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2 years ago

What is the area of the trapezoid with height 10 units?

Mathematics

1 answer:

aleksley [76]2 years ago

3 0

If by "long leg lengths" you mean the hypotenuse then the area is 116 sq. units. If you mean the bases of the triangles then the area is 170 sq. units.

If the length of 12 is the hypotenuse, we first must find the base of the triangles using the Pythagorean theorem:

10² + b² = 12²

100 + b² = 144

b² = 44

b = √44 = 6.6

This means we have two triangles and a rectangle. The area of the rectangle is 5(10) = 50 sq. units. The area of each triangle is 1/2(6.6)(10) = 33. Adding all 3 together we have:

50+33+33 = 116 sq. units.

If the 12 is the base, then we have the rectangle with the area of 5(10) = 50 and two triangles each with an area of 1/2(12)(10) = 60:

50+60+60 = 170 sq. units.

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A) Findi

Romashka [77]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}$

Part B)

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

Step-by-step explanation:

We have the equation:

$\displaystyle x^2y+y^2x=6$

Part A)

We want to find the derivative of our function, dy/dx.

So, we will take the derivative of both sides with respect to x:

$\displaystyle \frac{d}{dx}\Big[x^2y+y^2x\Big]=\frac{d}{dx}\big[6\big]$

The derivative of a constant is 0. We can expand the left:

$\displaystyle \frac{d}{dx}\Big[x^2y\Big]+\frac{d}{dx}\Big[y^2x\Big]=0$

Differentiate using the product rule:

$\displaystyle \Big(\frac{d}{dx}\big[x^2\big]y+x^2\frac{d}{dx}\big[y\big]\Big)+\Big(\frac{d}{dx}\big[y^2\big]x+y^2\frac{d}{dx}\big[x\big]\Big)=0$

Implicitly differentiate:

$\displaystyle (2xy+x^2\frac{dy}{dx})+(2y\frac{dy}{dx}x+y^2)=0$

Rearrange:

$\displaystyle \Big(x^2\frac{dy}{dx}+2xy\frac{dy}{dx}\Big)+(2xy+y^2)=0$

Isolate the dy/dx:

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

Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}$

Part B)

We want to find the equation of the tangent line at (2, 1).

So, let's find the slope of the tangent line using the derivative. Substitute:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{2(2)(1)+(1)^2}{(2)^2+2(2)(1)}$

Evaluate:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{4+1}{4+4}=-\frac{5}{8}$

Then by the point-slope form:

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

Yields:

$\displaystyle y-1=-\frac{5}{8}(x-2)$

Distribute:

$\displaystyle y-1=-\frac{5}{8}x+\frac{5}{4}$

Hence, our equation is:

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

5 0

2 years ago

Simplify. c) <img src="https://tex.z-dn.net/?f=%5Csqrt%7B25%2B10%5Csqrt%7B5%7D%20%2B5%20%7D" id="TexFormula1" title="\sqrt{2

tatyana61 [14]

Answer:

$5+\sqrt{5}$

Step-by-step explanation:

Both are essentially same questions, considering 30 = 25 + 5.

Solving c)

$\sqrt{25+10\sqrt{5} +5} =$
$\sqrt{5^2+2*5*\sqrt{5} +(\sqrt{5} )^2} =$
$\sqrt{(5+\sqrt{5} )^2} =$
$5+\sqrt{5}$

8 0

2 years ago

Read 2 more answers

What is 30 times 5/3? Also what is 24 times 5/3?

LUCKY_DIMON [66]

Answer:

30 times 5/3 is 50

24 times 5/3 is 40

5 0

3 years ago

Read 2 more answers

Solve the following 4x-1/2=x+7

kipiarov [429]

Answer: x= 5/2

Step-by-step explanation::)

7 0

2 years ago

BRAINLIESTT ASAP! PLEASE HELP ME :) thanks!

fredd [130]

Answer:

A is correct, x=7, AB=20

Step-by-step explanation:

All of the options say x=7 so you can just input 7 into 4x-8 to find AB

4(7)-8=AB

28-8=AB

20=AB

Hope this helps, please mark brainliest :)

3 0

2 years ago