If a sphere of ice cream that was 2.5 inches in diameter was placed on top of the ice cream cone that had a height of 4 inches and a diameter of 1.75 inches and left to melt directly into the cone, would the all of the ice cream fit into the cone? Justify your answer using mathematics and a complete sentence answer.
Answer:
The cone would not the all of the ice cream fit into the cone.
Step-by-step explanation:
Geometrically speaking, the volume of the cone ([tex]V_{c}[/tex]), measured in cubic inches, is described by the following equation:
[tex]V_{c} = \frac{\pi}{3}\cdot r^{2}\cdot h[/tex] (1)
Where:
[tex]r[/tex] - Base radius, measured in inches.
[tex]h[/tex] - Height, measured in inches.
And the ice cream ball is described by the volume equation for the sphere ([tex]V_{s}[/tex]), measured in cubic inches:
[tex]V_{s} = \frac{4\pi}{3} \cdot R^{3}[/tex] (2)
Where [tex]R[/tex] is the radius of the ice cream ball, measured in inches.
In this case, the ice cream will fit into the cone if and only if [tex]V_{s} \le V_{c}[/tex]. That is:
[tex]\frac{4\pi}{3}\cdot R^{3} \le \frac{\pi}{3}\cdot r^{2}\cdot h[/tex]
[tex]4\cdot R^{3} \le r^{2}\cdot h[/tex]
If we know that [tex]r = 0.875\,in[/tex], [tex]h = 4\,in[/tex] and [tex]R = 1.25\,in[/tex], then the inequation is:
[tex]4\cdot (1.25\,in)^{3}\le (0.875\,in)^{2}\cdot (4\,in)[/tex]
[tex]6.25\,in^{3}\le 3.063\,in^{3}[/tex] (CRASH!)
Which leads to an absurd. Hence, the cone would not the all of the ice cream fit into the cone.
what is the range of the function f(x)=7-3x when the domain is {-4, -2, 0, 2}?
Answer:
{19,13,7,1}
Step-by-step explanation:
Since the domain is the input we have to plug in each of those numbers to get the range ( or the output.) When we plug in -4 we get 19. When we plug in -2 we get 13, when we plug in 0 we get 7 and when we plug in 2 we get 1. (:
A car travels down a highway at a constant speed shown in the graph below.
Find the speed of the car.
Answer:
80 km/he is the correct answer
Answer:
80kph
Step-by-step explanation:
On the chart it shows that on the x-axis 1 hour equals to 80 km.
Simplify: 26 - 2(7 + 3^2)
please answer with one of the options below:)
PLEASE HELP ILL GIVE BRAINLIEST Which set of ordered pairs represents a function?
Answer:
the 2nd on (B)
Step-by-step explanation:
The x does not repeat
18. Find the equation of the circle containing the points (-1.-1) and (3, 1) and with the centre on the line x-y + 10 = 0
Answer:
x^{2} +2x+y^{2}+2y= 18
Step-by-step explanation:
equation of circle is:
[tex]x^{2}+y^{2}=r^{2}[/tex]
using distance formula and substituting value,
[tex](3-(-1))^{2} +(1-(-1))^{2}=r^{2}[/tex]
solving,
r=[tex]2\sqrt{5}[/tex]
for equation of circle,
[tex](x-(-1))^{2} +(y-(-1))^{2} =20[/tex]
on solving,
[tex]x^{2} +2x+1+y^{2}+2y+1=20[/tex]
on solving,
[tex]x^{2} +2x+y^{2}+2y= 18[/tex]
hw is stressingg help meeee
B. 27.5%
because it says ‘all students,’ you look at the total, which is 55/200
and then you need to half that to get it out of 100, so 55/2=27.5
If you can buy 4 oz of candy for $5.40, how much would 6 oz of candy cost?
Twenty-four is ___% of 80
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
i really don't have a method for this, just try a number you think is close, go up, or down depending on the number
Anna spent $2.75 at the school store. She bought two erasers and some pencils. How many pencils did she buy? Write and Solve an equation. If needed, use P to represent the number of pencils, and E to represent the number of Erasers. (This is for Multi-step Linear Equations) Pencils: 0.75 each erasers: 0.25 each
Answer:
1.25 is what she spent so she got 5 pencils
Step-by-step explanation:
what is the value of k
-3(k+7)- 5k +4 = 23
a.) k=5 b.) k=-1 c.) k=5 d.)k=1
Answer:12.567
Step-by-step explanation:
I have to solve this system equation by graphing. by the way the equation is all in one,not separate
100 points!! ASAP (Will mark brainliest if right.)
Two similar triangles are shown on the following coordinate grid:
A coordinate plane is shown. Triangle ABC has vertices A at negative 3 comma 2, B at negative 1 comma 0, and C at negative 2 comma negative 1. Triangle A prime B prime C prime has vertices A prime at 6 comma 4, B prime at 2 comma 0, and C prime at 4 comma negative 2.
Which set of transformations has been performed on triangle ABC to form triangle A′B′C′?
A. Dilation by a scale factor of 4 followed by reflection over the x-axis
B. Dilation by a scale factor of 2 followed by reflection over the x-axis
C. Dilation by a scale factor of 4 followed by reflection over the y-axis
D. Dilation by a scale factor of 2 followed by reflection over the y-axis
Answer:
Reflection across the y-axis and a dilation by a factor of 2.
Step-by-step explanation:
Comparing the points from the pre-image, ABC, to the image, A'B'C', we see that both x- and y-coordinates seem to be doubled from the pre-image to the image. However, the sign of the x-coordinates in the image is different; this means that the x-coordinates are negated. A reflection across the y-axis will negate the x-coordinates.
To double both the x- and y-coordinates, we would then apply a dilation by a factor of 2, as the scale factor gets multiplied by every coordinate.
Answer:
The answer is d
Step-by-step explanation:
Suppose f(x)= 6x-5 . Describe how the graph of g compares with the graph of f. g(x)=f(x) +9
Answer:
Please check the graph attached.
Step-by-step explanation:
Given the function
f(x)= 6x-5
and
g(x)=f(x) +9
g(x)=f(x) +9 means 9 is added into the output of the parent function f(x).
It means the function g(x) would be shifted 9 units up.
Please check the attached diagram.
The red graph represents the graph f(x)= 6x-5.
It is clear that the y-intercept of the graph f(x)= 6x-5 is (0, -5)
The blue graph represents the graph g(x)=f(x) +9
It is clear that the y-intercept of the graph g(x)=f(x) +9 is (0, 4)
Conclusion:
It is clear that g(x)=f(x) +9 has been shifted up by 9 units from the f(x)= 6x-5.
Use the original price and the markdown or markup to find the retail price. Original price $43; markup 11.5%
Answer:
$47.945
Step-by-step explanation:
Given the following
Original price = $43;
markup = 11.5%
Markup price = 11.5% of the original price
Markup price = 11.5% of $43
Markup price = 0.115×43
Markup price = $4.945
Retail price = original price+markup price
Retail price = $43+$4.945
Retail price = $47.945
Yolanda needs to ship a 35 pound package. If she has to pay 52of a dollar per pound, what is the amount, in dollars, that she needs to pay for shipping?
Answer:
$1820
Step-by-step explanation:
35 x 52 = $1820
20 cm
5 Clear
Mark for Review
5 cm
4 cm
6 cm
5 cm
What is the total surface area of the triangular prism in square centimeters?
A240 cm
B320 cm
C368 cm
D344 cm
20+
5+4+6+5-=20
20+20=40
answer is A 240cm
What does the graph of the equation y = 6x – 1 look like?
A. Curve
B. Straight line
C. A V-shape
D. Parabola
Answer:
straight line
Step-by-step explanation:
The graph of the given line is a Straight line.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given that, an equation, y = 6x-1, we need to tell what type of graph will it make,
y = 6x-1
Put x = 0,
y = -1
Put x = 1
y = 5
Put x = 0.5
y = 2
Points =
x = 0, 1, 0.5
y = -1, 5, 2
Plotting the graph, we will get a straight line, also, we know that, a linear equation will always make a straight line,
Hence, the graph of the given line is a Straight line.
Learn more about graphs, click;
https://brainly.com/question/17267403
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What is an 8-bit binary number known as? Select one: a. variable b. algorithm c. code d. byte
Answer:
A Byte
Step-by-step explanation:
Answer:
It would be known as a byte.
Step-by-step explanation:
For example, 10110101 has eight digits and would therefore be known as a byte.
Can someone help me with this ASAP please and thanks
Answer:
1)a=12 2)b=13
Step-by-step explanation
a really good app to use for the rest of the answers is cymath! it shows you the work too
If a bike race covers 120 mi over 6 days and the
cyclists ride the same distance each day, how
many miles does each cyclist ride each day?
Answer:
The cyclists should be riding 20 miles every day. (Which is a lot for me)
Step-by-step explanation:
All we have to do to find how many Miles per Day, is to divided the miles by the days.
120 ÷ 6 = 20
So, the cyclists should be riding 20 miles every day.
Use the graph of the polynomial function to find the factored form of the related polynomial. Assume it has no constant factor.
Answer:
I had a slightly different question, but I think its option D
(x - 3)(x + 3)
Write down in terms of n
Answer:
a) -2n+14
b) -5n+30
Step-by-step explanation:
negative because it goes down, any other questions im here to help
Hello please help ASAP!!!
What are the questions asked on the FLVS (florida virtual school) module 4 DBA(discussion based assessment) for Pre Calculus Honors math?
Answer:
I have no question. ..............
What is the inverse function of d(x) = -2x - 6?
a.) d-^1(x) = 2x + 6
b.)d-^1(x) = 2x + 6
c.)d-^1(x) --2x-3
d.)d-^1(x) = -2x-3
Answer:
d(x)= -x/2 - 3
Step-by-step explanation:
What is the distance from M to N?
HELPPP ME PLEASE HURRY IM GIVING BRAINLIST!!!!!!!!
50 POINTS!!!!! NO TROLLING PLZ!!
Answer: B. 14 units
Step-by-step explanation:
Answer:
it’s not 14 units, that’s all i know
Step-by-step explanation:
got it wrong on ap3x
Evaluate the expression: 25
A.
2·5
B.
2·2·2·2·2
C.
2·2·2·2
D.
2+2+2+2+2
Answer:
None of those are correct because none equal 25
Answer:
none
of them equel 25 on edge 2021
Step-by-step explanation:
WILL MARK YOU BRAINLIEST
Answer:
15) The equation to find the sum of interior angles is
(n - 2).180
which means that a polygons interior angles will always be a multiple of 180 because they are multiplied by it.
PLS HELP WILL MARK U BRAINLIEST
