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igor_vitrenko [27]
3 years ago
13

Which of the following options represents the form of a linear equation that should be used to write the equation of a line when

the slope and a point on the line are given?
Mathematics
1 answer:
OLga [1]3 years ago
5 0
If you know the slope and a point, the best option is to represent the line in the point-slope form which is:

(y-y1)=m(x-x1), where (x1,y1) is the point and m=slope
You might be interested in
Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ
SOVA2 [1]

y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}

The arc length of the curve is

\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx

which has a value of about 5.99086.

Let f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}. Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

\ell_i=\dfrac{i-1}2

r_i=\dfrac i2

with 1\le i\le10.

These subintervals have midpoints given by

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4

Over each subinterval, we approximate f(x) with the quadratic polynomial

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

so that the integral we want to find can be estimated as

\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It turns out that

\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6

so that the arc length is approximately

\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086

5 0
3 years ago
If f(1)=2f(1)=2 and f(n)=f(n-1)^2-n
katrin [286]

Answer:

f(4)=-3

Step-by-step explanation:

f(1)=2

f(n)=f(n-1)^2-n

If n=2

f(2)=f(2-1)^2-2

f(2)=f(1)^2-2

f(2)=2^2-2

f(2)=4-2

f(2)=2

If n=3

f(3)=f(3-1)^2 - 3

f(3)=f(2)^2 - 3

f(3)=2^2-3

f(3)=4-3

f(3)=1

if n=4

f(4)=f(4-1)^2 - 4

f(4)=f(3)^2 - 4

f(4)=1^2 - 4

f(4)=1-4

f(4)=-3

6 0
3 years ago
Solve for x. Round to the nearesr tenth of a degree if necessary.
Ipatiy [6.2K]

Answer:

im not sure but i got 30.1

Step-by-step explanation:

\cos(x) =   \frac{45}{52}  \\ x = 30.1

7 0
3 years ago
Phoebe, Andy and Polly share £270.
Stella [2.4K]
*Given
Money of Phoebe            - 3 times as much as Andy
Money of Andy                - 2 times as much as Polly
Total money of Phoebe,  - <span>£270
</span>    Andy and Polly

*Solution

Let
B - Phoebe's money
A - Andy's money
L - Polly's money

1. The money of the Phoebe, Andy, and Polly, when added together would total <span>£270. Thus, 
</span>
                  B + A + L  = <span>£270                     (EQUATION 1)

2. Phoebe has three times as much money as Andy and this is expressed as
  
                  B = 3A

3. Andy has twice as much money as Polly and this is expressed as

                  A = 2L</span>                           (EQUATION 2)
<span>
4. This means that Phoebe has ____ as much money as Polly, 

                 B = 3A
                 B = 3 x (2L)
                 B = 6L                            </span>(EQUATION 3)<span>

This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only. 

5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes, 

                  6L + 2L + L = </span><span>£270
</span>                                9L = <span>£270
</span>                                  L = <span>£30

So, Polly has </span><span>£30. 

6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively. 
</span>
                  A = 2L                           
                  A = 2(£30)
                  A = £60

Andy has £60

                  B = 6L                         
                  B = 6(£30)
                  B = £180

Phoebe has £180

Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.
7 0
2 years ago
If line t is a transversal of lines l and m, name the angle relationship of the given angle pairs.
Ghella [55]

Answer:

\angle 1\ and\ \angle 3 are corresponding angles and are congruent to each other.

\angle 8\ and\ \angle 4 are alternate exterior angles and thus congruent to each other.

\angle 2\ and\ \angle 3 are interior angles on the same side, and they are supplementary(sum=180°).

Step-by-step explanation:

Given:

Line l\parallel m

Line t is traversal.

By angle properties we can name the angle relationship of given angle pairs.

\angle 1\ and\ \angle 3 are corresponding angles and are congruent to each other.

\angle 8\ and\ \angle 4 are alternate exterior angles and thus congruent to each other.

\angle 2\ and\ \angle 3 are interior angles on the same side, and thus they are supplementary.

8 0
3 years ago
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