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2 years ago

Please help see picture

Mathematics

1 answer:

Otrada [13]2 years ago

5 0

Answer:

688 cm²

Explanation:

Area of triangular prism = Base × Height + Length × (perimeter of base)

Here given:

Base: 6 cm

Height: 12 cm

Length: 20 cm

Perimeter of Base: (6 + 12.4 + 12.4) = 30.8 cm

============================================

Surface Area = 6 × 12 + 20 × (30.8) = 688 cm²

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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 $b=\frac{40}{13}$ .

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3 years ago

If 2 inches are equivalent to 5 centimeters, how many square centimeters are in one square inch

Sonja [21]

Answer:

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Step-by-step explanation:

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2 years ago

What is angle A in the following equation?

Lostsunrise [7]

Answer:

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Step-by-step explanation:

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3 years ago

The Queen Mary is a large cruise ship that has 8,123,700 cubic feet of cargo space. Express this number in scientific notation.

mixer [17]

<span>8,123,700 = 8.1237 x 10^6
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3 years ago

Read 2 more answers

I need help plz i dont know

ICE Princess25 [194]

Answer:

Hey! Ok so the height is C.10 ft.

Step-by-step explanation:

So to find the height I have to do

h=Vlw =540 12·4.5=10

So therefore its 10

Hope you have a great day! I'm Eve btw Hoped this helped and consider marking this brainiest!

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3 years ago