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Umnica [9.8K]
3 years ago
11

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

Mathematics
1 answer:
Elis [28]3 years ago
3 0

There is a formula which employs the use of determinants and which helps us calculate the area of a triangle if the vertices are given as (x_1,y_1),(x_2,y_2),(x_3,y_3). The formula is as shown below:

Area=\frac{1}{2}\begin{vmatrix}x_1&y_1&1 \\ x_2&y_2&1\\ x_3&y_3&1\end{vmatrix}

Now, in our case, we have: (x_1,y_1)=(3,3)

(x_2,y_2)=(3,-1), and

(x_3,y_3)=(-2,-5)

Thus, the area in this case will become:


Area=\frac{1}{2}\begin{vmatrix}3&3&1 \\ 3&-1&1\\ -2&-5&1\end{vmatrix}

Therefore, Area=\frac{1}{2}\times [[3(-1\times 1-(-5)\times 1]-3[3\times 1-(-2)\times 1]+1[3\times -5-2]]= \frac{1}{2}\times -20=-10

We know that area cannot be negative, so the area of the given triangle is <u>10 squared units</u>.



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Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.
wlad13 [49]

Answer:

\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}

Step-by-step explanation:

To solve the question we refresh our knowledge of the quotient rule.

For a function f(x) express as a ratio of another functions u(x) and v(x) i.e

f(x)=\frac{u(x)}{v(x)}\\, the derivative is express as

\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }

from y=lnx/x^{2}

we assign u(x)=lnx and v(x)=x^2

and the derivatives

\frac{du(x)}{dx}=\frac{1}{x}\\\frac{dv(x)}{dx}=2x\\.

Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e y=lnx\\\frac{dy}{dx}=\frac{1}{x}

If we substitute values into the quotient expression we arrive at

\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}

8 0
3 years ago
Its 6 ya'll if you think it no it 6
snow_lady [41]

Answer:

HUH? What do you mean about that?

7 0
2 years ago
Easy points let’s gooo
Alina [70]

Answer:

12 x 10 = 120

120 divided by 2 = 60

Formula of a triangle:

B(base) x H(height) x 1/2(basically dividing by 2)

8 0
3 years ago
if PQ || RS and the slope of PQ= x-1/4 and the slope of RS is 3/8 then find the value of x justify algebraically and numerically
Artemon [7]

The value of x is 5/8.

<u>Step-by-step explanation</u>:

Given,

  • The lines PQ and RS are parallel to each other.
  • slope of PQ= x-1/4
  • slope of RS = 3/8

The slopes of parallel lines are equal.

slope of PQ = slope of RS

⇒ x-1/4 = 3/8

⇒ (4x-1)/4 = 3/8

⇒ 8(4x-1) = 4(3)

⇒ 32x-8 = 12

⇒ 32x = 20

x = 20/32

x = 5/8

5 0
3 years ago
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