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sladkih [1.3K]
3 years ago
9

Please help me ASP please

Mathematics
1 answer:
mylen [45]3 years ago
5 0

trapezoid area = 1/2(a+b) h

area= 1/2 (120 + 145) 50

area = 25(265)

= 6,625 yards

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Which expression is equivalent to -2-7?
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Answer:7

Step-by-step explanation:

just because

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If tan (θ )=0.532 , and α is the complement of θ , then tan (α) =
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tan(α) = 89.468

Step-by-step explanation:

90 - 0.532

6 0
2 years ago
DESPERATE WILL GIVE BRAINLIST AND THANKS
Nonamiya [84]

Answer:

90 counterclockwise

Step-by-step explanation:

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3 years ago
2. (15 points) Find the volume of the solid generated by revolving the region bounded by the curves x=
dangina [55]

Step-by-step explanation:

First, graph the region.  The first equation is x = 3y² − 2, which has a vertex at (-2,0).  The second equation is x = y², which has a vertex at (0, 0).  The two curves meet at the point (1, 1).  The region should look kind of like a shark fin.

(a) Rotate the region about y = -1.  Make vertical cuts and divide the volume into a stack of hollow disks (washers).

Between x=-2 and x=0, the outside radius of each washer is y₁ + 1, and the inside radius is 1.  Between x=0 and x=1, the outside radius of each washer is y₁ + 1, and the inside radius is y₂ + 1.

The thickness of each washer is dx.

Solve for y in each equation:

y₁ = √(⅓(x + 2))

y₂ = √x

The volume is therefore:

∫₋₂⁰ {π[√(⅓(x+2)) + 1]² − π 1²} dx + ∫₀¹ {π[√(⅓(x+2)) + 1]² − π[√x + 1]²} dx

∫₋₂⁰ π[⅓(x+2) + 2√(⅓(x+2))] dx + ∫₀¹ π[⅓(x+2) + 2√(⅓(x+2)) − x − 2√x] dx

∫₋₂¹ π[⅓(x+2) + 2√(⅓(x+2))] dx − ∫₀¹ π(x + 2√x) dx

π[⅙(x+2)² + 4 (⅓(x+2))^(3/2)] |₋₂¹ − π[½x² + 4/3 x^(3/2)] |₀¹

π(3/2 + 4) − π(½ + 4/3)

11π/3

(b) This time, instead of slicing vertically, we'll divide the volume into concentric shells.  The radius of each shell y + 1.  The width of each shell is x₂ − x₁.

The thickness of each shell is dy.

The volume is therefore:

∫₀¹ 2π (y + 1) (x₂ − x₁) dy

∫₀¹ 2π (y + 1) (y² − (3y² − 2)) dy

∫₀¹ 2π (y + 1) (2 − 2y²) dy

4π ∫₀¹ (y + 1) (1 − y²) dy

4π ∫₀¹ (y − y³ + 1 − y²) dy

4π (½y² − ¼y⁴ + y − ⅓y³) |₀¹

4π (½ − ¼ + 1 − ⅓)

11π/3

As you can see, when given x = f(y) and a rotation axis of y = -1, it's easier to use shell method.

(c) Since we're given x = f(y), and the rotation axis is x = -4, we should use washer method.

Make horizontal slices and divide the volume into a stack of washers.  The inside radius is 4 + x₁, and the outside radius is 4 + x₂.

The thickness of each washer is dy.

The volume is therefore:

∫₀¹ π [(4 + x₂)² − (4 + x₁)²] dy

∫₀¹ π [(4 + y²)² − (3y² + 2)²] dy

∫₀¹ π [(y⁴ + 8y² + 16) − (9y⁴ + 12y² + 4)] dy

∫₀¹ π (-8y⁴ − 4y² + 12) dy

-4π ∫₀¹ (2y⁴ + y² − 3) dy

-4π (⅖y⁵ + ⅓y³ − 3y) |₀¹

-4π (⅖ + ⅓ − 3)

136π/15

5 0
2 years ago
What can you conclude and reason
SSSSS [86.1K]

Answer:

ABC is an isosceles triangle.

Because it consists of two congruent triangles created by CD, side AC = CB, making it an isosceles triangle.

Step-by-step explanation:

I can conclude that triangle ABC is an isosceles triangle.

Perpendicular means intersecting at 90°. Bisector means intersecting at the midpoint, halfway between the two ends.

Since CD is dropped from vertex C and is a perpendicular bisector of AB, angle C is also bisected.

Therefore angle C for both triangles CDA and CDB is of equal measure.

We know angle D for both triangle CDA and CDB is of equal measure, 90°, because CD is a <em>perpendicular </em>bisector of AB.

The two triangles also share the same side CD.

Triangles CDA and CDB are congruent for having 2 equal angles and 1 equal side (ASA property).

Since they are congruent, AD = AB and AC = CB. Therefore triangle ABC is an isosceles triangle.

6 0
2 years ago
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