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Dimas [21]
1 year ago
15

A sphere with a radius of 4 cm is enlarged by a scale factor of 2. What is the approximate volume of the new sphere in cubic cen

timeters?
Mathematics
1 answer:
Lisa [10]1 year ago
5 0

\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ \stackrel{original}{r=4}\\ \stackrel{enlarged}{r=(4)(2)} \end{cases}\implies \begin{array}{llll} V=\cfrac{4\pi (\stackrel{enlarged}{~~(4)(2)~~})^3}{3} \\\\\\ V=\cfrac{2048\pi }{3}\implies V\approx 2144.66~cm^3 \end{array}

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The parameters of a linear function are the slope and the y-intercept
taurus [48]

Answer:

see the explanation

Step-by-step explanation:

we know that

A linear function in slope intercept form is equal to

f(x)=mx+b

where

m is the slope or unit rate

b is the y-intercept

x is the independent variable or input value

f(x) is the dependent variable or output value

In this problem we have

f(m)=5+3m

where

m is the number of miles

f(m) is the cab company's fare in dollars

we have that

In this context

<em>Slope</em>

The slope or unit rate is equal to the cost per mile for the riders trip

The slope is $3 per mile

<em>Y-intercept</em>

The y-intercept is the cost of the riders trip when the number of miles is equal to zero, also is called the initial value.

The y-intercept is $5

3 0
3 years ago
Someone please help!! :^(
sineoko [7]

Answer:

equation of the table is y=30x+60

60 degrees is what the temperature starts at

to get to 440 degrees he needs 12 minutes and 40 seconds

Step-by-step explanation:

the change in y over change in x is 90/3 which is the slope

slope is 30

if slope is 30 then 30*2+b=120 60+b=120 so b=60 and it is the y intercept

440=30x+60

380=30x

x=12 2/3

x= 12 minutes and 40 seconds

8 0
3 years ago
Plums cost $0.77 per pound Mangoes cost $1.32 per pound Write an expression that can be used to find the cost of buying p pounds
marissa [1.9K]

Answer:

The graphs below show the cost y of buying x pounds of fruit. One graph shows the cost of buying x pounds of peaches, and the other shows the cost of buying x pounds of plums.

Which kind of fruit costs more per pound? Explain.

Bananas cost less per pound than peaches or plums. Draw a line alongside the other graphs that might represent the cost y of buying x pounds of bananas.

IM Commentary

This task allows students to reason about the relative costs per pound of the two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

Solutions

Solution: Slope as Unit Rate

The graph that represents the cost of x pounds of peaches is steeper, so it must have a larger slope. The slope can be interpreted as the unit rate; in this case it tells you the cost of a single pound of fruit.

Since the slope for the peach graph is greater than the slope of the plum graph, the cost of a pound of peaches is greater than the cost of a pound of plums.

For b, students should realize that the cost per pound of bananas will be represented by a slope that is less than either of the other two, and draw a line through the origin labeled "Bananas" and lying below both of the other graphs.

Solution: Adding a scale to the graph

Students who prefer to work with specific numbers can approach this problem by sketching in a scale on the x-axis and y-axis. For example, if they decided that a pound of peaches might cost a dollar, then they might plot the point (1,1) on the line labeled "Peaches", then fill out the rest of the scale accordingly. They could then read off the cost of a pound of plums and see that it is less than for peaches.

For the second question, they could choose any price per pound b for bananas that is less than the one they read off for plums, and then draw a line from the origin through the point (b, 1), and label it "Bananas".

4 0
2 years ago
Which expression is equivalent to ^
mash [69]

Answer:

Step-by-step explanation:

lets break down 120 to see what it is divisible by and see if any of those numbers are perfect squares.

120/2=60

120/3=40

120/4=30

we can stop there because 4 is a perfect square and 30 can not be reduced any further to produce a perfect square.

do not forget there is only one x so it must stay in side the  radical.

your answer is 2sqrt(30x)

5 0
2 years ago
2. A hemispherical water tank with a volume of 2094 m will have a radius of which
Ivahew [28]
2.5 m jsjwnejdogondbsjsofj find
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