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3 years ago

Everyone can solve this : why tan(arctanx)= x. Thank you

Mathematics

1 answer:

Vsevolod [243]3 years ago

4 0

Explanation:

tan(arctan x) = x

This is because arctan is the reciprocal of tan. You can view this as the same as 5(1/5x) = x. Since they are reciprocals, when they are multiplied by each other, they cancel each other out.

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The cost (c) to hire a dog trainer is varies directly with the amount of time (h) in hours spent training the dog.

NNADVOKAT [17]

Answer:

Part A) The proportional equation is $c=55h$

Part B) 8 hours of training

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

Let

c -----> the cost to hire a dog

h ----> the amount of time in hours

The linear equation is equal to

$c=kh$

Sue spent $660 on 12 hours of obedience training for her dog Muffin

Find the value of k (constant of proportionality)

$k=y/x$

substitute the values

$k=660/12=55$

therefore

The linear equation is

$c=55h$

For $c=\$440$

Find the value of h

substitute in the equation and solve for h

$440=55h$

$h=440/55=8\ hours$

5 0

3 years ago

Is it impossible unlikely as likely as not likely or certain of there are 10 shirts in a drawer 8 of the shirts have short sleev

matrenka [14]

Answer:8/10

Step-by-step explanation

There are 8 t shirts and 10 shirts so there will be a 8 out of ten Vance of wearing a short sleeve shirt

6 0

3 years ago

How do you work out the rate, time and principal from the compound interest formula?

wlad13 [49]

Answer:

Part 1) $P=A/(1+\frac{r}{n})^{nt}$ (see the explanation)

Part 2) $r=n[\frac{A}{P}^{1/(nt)}-1]$ (see the explanation)

Part 3) $t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$ (see the explanation)

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

Part 1) Find the Principal P

The values of A,r,n and t are given

Isolate the variable P

$A=P(1+\frac{r}{n})^{nt}$

Divide both side by $(1+\frac{r}{n})^{nt}$

$P=A/(1+\frac{r}{n})^{nt}$

Part 2) Find the rate r

The values of A,P,n and t are given

Isolate the variable r

$A=P(1+\frac{r}{n})^{nt}$

Divide both sides by P

$\frac{A}{P} =(1+\frac{r}{n})^{nt}$

Elevated both sides to 1/(nt)

$\frac{A}{P}^{1/(nt)} =(1+\frac{r}{n})$

subtract 1 both sides

$\frac{A}{P}^{1/(nt)}-1 =\frac{r}{n}$

Multiply by n both sides

$r=n[\frac{A}{P}^{1/(nt)}-1]$

Part 3) Find the time t

The values of A,P,r and n are given

Isolate the variable t

$A=P(1+\frac{r}{n})^{nt}$

Divide both sides by P

$\frac{A}{P} =(1+\frac{r}{n})^{nt}$

Apply log both sides

$log(\frac{A}{P})=log(1+\frac{r}{n})^{nt}$

Apply property of exponents

$log(\frac{A}{P})=(nt)log(1+\frac{r}{n})$

Divide both side by $(n)log(1+\frac{r}{n})$

$t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$

3 0

3 years ago

Determine the equation, in vertex form, of a parabola that has been:

Dennis_Churaev [7]

Answer:

$a)\ y=-(x-5)^2;\\b)\ y=4x^2-5;\\c)\ (y-2)^2=4*(x+3).$

Good luck!

4 0

2 years ago

What is 47 - -3 ? i haven't found a answer to this - please hurry to answer this , it's a question on my quiz

Paul [167]

Answer:

Here you go, hope this helps

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers