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3 years ago

Write the equation of a line passing through (6,-2) and perpendicular to -2x + 3y= -6

1 answer:

4 0

Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.

-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3

The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.

y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b

The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.

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Please help im doing my girl friend work and i dont know not a thing

Nadusha1986 [10]

Answer:

See below, please!

Step-by-step explanation:

We can set up a system of equations to model this problem. Let's consider the student's ticket as x, and y for the adult ticket.

So since the student ticket is $1.50, and adult is $4, we can set up the following equation: $1.5x+4y=5050$ , since they collected $5050 total.

We can set up another equation modeling the number of people who came to the game. This would be x+y=2200.

Solve this, and we get x= 1500 and y=700. So, they sold 1500 student tickets and 700 adult tickets.

Hope this helped!

4 0

2 years ago

The Bessel function or order zero of the first kind may be defined by. Find the radius of convergence of J0(x).

fenix001 [56]

Answer:

Step-by-step explanation:

The Bessel function or order zero of the first kind may be defined by the solution - to Bessel's differential equation - which is a finite value at the origin X=0 for positive or negative whole numbers (integers) or positive alpha (α) values.

6 0

3 years ago

Seorang ayah memberikan sebuah tantangan kepada anaknya untuk i menghitung jumlah uang koin yang diperlukan untuk memenuhi papan

VashaNatasha [74]

The total number of coins required to fill all the $64$ boxes are $\boxed{\bf 18446744073709551615}$ .

Further explanation:

In a chessboard there are $64$ boxes.

The objective is to determine the total number of coins required to fill the $64$ boxes in chessboard.

In the question it is given that in the first box there is $1$ coin, in the second box there are $2$ coins, in the third box there are $8$ coins and it continues so on.

A sequence is formed for the number of coins in different boxes.

The sequence formed for the number of coins in different boxes is as follows:

$\boxed{1,2,4,8,...}$

The above sequence can also be represented as shown below,

$\boxed{2^{0},2^{1},2^{2},2^{3},...}$

It is observed that the above sequence is a geometric sequence.

A geometric sequence is a sequence in which the common ratio between each successive term and the previous term are equal.

The common ratio $(r)$ for the sequence is calculated as follows:

$\begin{aligned}r&=\dfrac{2^{1}}{2^{0}}\\&=2\end{aligned}$

The $n^{th}$ term of a geometric sequence is expressed as follows:

$\boxed{a_{n}=ar^{n-1}}$

In the above equation $a$ is the first term of the sequence and $r$ is the common ratio.

The value of $a$ and $r$ is as follows:

$\boxed{\begin{aligned}a&=1\\r&=2\end{aligned}}$

Since, the total number of boxes are $64$ so, the total number of terms in the sequence is $64$ .

To obtain the number of coins which are required to fill the $64$ boxes we need to find the sum of sequence formed as above.

The sum of $n$ terms of a geometric sequence is calculated as follows:

$\boxed{S_{n}=a\left(\dfrac{r^{n}-1}{r-1}\right)}$

To obtain the sum of the sequence substitute $64$ for $n$ , $1$ for $a$ and $2$ for $r$ in the above equation.

$\begin{aligned}S_{n}&=1\left(\dfrac{2^{64}-1}{2-1}\right)\\&=\dfrac{18446744073709551616-1}{1}\\&=18446744073709551615\end{aligned}$

Therefore, the total number of coins required to fill all the $64$ boxes are $\boxed{\bf 18446744073709551615}$ .

Learn more:

1. A problem on greatest integer function brainly.com/question/8243712

2. A problem to find radius and center of circle brainly.com/question/9510228

3. A problem to determine intercepts of a line brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Sequence

Keywords: Series, sequence, logic, groups, next term, successive term, mathematics, critical thinking, numbers, addition, subtraction, pattern, rule., geometric sequence, common ratio, nth term.

3 0

3 years ago

After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.5 6/ (t+4)3 feet per year, where

kipiarov [429]

Answer:

Step-by-step explanation:

Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).

The amount of growth can be gotten by integrating the given rate equation as shown;

$\int\limits {0.5 + \frac{6}{(t+4)^{3} } } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} } } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \ where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C$

a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2

$\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet$

b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3

$\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet$

c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown

$\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet$

8 0

2 years ago

PQ and RS are two lines that intersect at point T, as shown below:

Setler79 [48]

Our approach to answering this question is to eliminate the choices until we are left with only one.

(1) FALSE. The given figures are lines and can extend indefinitely.
(2) FALSE. The lines are not given to intersect in right angles.
(3) TRUE. The angles are vertical (which means that they line in opposite side of the intersection.
(4) FALSE. The angles are not supplementary because the lines are vertical. They can only be supplementary if both are right angles.

3 0

3 years ago