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Leni [432]
3 years ago
11

Need help in geometry!!!

Mathematics
1 answer:
8_murik_8 [283]3 years ago
6 0
Given:
JKLM: J(8,4) ; K(4,10) ; L(12,12) ; M(14,10) 

I'll just use the first vertex of every quadrilateral in comparison with J(8,4)

A(-8,-4) ; B(-4,-10) ; C(-12,-12) ; D(-14,-10) → a sequence of reflections across the x and y-axes, in any order. This is easy because each vertex has the same number but different signs. 

E(11,2) ; F(7,8) ; G(15,10) ; H(17,8) → a translation of 3 units left and 2 units up. As you can envision with a graph, from 11 to 8, you need to move to the left of the x-axis. from 2 to 4, you need to move up of the y-axis.

O(6,7) ; P(2,13) ; Q(10,15) ; R(12,13) → a translation 2 units right and 3 units down. From 6 to 8 of the x-axis and from 7 to 4 of the y axis. 

S(4,16) ; T(10,20) ; U(12,12) ; V(10,10) → This one has no pair but it seems as though this is rotated along the point U.

W(11,7) ; X(7,13) ; Y(15,15) ; Z(17,13) → a translation 3 units down and 3 units left. 
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Perform a first derivative test on the function ​f(x)equals2 x cubed plus 3 x squared minus 120 x plus 6​; ​[minus5​,8​]. Bold
maria [59]

Answer:

a) Critical points

x = 4 and x = -5

b) x = 4 corresponds to a minimum point for the function f(x)

x = - 5 corresponds to a maximum point for the function f(x)

c) The minimum value of f(x) in the interval = -298

The maximum value of f(x) in the interval = 431;

Step-by-step explanation:

f(x) = 2x³ + 3x² - 120x + 6 in the interval [-5, 8]

a) To obtain the critical points, we need to obtain the first derivative of the function with respect to x. Because at critical points of a function, f(x), (df/dx) = 0

f'(x) = (df/dx) = 6x² + 6x - 120 = 0

6x² + 6x - 120 = 0

Solving the quadratic equation,

x = 4 or x = -5

The two critical points, x = 4 and x = -5 are in the interval given [-5, 8] (the interval includes -5 and 8, because it's a closed interval)

b) To investigate the nature of the critical points, we obtain f"(x)

Because f'(x) changes sign at the critical points

If f"(x) > 0, then it's a minimum point and if f"(x) < 0 at c, then it's a maximum point.

f"(x) = (d²f/dx²) = 12x + 6

at critical point x = 4

f"(x) = 12x + 6 = 12(4) + 6 = 54 > 0, hence, x = 4 corresponds to a minimum point.

at critical point x = -5

f"(x) = 12x + 4 = 12(-5) + 4 = -56 < 0, hence, x = -5 corresponds to a maximum point.

c) At x = 4,

f(x) = 2x³ + 3x² - 120x + 6 = 2(4)³ + 3(4)² - 120(4) + 6 = -298

At x = - 5

f(x) = 2x³ + 3x² - 120x + 6 = 2(-5)³ + 3(-5)² - 120(-5) + 6 = 431

7 0
3 years ago
Which expression represents the volume, in cubic units, of the shaded part of the sphere? four-thirdsπ(103) four-thirdsπ(43) fou
oee [108]

The volume of the shaded part in cubic units is  4/3π(20)³ -  4/3π(4)³

<h3>Volume of composite object</h3>

The sphere is a a solid 3-dimensional object. THe formula for calculating its volume is expressed as:

V = 4/3πr³

where:

r is the radius of the sphere

<u>For the outer sphere:</u>

V = 4/3π(20)³

<u>For the inner sphere:</u>

V = 4/3π(4)³

The volume of the shaded part in cubic units is  4/3π(20)³ -  4/3π(4)³

Learn more on volume of sphere here: brainly.com/question/10171109

#SPJ4

6 0
2 years ago
Answer the questions
Flauer [41]
10) 1 gallon of water for every inch of the fish's body length.
a) 2 1/2 inches long fish needs 2 1/2 gallon of water.
b) tank: l = 7 inches ; w = 5 inches; h = 7 ; volume = 7in * 5in * 7in = 245 in³
c) no. her fish tank is not large enough for the fish.
volume of 1 gallon of water is 231 in³, water needed is 2 1/2 gallon, so 5/2 * 231 in³ = 577.50 in³ volume.

11) volume = 7in * 3.5in * 1.75 in = 42.875 in³ 
weight of the brick = 0.1 pound per cubic inch ⇒ 42.875 in³ * 0.1 lb = 4.2875 pounds
weight of the gold bar = 0.7 pound per cubic inch ⇒ 42.875 in³ * 0.7 lb = 30.0125 pounds

12) l = 55cm ; w = 40cm ; h = 30 cm
volume = 55cm * 40cm * 30cm = 66,000 cm³

7 0
3 years ago
Let n be even number, then the next even number greater than n is
Olin [163]

Answer:

If N is 38, next even number would be 40

Step-by-step explanation:

Any number ending with 0 2 4 6 8 is even, sorry if this ins't what you were asking I didn't understand completely

4 0
3 years ago
Find the length of the hypotenuse of a right triangle with legs measuring 7 cm and 9 cm. Round your answer to the nearest tenth.
DaniilM [7]

Answer:

Hypotenuse = 11.4 cm

Step-by-step explanation:

Hypotenuse ² = opposite ² + adjacent ²

Opposite = 7 cm

Adjacent = 9 cm

Hypotenuse ² = opposite ² + adjacent ²

= 7² + 9²

= 49 + 81

Hypotenuse ² = 130

Hypotenuse = √130

= 11.40

Hypotenuse = 11.4 cm

6 0
3 years ago
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