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3 years ago

12

Square root of 90 to the nearest tenth

1 answer:

stellarik [79]3 years ago

8 0

9.5
is the square root of 90
rounded to the nearest tenth

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Fully Factorise 3x-12

artcher [175]

Answer:

3(x-4)

Step-by-step explanation:

3×4=12 and 3 also goes into 3x

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3 years ago

An investment grows by 22% over a 5 year period. What is its effective annual percent growth rate

iren2701 [21]

Since annual means per year, then you need to divide 22 by 5.

5 / 22 = 4.4

Now lets check our work.

4.4 x 5 = 22

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3 years ago

What is the solution?

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Answer: The solution is (4, -4)

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3 years ago

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

4/9x + 1/5x =58 need help solving this

iogann1982 [59]

Answer:

x=90

Step-by-step explanation:

First, it would help to make it so that the x's are not next to fractions. To do this, you can multiply all terms in the equation by 45. 45 is the closest common factor of 9 and 5, the denominators of the fractions. The answer would be;

20x+9x=2610

Then solve.

29x=2610

x=90

6 0

4 years ago