100 POINTS! PLS DO NOT STEAL THE POINTS AND ACTUALLY ANSWER TY
A scoop of ice cream in the shape of a whole sphere sits in a right cone. the radius of the ice cream scoop is 2.5 cm and the radius of the cone is 2.5 cm. How tall must the height of the cone be to fit all the ice cream without spilling if it melts? Show all your work.

Solution :

Given :

The rate of change of y is proportional to y.

Therefore, [tex]$\frac{dy}{dt} \propto y$[/tex]

[tex]$\frac{dy}{dt} = k y$[/tex] ,             where k is the proportionality constant

[tex]$\frac{dy}{y}=k \ dt$[/tex]

Taking integration on both the sides,

[tex]$\int \frac{dy}{y}=\int kdt$[/tex]

[tex]$\int \frac{dy}{y}=k\int dt$[/tex]

[tex]$\ln |y| = kt+C$[/tex],    where C is the integration constant

[tex]$y=e^{kt+C}$[/tex]

[tex]$y=e^{kT}e^C$[/tex]

[tex]$y(t)=C_1e^{kt}$[/tex]  ....................(1)

When t = 0, y = 2, so

[tex]$2=c_1e^{k\times 0}$[/tex]

[tex]$2=c_1e^{ 0}$[/tex]

[tex]$2=C_1$[/tex]

From equation (1),

[tex]$y=2e^{kt}$[/tex] ........................(2)

when t = 2, y = 4

[tex]$4=2e^{k\times 2}$[/tex]

[tex]$e^{2k}=\frac{4}{2}$[/tex]

[tex]$e^{2k}=2$[/tex]

[tex]$2k= \ln(2)$[/tex]

[tex]$k=\frac{1}{2} \ln(2)$[/tex]

From (2),

[tex]$y=2e^{\frac{1}{2}\ln(2)t}$[/tex]

[tex]$y=2e^{\frac{t}{2}\ln(2)}$[/tex]

[tex]$y=2e^{\ln(2)^{t/2}}$[/tex]

[tex]$y=2.2^{t/2}$[/tex]

When t = 3,

[tex]$y = 2 . 2 ^{3/2}$[/tex]

[tex]$y=2[(\sqrt2)^2]^{3/2}$[/tex]

[tex]$y= 2. 2\sqrt2$[/tex]

[tex]$y=4 \sqrt2$[/tex]

Answer:

5

Step-by-step explanation:

5÷1

i m not sure but i like its ans

Answer:

Y = 4x + 1

Step-by-step explanation:

1 × 4 + 1 = 5

2 × 4 + 1 = 9

3 × 4 + 1 = 13

4 × 4 + 1 = 17

Answer:

correct answer

Step-by-step explanation:

Answer:

Number 4

Step-by-step explanation:

A theoretical probability chance is a probably where all the other chances are equal. In this case, you can roll 6 different types of numbers on the dice: 1, 2, 3, 4, 5, and 6. And the number of times the dice was rolled was 60 times. So, we can divide 60/6 because there were 60 rolls and 6 different possibilities. 60/6=10, so 10 is the theoretical probability. As you can see, the graph shows that the number 4 was rolled 10 times, which means that number 4 is the experimental probability that matched the theoretical probability.

Answer:

either A,B,C, or D?

Step-by-step explanation:

Answer:

14 tons of sugar

$9603.5

Step-by-step explanation:

For what amount of sugar do the two companies charge the same?

What is the cost when the two companies charge the same?

Let

x = ton of sugar

Company A:

7500 + 150.25x

Company B:

7143 + 175.75x

1. Equate company A and company B

7500 + 150.25x = 7143 + 175.75x

7500 - 7143 = 175.75x - 150.25x

357 = 25.50x

x = 357/25.50

x = 14 tons of sugar

2. Cost when both companies charge the same

Company B:

7143 + 175.75x

= 7143 + 175.75(14)

= 7143 + 2460.5

= 9603.5

Company B = $9603.5

Company A:

7500 + 150.25x

= 7500 + 150.25(14)

= 7500 + 2103.5

= 9603.5

Company A = $9603.5

Answer:

Obtuse

Step-by-step explanation:

x = missing angle

20+30+x=180

50+x=180

x=130

90<130

Thus, the triangle is obtuse

B. 2x^4-11x^3+7x^2+5x-3

Answer:

A

Step-by-step explanation:

BECAUSE IM DIFFERENT

Answer:

ST, WX

Step-by-step explanation:

Answer:

ST and WX are congruent

Answer:

Step-by-step explanation:

7x + 8y = -5

       8y = -7x - 5

Divide the whole equation by 8

[tex]\frac{8y}{8}=\frac{-7x}{8}-\frac{5}{8}\\\\y =\frac{-7}{8}x-\frac{5}{8}[/tex]

Parallel lines have same slope

Slope of the parallel line = (-7/8)

Slope of the line perpendicular to this line = -1/m  = -1 ÷ (-7/8)

                                                                      [tex]= (-1)*\frac{8}{-7}\\\\= \frac{8}{7}[/tex]

Answer:

We have the function:

f(x) = 2*sin(x) - 3

To graph this type of functions is useful to understand the parts of the function.

A general one is written as:

g(x) = A*sin(w*x + p) + M

where:

A is the amplitude

w is the angular frequency.

p is the phase

M is the midline.

Then in this case we have an amplitude of 2, an angular frequency of 1, a phase of 0 radians and the midline y = -3

Now we can evaluate the function in different points and (knowing how a sine function behaves) connect them, the graph will look something like this:

Answer:

y=2x+5

Step-by-step explanation:

To find a linear equation you must find the slope and y intercept to create an equation in y=mx+b form (slope-intercept form)

So slope is = y2-y1 / x2-x1 [2 and 1 are subscripts] so 11-7/3-1 so m=4/2 = 2

Slope = 2, now find b

So using y = mx + b, substitute what you know so 7 = 2(1) + b so b=7-2 = 5

Put it all together y = 2x + 5

Answer:

Step-by-step explanation:

SVT and TVU

Hope that helps!

Answer:

x

2

+

2

x

−

3

=

0

x

2

−

3

x

=

0

3

x

2

−

15

x

=

0

Step-by-step explanation:

Answer:

2(1/2 x 4 x 6) = x

expaination:

area of triangle = 1/2 x 2 x 6 sq yards

multiply by $2/sq yard

Answer: $24

Step-by-step explanation:

The formula for a triangle is 1/2 times base times height

so 0.5 x 4 x 6

0.5 x 4 = 2

2 x 6 = 12

12 x $2 = 24

so you charge $24 dollars

Hope this helps.

Answer: Graph the inequality by finding the boundary line, then shading the appropriate area. In slope intercept form its y>-6 + 2x/3. Graph the y intercept -6, then use rise/run and go up 2 points and then to the right 3 points. Then shade the upper right because it is a greater sign and make the lines dashed.

Step-by-step explanation: Hope this helps :)

Answer:

2.5

Step-by-step explanation:

8 times 4 is 32, and 80/32 is 2.5. When you have to find another measurement and you know 2 of them, you just have to divide the total of the 2 measurements with the volume. it would be 2.5 feet as the height.

Answer:

y + 2 = 4(x - 3)

Step-by-step explanation:

Answer: y+2= 4(x-3)

Step-by-step explanation:

Answer:

The slope of the line is 5

Step-by-step explanation:

When we talk of the slope of a straight line graph, we refer to the rate at which the values on the y-axis changes as a ratio of the changes we have on the x-axis

Now, from the question, number of hours is placed on x-axis, while we have the amounts on the y-axis

having $5 per hour means the rate of change of what is earned to number of hours worked is 5 and this is the slope of the line

Answer:

x = 20

Step-by-step explanation:

Assuming that both lines are straight lines, we can make opposite sides equal. So... 3x+50 = 6x-10 --> 3x+60=6x --> 60=3x --> x=20

Answer:

39/7

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

7 × 5 = 35

Step 2

Add the answer from Step 1 to the numerator

35 + 4 = 39

Step 3

Write answer from Step 2 over the denominator

39/7

Answer: t ≈9.9543..

Step-by-step explanation:

Answer:

T= 9.6... or 10

Step-by-step explanation:

29= 29/3

=9.6...

Answer:

yellow area = 5.37 ft²

Step-by-step explanation:

area of square = L x W = 5 x 5 = 25 ft²

radius = 2.5 ft

area of circle = PiR² = (3.14)(2.5²) = 19.63 ft²

25 - 19.63 = 5.37 ft²

The area of the yellow region is 5.375 square feet.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, the side of a square = 5 feet and radius of a circle = 2.5 feet.

Here, area of a square = side²

= 5²

= 25 square feet

Area of a circle = πr²

= 3.14×2.5²

= 19.625 square feet

So, the area of the yellow region = 25-19.625

= 5.375 square feet

Therefore, the area of the yellow region is 5.375 square feet.

Learn more about the area here:

https://brainly.com/question/27683633.

#SPJ2

Answer:

8

Step-by-step explanation:

18-10=8 units

Answer:

 8

Step-by-step explanation:

The total height of the rectangle and triangle is given as 18

The height of the rectangle is given as 10 , then

height of triangle = 18 - 10 = 8

Answer:

I think the surface area is 276 if I'm not mistaken hope this helps!

Answer:

Part A) [tex](3x^2 - 6x - 10) + (5x^2 + 9x - 8 ) =8x^2 + 3x - 18[/tex]

Part B) [tex](10x^2 - x - 3) - (8x^2+3x-18) = 2x^2 -4x+15[/tex]