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2 years ago

How many different four-digit numbers can be formed with the numbers 7; 4; 5; 1; 2; 9; and 8?

Mathematics

1 answer:

Masja [62]2 years ago

7 0

Answer:

If I'm correct, the answer is 1296.

Step-by-step explanation:

6 x 6 x 6 x 6 = 1296

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Find an equation of the tangent to the curve x =5+lnt, y=t2+5 at the point (5,6) by both eliminating the parameter and without e

svet-max [94.6K]

ANSWER

$y = 2x -4$

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

$x = 5 + ln(t)$

$y = {t}^{2} + 5$

From the first equation we make t the subject to get;

$x - 5 = ln(t)$

$t = {e}^{x - 5}$

We put it into the second equation.

$y = { ({e}^{x - 5}) }^{2} + 5$

$y = { ({e}^{2(x - 5)}) } + 5$

We differentiate to get;

$\frac{dy}{dx} = 2 {e}^{2(x - 5)}$

At x=5,

$\frac{dy}{dx} = 2 {e}^{2(5 - 5)}$

$\frac{dy}{dx} = 2 {e}^{0} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

$y-y_1=m(x-x_1)$

$y - 6 = 2(x - 5)$

$y = 2x - 10 + 6$

$y = 2x -4$

Without eliminating the parameter,

$\frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }$

$\frac{dy}{dx} = \frac{ 2t}{ \frac{1}{t} }$

$\frac{dy}{dx} = 2 {t}^{2}$

At x=5,

$5 = 5 + ln(t)$

$ln(t) = 0$

$t = {e}^{0} = 1$

This implies that,

$\frac{dy}{dx} = 2 {(1)}^{2} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

$y-y_1=m(x-x_1)$

$y - 6 = 2(x - 5) =$

$y = 2x -4$

5 0

3 years ago

Let g be the function given by g(x)=√ 1−sin2x. Which of the following statements could be false on the interval 0≤x≤π ?

zysi [14]

Answer:

yooooooooooooooooooooooooo

Step-by-step explanation:

yesirskiii\

6 0

2 years ago

Solve the system of equations by finding the reduced row echelon form of the augmented matrix. Write the solutions for x and y i

Gwar [14]

Answer:

The solutions for the given system of equations are:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

Step-by-step explanation:

Given the equation system:

$\left \{ {{3x+y+4z=-3} \atop {-x+y+4z=17}} \right.$

We obtain the following matrix:

$\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]$

Step 1: Multiply the fisrt row by 1/3.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]$

Step 2: Sum the first row and the second row.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]$

Step 3: Multiply the second row by 3/4.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]$

Step 4: Multiply the second row by -1/3 and sum the the first row.

$\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]$

The result of the reduced matrix is:

$\left \{ {{x=-5} \atop {y+4z=12}} \right.$

This is equal to:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

These are the solutions for the system of equations in terms of z, where z can be any number.

6 0

3 years ago

What is the area of the triangular flag below?

alexandr1967 [171]

Answer:

Here is your answer

Step-by-step explanation:

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AND PLEASE MARK ME AS "BRAINLIEST" ANSWER 

HOPE IT HELPS YOU 

4 0

2 years ago

In circle c with diameter SP, what is the measure of PCQ?

Eva8 [605]

Answer:

i dont know

Step-by-step explanation:

3 0

3 years ago