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2 years ago

6

What is the area, in square units, of triangle STU?

1 answer:

Zolol [24]2 years ago

4 0

Answer:

4 units squared

Step-by-step explanation:

The area of the rectangle is 9 units squared

The area of the two wedge-shaped triangles on the outside of the larger triangle is 3 units squared. The final triangle area is 2 units squared. Thus 9 - 5 = 4 units squared.

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Suppose f(x, y) is a differentiable function of x and y and let g(r, s) = f (2rs, 8s − 2r). Use

worty [1.4K]

By the chain rule,

$\dfrac{\partial g}{\partial r} = \dfrac{\partial f}{\partial r} \\\\ ~~~~~ = \dfrac{\partial f}{\partial x} \dfrac{\partial x}{\partial r} + \dfrac{\partial f}{\partial y} \dfrac{\partial y}{\partial r} \\\\ ~~~~~ = 2 s \dfrac{\partial f}{\partial x} - 2 \dfrac{\partial f}{\partial y}$

where $x(r,s)=2rs$ and $y(r,s)=8s-2r$ .

If $r=2$ and $s=1$ , then

$x = 2\cdot2\cdot1 = 4$

$y=8\cdot1-2\cdot2 = 4$

so that

$g_r(2,1) = 2\cdot1 f_x(4,4) - 2 f_y(4,4) = 2\cdot2-2\cdot3 = \boxed{-2}$

5 0

1 year ago

How do you use the pythagoreum theorum again? i know the formula is a^2+b^2=c^2 but how do you use it. Use the example 15^2+20^2

kiruha [24]

It would be 225+400=c^2. square both sides to result in 25.

3 0

4 years ago

Read 2 more answers

Write each expression with fewer terms. Show or explain your reasoning.

liraira [26]

1. 103-22 = 81
2 10.2-3y+2x is already in simplest form

6 0

3 years ago

!!!!!!!!!!!!!!!!!!!!

Andru [333]

Answer:

$f^{-1}(x)=4x+20$

Step-by-step explanation:

<u>Given</u>

<u /> $f(x)=\frac{x}{4}-5\\ \\y=\frac{x}{4}-5$

<u>Swap x and y and solve for y</u>

<u /> $y=\frac{x}{4}-5\\ \\x=\frac{y}{4}-5\\ \\x+5=\frac{y}{4}\\ \\4(x+5)=y\\\\y=4x+20$

<u>Final answer</u>

<u /> $f^{-1}(x)=4x+20$

Keep in mind that we need to swap the variables because a function and its inverse are symmetrical about the line y=x. See the graph below.

3 0

3 years ago

Reagan uses 2 3/4 cups of vinegar in her salad dressing recipe. How much vinegar would Reagan use to make 5 recipes?

igor_vitrenko [27]

Answer:

13 3/4

Step-by-step explanation:

2 3/4 is 11/4 when converted into an improper fraction.

5 is 5/1 when converted into a fraction.

11*5 is 55 (numerators)

4*1 is 4 (denominators)

55/4 is 13 with 3/4 remaining

13 3/4

5 0

3 years ago

Read 2 more answers