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labwork [276]
3 years ago
9

What is the area of a triangle whose vertices are D(3, 3) , E(3, −1) , and F(−2, −5) ?

Mathematics
1 answer:
kirill [66]3 years ago
7 0

We are given vertices of the triangle DEF as:

D(3, 3) , E(3, −1) , and F(−2, −5) .

Let us plot those points on the graph.

Formula of area of the triangle with vertices (x1,y1), (x2,y2) and (x3,y3).

Area = 1/2 [ (x2-x1)(y3-y1)-(x3-x1)(y2-y1)]

We have x1=3, x2=3, x3=-2, y1=3, y2 =-1 and y3 = -5.

Plugging values in formula, we get

Area = |1/2 [ 3-3)(-5-3)-(-2-3)(-1-3)]|

= |1/2 [ 0(-8) - (-5)(-4)]|

=| 1/2 [0 - 20]|

= |-10|

=10.

<h3>Therefore, area of the triangle with given vertices is 10 square units.</h3>
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Given z=f(x,y),x=x(u,v),y=y(u,v), with x(1,3)=2 and y(1,3)=2, calculate zu(1,3) in terms of some of the values given in the tabl
stich3 [128]

The value of zu(1,3) using the data elements represented on the table of values is q + p

<h3>How to solve the calculus expression?</h3>

The given parameters are:

z = f(x, y)

x = x(u, v)

y = y(u, v)

Where

x(1, 3) = 2 and y(1, 3) = 2

To calculate zu(1,3), we make use of:

z_u(1,3) = f_x(x,y) * x_u(1,3) +  f_y(x,y) * y_u(1,3)

The values x(1, 3) = 2 and y(1, 3) = 2 mean that:

(x,y) = (2,2).

So, we have:

z_u(1,3) = f_x(2,2) * x_u(1,3) +  f_y(2,2) * y_u(1,3)

From the table of values, we have:

f_x(2,2) = q

x_u(1,3) = 1

f_y(2,2) = 1

y_u(1,3) = p

So, the equation becomes

z_u(1,3) = q * 1 +  1 * p

Evaluate the product

z_u(1,3) = q + p

Hence, the value of zu(1,3) is q + p

Read more about calculus at:

brainly.com/question/5313449

#SPJ1

3 0
2 years ago
Hi hottie, pls help me !
yulyashka [42]

Answer:

1200

0.65

The answers are in the function

6 0
2 years ago
Trigonometry
Natasha_Volkova [10]

Answer:

Step-by-step explanation:

For a triangle the area is

A=\frac{1}{2}bh

If our triangle is isosceles and the 2 congruent sides each measure 4 and they include an angle of 40 degrees, let's say that the vertex angle is 40 and the sides that are not the base each measure 4.  If we drop an altitude from the vertex to the base, we cut the triangle into 2 right triangles, with the vertex angle being 20 degrees and the hypotenuse being 4.  To find the base, then, which is opposite the angle, we use the sin ratio:

sin(20)=\frac{b}{4} and

4sin(20) = b so

b = 1.368

But we need the whole base, and that is only half of it.  So

2b = 2.736

To find the height, which is adjacent to the angle, we use the cos ratio:

cos(20)=\frac{h}{4} and

4cos(20) = h so

h = 3.759

Now we have enough info to find the area of the triangle using the triangle area formula from above:

A=\frac{1}{2}(2.736)(3.759) and

A = 5 meters squared.

7 0
2 years ago
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