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sertanlavr [38]
1 year ago
7

You have 16 digs for your current volleyball season. There are 3 games left in the season. You want to break your previous recor

d of 20 digs in a
season. Write and solve an inequality that represents the number 2 of digs you must get in the remaining 3 games to break your record
Mathematics
1 answer:
natulia [17]1 year ago
7 0

Answer: 16+d>20

d>4

Step-by-step explanation:

d=digs

16+d>20

16-16+d>20-16

d>4

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2
HACTEHA [7]

This question is incomplete, the complete question is;

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis

Answer:

V = π (512/15)

Step-by-step explanation:

Given that;

region of rotation

y² = 2x, x = 2y

Region is rotated about y-axis as shown in the image

for the point of intersection,

y²/2 = 2y

y² - 4y = 0

y(y-4) = 0

∴ y = 0, y = 4

so the region lies in 0 ≤ y ≤ 4

Now cross section area of washer is

A(y) = π(outer radius)² = π(inner radius)²

A(y) = π(2y)² - π(y²/2)²

A(y) = π(4y²) - π(y⁴/4)

A(y) = π(4y² - (y⁴/4))

now volume of the solid of revolution is

V = ⁴∫₀ A(y) dy

V = ⁴∫₀ π(4y² - (y⁴/4))dy

V =  π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }

V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }

V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }

V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }

V = π { 256/3 - 1024/20 }

V = π { (5120 - 3072) / 60 }

V = π (512/15)

8 0
3 years ago
Triangle ABC is dilated to create triangle DEF on a coordinate grid. You are given that angle A is congruent to angle D. What ot
Marina CMI [18]

Answer:

They must meet at least three requirements like those in the explanation.

Step-by-step explanation:

-The other angles are also corresponding for example: B is congruent to E and C to F.

- Its sides are proportional to each other

-These two triangles can have the same shape no matter what size each one is

4 0
2 years ago
Are the lines described by the equations y=x+2 and x+y=6 intersecting, coinciding, or parallel? Explain
Novosadov [1.4K]
<span>y = slope*x + y-intercept;
</span>We can rewrite our equation in a shorter form : y = mx + b;
y = x + 2 ; m1 = 2 and b1 = 2;
y = -x + 6; m2 = -1 and b2 = 6;
<span>Set the two equations for y equal to each other:
</span>x + 2 = -x + 6 ;
<span>Solve for x. This will be the x-coordinate for the point of intersection:
</span>2x = 4;
x = 2;
<span>Use this x-coordinate and plug it into either of the original equations for the lines and solve for y. This will be the y-coordinate of the point of intersection:
</span>y = 2 + 2 ;
y = 4;
<span>The point of intersection for these two lines is (2 , 4).</span>

7 0
3 years ago
Please help me please !!
sweet [91]

Answer:

Acute

Step-by-step explanation:

7² + 9² ? 11²

49 + 81 ? 121

130 is greater than 121, so it is an acute triangle

8 0
2 years ago
Find the average. football yardage: 10 yd, –5 yd, 7 yd, 9 yd, –11 yd
CaHeK987 [17]

Answer:

10

Step-by-step explanation:

Add all of the numbers up and divide by the amount of numbers there are. You subtract for the negatives.

5 0
2 years ago
Read 2 more answers
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