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3 years ago

List the 6 congruency statements given ABC = DEF

Mathematics

1 answer:

galina1969 [7]3 years ago

5 0

Answer:

∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF

Step-by-step explanation:

Given that triangles ABC and DEF are congruent. Now we need to choose correct congruency statements from the given choices.

We know that corresponding angles of congruent triangles are equal so we can write:

∠A ≅ ∠D

∠B ≅ ∠E

∠c ≅ ∠F

We know that corresponding sides of congruent triangles are equal so we can write:

AB = DE

BC = EF

AC = DF

comparing these with given choices we see that, First choice is correct.

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4 years ago

Set up (do not evaluate) the integral which gives the volume when region bounded by curves y=Ln(x), y=2, and x=1 is revolved aro

ladessa [460]

Step-by-step explanation:

Graph the region: desmos.com/calculator/rbe6rq61a2

When the region is rotated about y=-2, the resulting shape is a horizontal, hollow cylinder. The volume can be found with either washer method or shell method.

To use washer method, cut a thin vertical slice of the region. Rotated around y=-2, this slice becomes a washer. The width of this washer is dx. The outer radius is 2 − (-2) = 4. The inner radius is y − (-2) = y + 2. The volume of the washer is:

dV = π (4² − (y + 2)²) dx

dV = π (4² − (ln x + 2)²) dx

The total volume is the sum of the washers from x=1 to x=e².

V = ∫ dV

V = ∫₁ᵉ² π (4² − (ln x + 2)²) dx

To instead use shell method, cut a thin horizontal slice of the region. Rotated around y=-2, this slice becomes a cylindrical shell. The thickness of the shell is dy. The radius is y − (-2) = y + 2. The width is x − 1. The volume of the shell is:

dV = 2π (y + 2) (x − 1) dy

dV = 2π (y + 2) (eʸ − 1) dy

The total volume is the sum of the shells from y=0 to y=2.

V = ∫ dV

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3 years ago

Specialized license plates have seven permissible characters: letters, numbers, a dash (-)

ss7ja [257]

Answer:

$Total = 38^7$

Step-by-step explanation:

Given

$Plate\ Number = 7\ characters$

$Letters \to 26$ $\to [A- Z]$

$Numbers \to 10$ $\to [0 - 9]$

$Dash \to 1$ $\to [ - ]$

$Ampersand \to 1$ $\to [\&]$

Required

Number of possible characters

Since the order and ways of selecting each character is not selected, then it means that any of the permissible character can occupy any of the 7 available spaces, with repetition.

The total possible characters (n) is:

$n = 26 +10 + 1 + 1$