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mrs_skeptik [129]
4 years ago
13

The tip of a solid metal cone was placed into a cube that has 10 inch edges, as shown.

Mathematics
1 answer:
Licemer1 [7]4 years ago
7 0

Answer:

r=\sqrt{\dfrac{75}{\pi}}\approx 4.89\ in

Step-by-step explanation:

If the water in the cube rose from 6 inches to 8 inches when the cone was placed in the cube, then the difference in volumes is the volume of the submerged portion of the cone.

Initially, 10 in by 10 in by 6 in:

V_{initial}=10\cdot 10\cdot 6=600\ in^2.

At he end, 10 in by 10 in by 8 in:

V_{final}=10\cdot 10\cdot 8=800\ in^3.

Thus,

V_{submerged \ cone}=800-600=200\ in^3.

Use cone's volume formula

V_{cone}=\dfrac{1}{3}\pi r^2 \cdot h,

where r is the radius of the cone's base, h is the height of the cone.

From the diagram, h=8 in, then

200=\dfrac{1}{3}\cdot \pi\cdot r^2\cdot 8\\ \\\pi r^2=75\\ \\r^2=\dfrac{75}{\pi}\\ \\r=\sqrt{\dfrac{75}{\pi}}\approx 4.89\ in

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4x + 5y = 102<br> 7y + 5y = 126
galina1969 [7]

Answer:

hope you like my question

Step-by-step explanation:

Hi -

What you want to do here is solve the equation by substitution.

To do that, you solve one of the equations for y. then plug that into the other equation so you have an equation with only x as the variable.

1) Solve either equation for y. Lets go with the first one:

4x+5y=102

Subtract 4x from each side:

5y=102-4x

Divide both sides by 5

y=(102-4x)/5

2) Plug this value for y into the other equation we started with:

7x+5y = 126

7x + 5((102-4x)/5) = 126

3) Solve the resulting equation for x.

Since we are multiplying and dividing (102-4x) by 5 the 2 5s cancel each other out

7x + 5((102-4x)/5) = 126

7x + 102 - 4x = 126

Combine the 2 x terms:

3x+102=126

subtract 102 from each side:

3x = 24

Divide both sides by 3:

x=8

Once we have a value for x, we can plug that number into either one of our starting equations to solve for y.

4x + 5y = 102; if x = 8

32+5y = 102

subtract 32 from each side:

5y = 70

Divide both sides by 5:

y = 14

So x = 8 and y = 14.

You can check your work by plugging these numbers both into your 2 initial equations.

4x+5y=102; 4*8+5*14 = 102

7x+5y=126; 7*8 +5*14 = 126

3 0
3 years ago
Solve 2,401 = 76 – 2x.
inessss [21]

Answer:

The answer would be -1162.5

Step-by-step explanation:

7 0
3 years ago
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Minimum and maximum of this graph??
shtirl [24]

Hi!

The minimum is the lowest possibility on the graph, and the maximum is the highest.

In this graph, the highest point (the maximum) is (10,11) and the lowest point (the minimum) is (3, 1).

Hope this helps! :D

6 0
3 years ago
This high school stadium contains a track that surrounds a soccer field. The soccer field is 100 yards long and 70 yards
liberstina [14]

Answer:

Given : The high school stadium contains a track that surrounds a soccer field. The soccer field is 100 yards long and 70 yards wide.

The school decided to cover the semicircles with grass to create a space for stretching and other activities.

To Find: area of one of the semicircles at either end of the track

How many square yards of grass will the school need to cover the entire circle?

Solution:

Diameter of semicircle = 70 yards

Radius of semicircle = 70/2 = 35 yards

Area of semicircle at one end = (1/2)πr²

= (1/2)(22/7)35²

= 1,925 sq yards

area of one of the semicircles at either end of the track = 1,925 sq yards

square yards of grass will the school need to cover the entire circle

= 2 x   1,925

= 3850 sq yards

distance around one of the semicircles at either end of the soccer field = πr  = (22/7) 35 = 110 yards

distance around the inner lane of the track  = 100 + 100 + 110 + 110

= 420 yards

Please Mark as Brainliest

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The laptop was $500<br> and is now $400. What<br> is the percent of change?
snow_lady [41]

Answer:

20%

Step-by-step explanation:

6 0
3 years ago
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