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3 years ago

In the accompanying diagram, isosceles triangle ABC has coordinates A(-4,0), B(4,0), C(0,4). Find the area of ABC.

Mathematics

1 answer:

kari74 [83]3 years ago

4 0

Answer:

The area of triangle ABC is $16\ units^{2}$

Step-by-step explanation:

we know that

The area of a triangle is equal to

$A=\frac{1}{2}(b)(h)$

In this problem we have

$b=AB=4-(-4)=8\ units$ ---> the length of the base b is the difference of the x-coordinates between A and B

$h=OC=4-0=4\ units$ ---> the height h is the difference of the y-coordinates between C and the origin O

substitute the values in the formula

$A=\frac{1}{2}(8)(4)$

$A=16\ units^{2}$

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10kg 20kg 24kg ?kg plz answer this for me

luda_lava [24]

Answer:

27KG

Step-by-step explanation:

Mouse- M , Cat - C, Dog - D

M + C = 10 ----- (1)

M + D = 20 -------(2)

C + D = 24 --------(3)

(1) - (2) => C - D = -10 ---- (4)

(3) + (4) => 2C = 14

=> C = 7

Substitute C in (1) => M + 7 = 10

=> M = 3

Substitute M in (2) => 3 + D = 20

=> D = 17

Therefore C + M + D = 7 + 3 + 17 = 27KG

3 0

3 years ago

Find the unit vector that has the same direction as the vector v. v = 3i + j

Alchen [17]

$\bf \textit{unit vector for \underline{v}}\qquad v=\ \textless \ a,b\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{a}{\sqrt{a^2+b^2}}~,~\cfrac{b}{\sqrt{a^2+b^2}}}\\\\
-------------------------------\\\\
v=3i+j\implies v=\ \textless \ 3,1\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{3}{\sqrt{3^2+1^2}}~,~\cfrac{1}{\sqrt{3^2+1^2}}}
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\left( \cfrac{3}{\sqrt{10}}~,~\cfrac{1}{\sqrt{10}} \right)$

5 0

3 years ago

Read 2 more answers

Which is precisely defined using the undifined terms point and plane

LuckyWell [14K]

A line segment is precisely defined using the undefined terms point and plane. These three terms are undefined terms in geometry. A point has no dimension. A plane has no thickness but extends at all directions. A line has no thickness but extends in one dimension

8 0

4 years ago

Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1). g

Anika [276]

Complete Question:

Find the directional derivative of g(x,y) = $x^2y^5$ at the point (1, 3) in the direction toward the point (3, 1)

Answer:

Directional derivative at point (1,3), $D_ug(1,3) = \frac{162}{\sqrt{8} }$

Step-by-step explanation:

Get $g'_x$ and $g'_y$ at the point (1, 3)

g(x,y) = $x^2y^5$

$g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486$

$g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405$

Let P = (1, 3) and Q = (3, 1)

Find the unit vector of PQ,

$u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\$

$|\bar{PQ}| = \sqrt{8}$

The unit vector is therefore:

$u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }$

The directional derivative of g is given by the equation:

$D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }$

8 0

3 years ago

A hot air balloon descends at a rate of 320 ft per minute for 3 minutes use integers to calculate represent the balloons total c

Licemer1 [7]

Let x = the amount of feet descended in 3 minutes (thus the total change of altitude of the balloon)

320 (feet per minute) / 1 (minute) = x (feet per minute) / 3 (minutes)

1) Divide: 320/1 = 320.
2) Multiply: 320 x 3= 960.

The balloon that descends at a rate of 320 feet/minute (so, every minute, it descends 320 feet) descends a total of 960 feet in 3 minutes.

The balloon's total change in altitude is -960<span>

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4 0

3 years ago