The magnitude of the volume of the balloon increases at a faster rate than
the radius of the balloon.
The rate of change of the volume of the balloon with respect to radius is not constant.Reasons:
The rate at which the volume of the balloon is increasing, [tex]\dfrac{dV}{dt} = 15 \ cm^3/s[/tex]
The initial volume of the balloon, V = 30 cm³
The rate of change of the volume of the balloon with radius is given as follows;
[tex]\dfrac{\Delta V}{\Delta r}= \dfrac{V_2 - V_1}{r_2 - r_1}[/tex]
[tex]Volume \ of \ the \ balloon, \ V = \dfrac{4}{3} \cdot \pi \cdot r^3[/tex]
[tex]V = 30 + \dfrac{dV}{dt} \times t[/tex]
∴ V = 30 + 15·t
At t = 0, V = 30 cm³
Where;
[tex]r =\sqrt[3]{ \dfrac{3 \cdot V}{4 \cdot \pi} }[/tex]
When V = 30
[tex]r =\sqrt[3]{ \dfrac{3 \times 30}{4 \cdot \pi} } \approx 1.93[/tex]The radius, r ≈ 1.93 cm.
At t = 10 s., we have;
V = 30 + 15 × 10 = 180
[tex]r =\sqrt[3]{ \dfrac{3 \times 180}{4 \cdot \pi} } \approx 3.5[/tex]At t = 20 s., we have;
V = 30 + 15 × 20 = 330
[tex]r =\sqrt[3]{ \dfrac{3 \times 330}{4 \cdot \pi} } \approx 4.29[/tex]Therefore;
Between 0 s. and 10 s., we have;
[tex]\dfrac{\Delta V}{\Delta r}=\dfrac{180 - 30}{3.5-1.93} \approx 96[/tex]Rate of change of the volume of the balloon with respect to the radius of the balloon to the nearest centimeter, between 0 s and 10 s is 96 cm³/cm.
Between 10 s. and 20 s., we have;
[tex]\dfrac{\Delta V}{\Delta r}=\dfrac{330 - 180}{4.29 - 3.5} \approx 190[/tex]Between 10 s. and 20 s. the rate of change is approximately 190 cm³/cm.
Therefore;
The rate of change of the volume of the balloon with respect to radius is not constant, but increases as the volume of the balloon increases.
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Please help !!!! I need this
Answer:
xy²/5= 2×1²/5 = 2/5
...........
Answer:
0.8
Step-by-step explanation:
Find two numbers with a sum of 20 and a difference of 6
Answer:
So the answer is 13 and 7
Step-by-step explanation:
If we consider the case i.e. second-first =6
Rotate the point (-3,-4) around the origin
180 degrees. State the image of the point.
va
a) (-4,-3)
b) (-4,3)
I c) (4,-3)
d) (3,4 )
Pipe A can fill a tank in 5 hours. Pipe B can fill the same tank in 7 hours. If both pipes were open, how long would it take them to fill an empty tank?
Answer:
It would take them 6 hours to fill an empty tank.
Step-by-step explanation:
Add the amount of time it takes Pipe A and Pipe B to fill an empty tank together (5 + 7) and then divide your sum by two. You should get 12 / 2 = 6.
Hope This Helps!
Find the x- and y-intercepts.
3.
8x + 7y= 28
Answer:
dees nuts
Step-by-step explanation:
Determine whether the equation is a linear equation. If so, write the equation in standard form.
13. y + 9 = -2x3
Answer:
y=[tex]-2x^{3}[/tex]-9
Step-by-step explanation:
Which model represent the factors of 4x2-9
Step-by-step explanation:
4x²-9
4x²+6x-6x-9
4x²+6x-6x-9
2x(2x+3)-3(2x+3)
2x(2x+3)-3(2x+3)
(2-3)(2x+3)
solution
(8x-3)(2x+3)
I need the answers asap
Answer:
1. B
2. G
3. D
4. C
Step-by-step explanation:
1.
-(7x-8) = 2-5x
-7x + 8 = 2 - 5x
-2x + 8 = 2
-2x = -6
x = 3
2.
5(3+2x) = 10x-4
15 + 10x = 10x - 4
No Solution
3.
x+5 = (3x+13) / 2
x + 5 = 1.5x + 6.5
x = 1.5x + 1.5
-0.5x = 1.5
x = -3
4.
2 + 6x = 2(3x + 2) - 2
2 + 6x = 6x + 4 - 2
2 + 6x = 6x + 2
Infinite Solution
1. 6.208 + 1.6 =
how to multiply and divide decimals
[tex]\\ \sf\longmapsto 6.208+1.6[/tex]
[tex]\\ \sf\longmapsto 1.600+6.208[/tex]
[tex]\\ \sf\longmapsto 2.208[/tex]
Just count 0 s at right
the liter is the metric base unit of measurement for
Answer:
Volume
Step-by-step explanation:
Finally, the basic metric unit of volume is the liter. A liter is slightly larger than a quart. The handle of a shovel is about 1 meter.
Select the expression that is equivalent to (2x^2 +5)-5/2
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's solve :
[tex]{(2 {x}^{2} + 5) }^{ - \frac{5}{2} } [/tex][tex] \dfrac{1}{{(2 {x}^{2} + 5) }^{ \frac{5}{2} } } [/tex][tex] \dfrac{1}{ \sqrt{( 2{x}^{2} + 5) {}^{5} } } [/tex]therefore, the correct choice is :
ACan you help me please.
Step-by-step explanation:
ranges are,
-1 , -11 and 7
hope this answer helps you dear!
Answer:
R = { - 11, - 1, 7 }
Step-by-step explanation:
Substitute the values from the domain into f(x) for range
f(2) = - 2(2)² + 7 = - 2(4) + 7 = - 8 + 7 = - 1
f(- 3) = - 2(- 3)² + 7 = - 2(9) + 7 = - 18 + 7 = - 11
f(0) = - 2(0)² + 7 = - 2(0) + 7 = 0 + 7 = 7
Then
R = { - 11, - 1, 7 }
I need help plz no spam...
[tex](4 \sqrt{3} + 3 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} )[/tex]
By using formula,
[tex](a + b)(a - b) = {a}^{2} - {b}^{2} \: \: we \: get[/tex]
[tex](4 \sqrt{3} + 3 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} ) \\ = (4 \sqrt{3)}^{2} - (3 \sqrt{2} ) ^{2} \\ = (4 \sqrt{3} \times 4 \sqrt{3} ) - (3 \sqrt{2} \times 3 \sqrt{2} ) \\ = (4 \times 4 \times \sqrt{3} \times \sqrt{3} ) - (3 \times 3 \times \sqrt{2} \times \sqrt{2} ) \\ = (16 \times 3) - (9 \times 2) \\ = 48 - 18 \\ = 30[/tex]
Answer:30
The length of e rectangle is three times the width. The perimeter of the rectangle is 72 cm. Find the dimensions of the rectangle.
Answer:
Step-by-step explanation:
Let the width be w. The length is then 3w (length is 3 times its width).
The formula for the perimeter is 2l + 2w (2 times the length + 2 times the width)
So, in our case we have 2(3w) + 2w = 72
6w + 2w = 72
8w = 72 divide both sides by 8
w = 9
So the length = 3w = 3 x 9 = 27
Double check: we have l = 27 and w= 9. (2 x 27) + (2 x 9) = 54 + 18 = 72 Yay!!!
Graph the following
y=3-4x
Answer correct and tell me the points to graph it on or show a picture of the graph, and ill give you the brainiest.
Answer:
Step-by-step explanation:
y = -4x +3
Y-intercept = 3
The slope is negative: - 4/1
4 down ( from y = 3) and one to the right or
4 up (from y=3) and 1 to the left.
(You only need 2 points to trace a line)
PLEASE HELP ME PLEASE I WILL GIVE U A LOT OF POINTS
Charlie's Computer Company charges $0.65 per pound to ship computers. Part A: Write an equation to determine the total cost, c, to ship p pounds of computers. Use your equation to determine the cost of shipping 2 pounds of computers. (6 points) Part B: If the company reduces the cost to ship computers by $0.05 per pound, write an equation to determine the total cost, c, to ship p pounds of computers with the reduced cost. (4 points)
Answer:
Part A:
Equation: 0.65p=c
Answer: $1.30
Part B:
Equation: 0.05p=c
Answer: $0.10, or ten cents (if two pounds of computers where shipped at this reduced price)
Step-by-step explanation:
To find the total cost, first find the elements you will need. We know that we need to equal c, the cost, and we know that the pounds times 65 cents equals the cost.
0.65p=c
Now, to solve, plug in the amount of pounds.
0.65(2)=c
1.3=c
So the cost of shipping two pounds of computers is $1.30.
Now, to solve part b, we do the same as what we did in part a, except this time it only costs five cents per pound.
Make the equation.
0.05p=c
Also, at the top I put the extra, if two pounds were shipped at the reduced price just in case. But for the explantion to it, just plug to into the equation, then find the answer.
Part A: The equation for the total cost, c, to deliver p pounds is:
c = 0.65p.
The cost for shipping 2 pounds is $1.30.
Part B: The equation, after the reduction of $0.05 in the shipping of per pound is:
c = 0.6p.
What are equations?Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.
How to solve the question?In the question, we are informed that Charlie's Computer Company charges $0.65 per pound to ship computers.
Part A:-
We are asked to write an equation to determine the total cost, c, to ship p pounds of computers.
We know that the total cost equation is designed as:
Total cost = fixed cost + (per unit cost)*(number of units).
Thus, the required equation is:
c = 0 + 0.65p, {Since c is the total cost, the fixed cost is 0, the quantity of computers shipped is p pounds, and per pound cost of shipping is $0.65}
or, c = 0.65p.
The cost for shipping 2 pounds, can be calculated by substituting p = 2 in the above equation.
Thus, c = 0.65*2 = 1.30.
Thus, the cost of shipping 2 pounds is $1.30.
Part B:-
We are asked to write an equation for the total cost, c, to ship p pounds of computers, when the company reduces the cost to ship computers by $0.05 per pound.
Now, the unit cost of shipping one pound of computers is $0.65 - $0.05 = $0.60.
We know that the total cost equation is designed as:
Total cost = fixed cost + (per unit cost)*(number of units).
Thus, the required equation is:
c = 0 + 0.60p, {Since c is the total cost, the fixed cost is 0, the quantity of computers shipped is p pounds, and per pound cost of shipping is $0.60}
or, c = 0.60p.
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Solve: (i) 3/x-1 + 1/x-3 = 4/x-2.
Answer:
[tex]\longrightarrow\sf{ \dfrac{3}{x - 1} + \dfrac{1}{x - 3} = \dfrac{4}{x - 2}}[/tex]
[tex]\\ \longrightarrow\sf{ \dfrac{3(x - 3) + 1(x - 1)}{(x - 1) (x - 3)} = \dfrac{4}{x - 2}}[/tex]
[tex]\\ \longrightarrow\sf{ \dfrac{3x - 9 + x - 1}{x(x - 3) - 1(x - 3)} = \dfrac{4}{x - 2}}[/tex]
[tex]\\ \longrightarrow\sf{ \dfrac{3x + x - 9 - 1}{{x}^{2} - 3x - x + 3} = \dfrac{4}{x - 2}}[/tex]
[tex]\\ \longrightarrow\sf{ \dfrac{4x - 10}{{x}^{2} - 4x + 3} = \dfrac{4}{x - 2}}[/tex]
[tex]\\ \longrightarrow\sf{ (4x - 10) (x - 2) = 4({x}^{2} - 4x + 3)}[/tex]
[tex]\\ \longrightarrow\sf{4x ( x -2 ) - 10 (x - 2) = 4{x}^{2} - 16x + 12}[/tex]
[tex]\\ \longrightarrow\sf{4{x}^{2} - 8x - 10x + 20 = 4{x}^{2} - 16x + 12}[/tex]
4x² get cancelled on both sides .
[tex]\\ \longrightarrow\sf{ - 18x + 20 = - 16x + 12}[/tex]
[tex]\\ \longrightarrow\sf{ - 18x + 16x = 12 - 20}[/tex]
[tex]\\ \longrightarrow\sf{ -2x = - 8}[/tex]
[tex]\\ \longrightarrow\sf{ x = \dfrac{- 8}{-2}}[/tex]
[tex]\\ \longrightarrow\sf{ x = 4}[/tex]
Jack borrows $2,700 at a rate of 8.2% per year. How much simple interest will he owe if it takes 3 months to repay the loan? Round to the nearest cent.
Answer: $55.35
Step-by-step explanation:
The simple interest on $2700 at a rate of 8.2% per year for 3 months will be $55.35.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Given that,
Jack borrows $2,700 at a rate of 8.2% per year.
Principle amount P = 2700
Rate of interest = 8.2% per year
Rate of interest per month ⇒ 8.2/12 = 0.683%
The simple interest for the T time period is given by,
Interest = PRT/100
Interest = (2700 × 0.683 × 3)/100 = $55.35
Hence "The simple interest on $2700 at a rate of 8.2% per year for 3 months will be $55.35".
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22. What is the median of these
numbers?
2, 7, 3, 6, 9, 1, 4
Answer:
the median in that numbers is 6
Step-by-step explanation
their are total 7 number which is odd
so the formula is
median = ( n + 1 /2 )^th term
now,
→ ( 7 + 1 / 2 )
→ 8/2
→ 4th term
therefore, 4th term is the median and 4th term is 6 itself.
hope this answer helps you dear...take care and may u have a great day ahead!
Find the solution of the system of equation 2x+8y=4
6x-y=13
Can someone help me with this please
Answer:
86°
Step-by-step explanation:
40 + x + 54 = 180
-> Move 40 and 54 to the other side by subtracting
x = 180-40-54
x = 86
if you jogged 3.5 miles in 3 hours, how many miles do you jog in 5 hours?
Answer:
How Long Does It Take to Run 5 Miles? Answering this question is extremely difficult since each runner is different. But the average time to run 5 miles is 50 minutes – that's 10 minutes per mile. If you're just starting out as a new runner, running 5 miles might take you an hour – or more.
Step-by-step explanation:
Answer:
~5.8mi
Step-by-step explanation:
3.5 3h
X 5h
X=(3.5×5)÷3=~5.8
In the figure BD||EG and the measure of angleACB=35 degree. What is the measure of angle GFH
A 35. B 55. C 135. D 145
Answer:
55
Step-by-step explanation:
...............................
If i have an 86% in my math class and i got 2.8/10 on an assignment how much would my grade drop
Square ABCD has points A(5, 10) and B(-4, 3). What is the slope of line segment BC?
Given the square ABCD with points A(5, 10) and B(-4, 3), the slope of the line segment BC is 7/9
The formula for calculating the slope of a line is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the coordinate point A(5, 10) and B(-4, 3)
Substituting the given coordinate into the formula for slope
[tex]m=\frac{3-10}{-4-5}\\m=\frac{-7}{-9}\\m=\frac{7}{9}[/tex]
Hence the slope of the line segment BC is 7/9
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Fill in the missing numbers to complete the pattern:
1.52, 1.77,
2.27,
2.77
Submit
Answer:
1.52,1.77,2.02,2.27,2.52+2.77
Step-by-step explanation:
The pattern is that it increases by 0.25
Hope this helps
Have a nice day! :D
Mark brainliest if possible
Sarah is going on a trip. She drives for 2 hours and 20 minutes, rests for 25 minutes and drives for another 2 hours 40 minutes. What is her total travel time in hours and minutes
Help needed! (will mark as brainliest)
Answer:
d. 2x-5y=-5
Step-by-step explanation:
I checked my answers with the screenshots.
The standard form of the graph equation is as follows:
-2x + 5y = 5The standard form equation is represented as follows;
Standard form equation:Ax + By = Cwhere A, B and C are constant. x and y are variables.
using y = mx + b
where
m = slope = 2 / 5
b = y-intercept
Therefore,
1 = 2 / 5(0) + b
b = 1
Therefore,
y = 2 / 5 x + 1
In standard form, it will be as follows:
y - 2 / 5 x = 15y - 2x = 5-2x + 5y = 5learn more on standard form equation : https://brainly.com/question/11255686
Which statement best describes a scatter plot
Answer:
a scatter plot shows how strongly two variables are related.
a scatterplot, also known as scatter graph is a graphic representation of the relationship between two numerical variables. One of the variables is represented on the horizontal axis (x-axis) while the other is represented on the vertical axis (y-axis).