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3 years ago

Factor the expression.

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

8 0

15n-18. This is 3(5n-6) because 3 times 5n is 15n and 3 times 6 is 18.

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Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

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

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

3 years ago

3(a+b)=19 if a=6, then a+b=?

aniked [119]

Hello!

In a really simple way, 3 times our answer is 19. We can just divide to find it.

19/3= 6 1/3

Anyway, it might be nice to solve the equation for b. If a=6, then b has to be 1/3, but let's check.

18+3b=19

3b=1

b=1/3

Therefore, a+b= 6 1/3

I hope this helps!

6 0

3 years ago

Read 2 more answers

A man bought a refrigerator, an air conditioner, a TV set and a gas cooker for $150.00, $400.00, $180.00 and $300.00 respectivel

MaRussiya [10]

Answer:

1184.5

Step-by-step explanation:

150+400+180+300=1030

1030 × 15% = 154.5

(15% is also 0.15)

1030 + 154.5 = 1184.5

I hope this helps you :)

4 0

3 years ago

Find the midpoint of the line segment joining the points (10,14) and (-7,7).

LekaFEV [45]

Answer:

(1.5, 10.5)

Step-by-step explanation:

$midpoint = \bigg( \frac{10 + ( - 7)}{2}, \: \: \frac{14 + 7}{2} \bigg) \\ \\ = \bigg( \frac{3}{2}, \: \: \frac{21}{2} \bigg) \\ \\ = = ( 1.5, \: \: 10.5 )$

3 0

3 years ago

Which of the statements are true regarding dot plots bar graphs and historgrams

andrey2020 [161]

the only statement that is true is the one in option D.

"Bar graphs are used to represent data that is discrete".

<h3>Which of the statements are true regarding dot plots, bar graphs, and histograms?</h3>

Dot plots, bar graphs, and histograms are used to repersent graphically data sets.

Thus, what these graphs do represent are populations in a data set with a given property.

Remember that data is usually discrete, so we usually use dot plots and bar graphs to represent discrete data.

Histograms show distributions of numerical data (it can be used for continuous or discrete data).

With all that in mind, we conclude that the only statement that is true is the one in option D.

"Bar graphs are used to represent data that is discrete".

If you want to learn more about data sets:

brainly.com/question/3514929

#SPJ1

3 0

1 year ago