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3 years ago

The acute angles of a ________ triangle are complementary

Mathematics

1 answer:

Mashcka [7]3 years ago

4 0

Answer:

Complementary angles are two angles that add up to 90 degrees. If angle C is a right angle, then it has a measure of 90 degrees. The angles in a triangle must sum to 180 degrees. If one angle is already 90 degrees, then the other two angles must sum to 90 degrees since 180- 90 = 90.

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(-5,-4) rotated 270° counterclockwise

stepladder [879]

Answer:

(4, - 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 270°

a point (x, y ) → (- y, x ) , thus

(- 5, - 4 ) → (4, - 5 )

6 0

3 years ago

An open metal tank of square base has a volume of 123 m^3

snow_lady [41]

Answer:

a) h = 123/x^2

b) S = x^2 +492/x

c) x ≈ 6.27

d) S'' = 6; area is a minimum (Y)

e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

123 = x^2·h

h = 123/x^2

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

$S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}$

c) The derivative of the area with respect to x is ...

$S'=2x-\dfrac{492}{x^2}$

When this is zero, area is at an extreme.

$0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583$

d) The second derivative is ...

$S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6$

This is positive, so the value of x found represents a minimum of the area function.

e) The minimum area is ...

$S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78$

The minimum area of metal used is about 117.78 m².

3 0

3 years ago

A taxi travels 25 kilometers east of an airport. Then it travels from that point to a point that is 40 kilometers west of the ai

kati45 [8]

25km east + 25km return+ 40km west + 40km return = 130km

Hope that helped :)

7 0

3 years ago

How do you find the area of a square

Lubov Fominskaja [6]

Answer:

width times length

Step-by-step explanation:

7 0

4 years ago

The coordinate of centroid of a triangle whose vertices are (1,3,-2), (4,5,0), (6,3,9) is = ……………….

Dominik [7]

Answer:

$C = (\frac{11}{3},\frac{11}{3},\frac{7}{3})$

Step-by-step explanation:

Given

$(x_1,y_1,z_1) = (1,3,-2)$

$(x_2,y_2,z_2) = (4,5,0)$

$(x_3,y_3,z_3) = (6,3,9)$

Required

Determine the coordinates of the centroid

Represent the coordinates with C.

C is calculated as follows:

$C = (\frac{1}{3}(x_1+x_2+x_3),\frac{1}{3}(y_1+y_2+y_3),\frac{1}{3}(z_1+z_2+z_3}))$

Substitute values of x and y in the given equation

$C = (\frac{1}{3}(1+4+6),\frac{1}{3}(3+5+3),\frac{1}{3}(-2+0+9}))$

$C = (\frac{1}{3}(11),\frac{1}{3}(11),\frac{1}{3}(7}))$

$C = (\frac{11}{3},\frac{11}{3},\frac{7}{3})$

<em>The above is the coordinate of the centroid</em>

8 0

3 years ago