by the following inverse trigonometric function:

$\theta = \cos^{-1} (\pm \frac{1}{2} )$

6 0

2 years ago

S KM ∥ JN? Why or why not?

bixtya [17]

Given: We have the given figure through which we can see

LK=16,

KJ=10,

LM=24,

MN=15

To Find: Whether KM || JN and the reasoning behind it.

Solution: Yes, KM || JN because $\frac{16}{10}= \frac{24}{15}$

Explanation:

For this solution, we use the concept of Similar Triangles.

Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Now, ∠MLK=∠NLJ

To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN

$LK:KJ=LM:LN\\\\ \frac{LK}{KJ} =\frac{LM}{LN}\\\\\frac{16}{26}= \frac{24}{39}\\\\$

which is true as both sides simplify to $\frac{8}{13}$

Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).

Therefore, KM || JN.

To come to the reasoning, notice that

$\frac{LK}{LJ} =\frac{LM}{LN}\\\\\frac{LK}{LK+KJ} =\frac{LM}{LM+MN}\\\\\frac{LK+KJ}{LK} =\frac{LM+MN}{LM}\\\\1+\frac{KJ}{LK}=1+ \frac{MN}{LM}\\\\\frac{LK}{KJ} =\frac{LM}{MN}$