The rate of change of an edge of the cube is 0.074 m/min.
What is the rate of change of volume of cube?The rate at which the volume of the cube changes is calculated as follows;
dv/dt = 2 m³/min
where;
v is the volume of the cubeThe length of edge of the cube will be denoted with a, and it is related to the volume of cube in the following equation.
v = a³
a = v^¹/₃
where;
a is the length of the edgeThe change in the edge with volume;
da/dv = 1/3 (1/v)^2/3
The change in edge of the cube with time is given as;
da/dt = da/dv . dv/dt
da/dt = 1/3 (1/v)^2/3 x 2 m³/min
da/dt = 1/3 (1/27)^2/3 /m² x 2 m³/min
da/dt = 1/27 x 2 m/min
da/dt = 2/27 m/min
da/dt = 0.074 m/min
Thus, the rate at which the edge of the cube changes with time is smaller compared to the volume.
Learn more about rate of change of volume here: https://brainly.com/question/22716418
#SPJ1
SOLVE ASAP PLEASE!!!!
===================================
Explanation:
Recall that [tex]i = \sqrt{-1}[/tex]
Square both sides to get [tex]i^2 = -1[/tex]
So,
[tex](i\sqrt{5})^2 = i^2*(\sqrt{5})^2 = -1*5 = -5[/tex]
Divide -2 1/8÷6 4/5 . Explain each step you used to find the quotient.
Answer: -85/272
Step-by-step explanation:
-17/8 divided by 34/5
then opposite reciprical
-17/8 x 5/34
-85/272 (check if you can simplify)
11.) You have $49.99 to spend for a pair of jeans. The sales tax is 7%. What is the
most the jeans can cost?
A) $46.49
B) $46.72
C) $29.41
D) $45.16
Answer:
B) $46.72
Step-by-step explanation:
Let j = cost of the jeans
j * 1.07 is the cost of the jeans with tax
j * 1.07 = 49.99
Divide each side by 1.07
j * 1.07 /1.07 = 49.99 / 1.07
j =46.72
The jeans can cost no more than 46.72
Answer:
B) $46.72
Step-by-step explanation:
The problem can be expressed as an equation you solve for "y"
y + y * 0.07 = 49.99
We factor out the "y" from the equation and we get
y * (1 + 0.07) = 49.99
Which is the same as
y * 1.07 = 49.99
We can then divide by 1.07 both sides
y = 49.99 / 1.07
Which yields
y = 46.719
If rounding is allowed the answer is B, otherwise the answer is A. I'll go with the rounded one
A construction crew is lengthening a road. The road started with a length of 53 miles, and the crew is adding 4 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked.
Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 36 days.
Answer:
L = 4D + 53
After 36 days of work, the road will be 197 miles long.
Step-by-step explanation:
This question requests that an equation is found to represent the relationship between the length of a road and the days that the workers spend working on the road.
We are given that the road is 53 miles long prior to the work done by the construction crew. This means that this will be added in addition to what we will find.
L represents the length of the road after D days. Since the road is lengthened by 4 miles each day, this could be represented by 4 * D, or simply 4D.
Therefore, the equation we find can be written as L = 4D + 53.
Since we need to find how many miles the road will be after 36 days of work, substitute 36 days as D and solve for L:
L = 4(36) + 53
L = 144 + 53
L = 197
Therefore, the road will be 197 miles long after 36 days of construction.
Triangle ABC has vertices A(-4, 1), B(-1, 1), and C(-1, 3) as shown. Reflect triangle ABC twice, first across the y-axis, then across the x-axis. Graph both reflections on one coordinate plane. Then rotate triangle ABC 180° about the origin. Graph the rotation.
As per the given question;
The coordinates of the original triangle ABC with vertices is ;
A(-4, 1), B(-1, 1), and C(-1, 3)
For the first reflection along y-axis, the coordinates of y will remain same and x will reverse to positive.
Y-axis reflection: A(4, 1), B(1, 1), and C(1, 3)
Now, the triangle is again reflected along x-axis.
Thus, for the first reflection along x-axis, the coordinates of x will remain same and y will reverse to positive.
x-axis reflection: A(4, -1), B(1, -1), and C(1, -3)
Rotation: The circular motion of an item around a center is referred to as rotation.
The rotation of triangle ABC 180° about the origin.
Rule for Rotation 180° (Clockwise and Counterclockwise);
(x, y) ----- > (-x, -y)
A(4, -1) ------> A(-4, 1)
B(1, -1) ------> B(-1, 1)
C(1, -3) ------> C(-1, 3)
Rotation 180° = A(-4, 1), B(-1, 1) and C(-1, 3)
Thus, the result of the coordinates of the new triangle with vertices are found.
To know more about reflection, here
https://brainly.com/question/4070544
#SPJ9
Solve for n. −2(n − 3.5) > 15 n > −4 n < −4 n > 4 n < 4
Answer: N > -4
Step-by-step explanation:
Cuz It's Right
The solution for inequality is n < -4.
The given inequality is −2(n − 3.5) > 15
An inequality will have the sign < , > , ≥ or ≤ instead of an equality in an equation. That is, an inequality compares two quantities on either sides of the inequality sign.
We are asked to solve the inequality −2(n − 3.5) > 15. That is, to find the possible values for n.
−2(n − 3.5) > 15
Dividing throughout by 2,
-(n - 3.5) > 15/2
⇒ -n +3.5 > 7.5
Subtracting 3.5 from both sides,
⇒ -n > 7.5 - 3.5
⇒ -n > 4
Multiply -1 on both sides of the inequality and the inequality will be reversed,
⇒ n < -4 is the solution for n.
The solution is the values of n less than -4.
Learn more about solving inequalities at https://brainly.com/question/9774970
#SPJ1
line m can be represented by the equation 3x-6y=18. Write an equation of the line perpendicular to line m that passes through the point (-4,1)
Step-by-step explanation:
the perpendicular line can be represented by bx-ay+k=0 ,So the second step Is Written
since the line passes through point (-4,1) ,the value of x and y is Substitute as written in answer
Answer:
y=-2x-7
Step-by-step explanation:
3x-6y=18 also equals 3x-18=6y
divide both sides by 3 to get x-6=2y or y=x/2-3 as same line then, to find inverse switch x and y, x=(y/2)=3 and solve for y, y-6=2x, -y=2x+6 is the inverse then to make it pass thru (-4,1) change b value, y=-2x-7
If f(a)= -4 what is the value of a
Suppose that you decide to buy a car for $27,635, including taxes and license fees. you saved $5000 for a down payment and can get a three-year car loan at 6.36%. Find the monthly payment and the total interest for the loan
the monthly payment of $ 668.75 will be paid for the loan for the car.
Total payment for the car = $ 27,635
Money for down payment = $ 5000
Interest for 3 year loan = 6.36 %
Amount on which this interest will be applied = $ 27,635 - $ 5000
Amount = $ 22,635
Interest = 6.36 % of $ 22,635
Interest = 6.36 / 100 × $ 22,635
Interest = 1440 (approx.)
Total amount of loan = $ 22,635 + $ 1440
= $ 24075
Number of months = 3 × 12 = 36 months
So, monthly payment = $ 24075 / 36
= $ 668.75
Therefore, we get that, the monthly payment of $ 668.75 will be paid for the loan for the car.
Learn more about payment here:
https://brainly.com/question/25793394
#SPJ1
Find the common ratio 2,2/3,2/9,2/27,2/81
Solve the equation for y. Then find the value of y for each value of x. y + 2x = 5; x = -2, 0, 4
please help me
Answer: y=9 when x=-2
y=5 when x=0
y=-3 when x=4
Step-by-step explanation:
y+2x=5
y=5-2x
y=5-2(-2)
y=5-(-4)
y=5+4
y=9 when x=-2
y=5-2(0)
y=5 when x=0
y=5-2(4)
y=5-8
y=-3 when x=4
which formula defines the sequence f(1)=2, f(2)=4, f(3)=8, f(4)=16, f(5)=32
please help !!
Ans: The formula that defines the sequence is Tn = 4n - 2
To learn more about Formulas refer:
https://brainly.com/question/21140562
#SPJ2
Solve the following problems using special product. SHOW YOUR SOLUTION.
2.) What is the area of a rectangle if its length measures (10y+4w)cm and its with measures (10y-4w)cm.
[tex]a = l \times w \\ a = (10y + 4w)(10y - 4w) \\ a = 10y(10y - 4w) + 4w(10y - 4w) \\ a = 100 {y}^{2} - 40wy + 40wy - 16 {w}^{2} \\ a = 100 {y}^{2} - 16 {w}^{2} [/tex]
ATTACHED IS THE SOLUTION
Write as
a Ratio : 18:11
Answer:
This is all ready written as a ratio. You could also write it as 11:18, but other than that, your good!
Step-by-step explanation:
Hope it helps! =D
Use an integer or a fraction to describe the slope of a line perpendicular to this line please!!!
A line with slope m then the slope of a line perpendicular to it is ;M = -2/3
What is the slope of a straight line?A straight line of the form y = mx + c has its slope as 'm'
It is constant for a line. The more the slope is, the steeper the line is.
Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.
To find the slope m of the given line using the slope formula
[tex]m = \dfrac{y-q}{x-p}[/tex]
with (p, q ) = (1, 0) and (x₂, y₂ ) = (x, y) 2 points on the line
m = (3 -0)/(3-1)
m = 3/2
ALso it is given that a line with slope m then the slope of a line perpendicular to it is ;
M = -2/3
Learn more about slope here:
https://brainly.com/question/2503591
#SPJ1
Using the graph as your guide, complete the following statement.The discriminant of the function is _____.
A.zero
B.positive
C.negative
The discriminant of the function will be negative.
Option C is true.
What is mean by Discriminant?
The discriminant of the function describe the roots of the function.
Which is defined as for a quadratic equation ax² + bx + c = 0;
D = b² - 4ac
Given that;
The graph of the function is shown in attached figure.
Now,
When the graph has any x - intercepts then the function has a real roots, so the discriminant must be positive.
Here, From the given graph of the function,
We have the function which have no any x - intercept, that is do not cross the x - axis at any point.
Hence, The graph of the function has no real roots.
Thus, We can say that;
The discriminant must be negative.
Therefore, The discriminant of the function is negative.
Learn more about the discriminant visit:
https://brainly.com/question/24730520
#SPJ1
Kylie went into a grocery store and bought 3 apples and 4 bananas, costing a total of
$6.50. Lily went into the same grocery store and bought 10 apples and , bananas,
costing a total of $17.50. Write a system of equations that could be used to determine
the price of each apple and the price of each banana. Define the variables that you
use
to write the system.
Answer:
0.87 cent
if i did this right.
Step-by-step explanation:
17.50 divided by 2 = 8.75
8.75 divided by 10 = 0.87
Four fifths of the product of x² and y
Answer:x^2*y/(4/5)
Step-by-step explanation:
That's the equation. Your question is the word form.
10 oranges and 20 grapefruits weigh 35 pounds total. 16 oranges and 10grapefruits weigh 23 pounds total. How much would 13 oranges and 15grapefruits weigh?A 28 poundsB 29 poundsC 30 poundsD 58 pounds20 Illuminate Education, Inc.
First, we will find the weight of each oranges and grape fruit
Let x be the unit weight of orange
Let y be the unit weight of grape fruit
If "10 oranges and 20 grapefruits weigh 35 pounds total"
Then this implies;
10x + 20 y = 35 -----------------(1)
And
If " 16 oranges and 10 grapefruits weigh 23 pounds total"
This implies;
16x + 10y = 23 ---------------------(2)
We can solve the two equations simultaneously.
Using elimination method;
we eliminate y and to do that, the y variables in the two equations must be same, Hence we can achieve that by multiply equation (1) by 10 and then multiply equation (2) by 20
100x + 200y = 350 ----------------------------(3)
320x + 200y = 460 ------------------------------(4)
subtract equation (3) from equation (4)
220x = 110
divide both-side of the equation by 220
x = 0.5
substitute x=0.5 into equation(1) and then solve for y
10(0.5) + 20y = 35
5 + 20y = 35
subtract 20 from both-side of the equation
20y = 35 - 5
20y = 30
divide both-side of the equation by 20
y = 1.5
"13 oranges and 15 grape fruits" = 13 x + 15y
substituting x = 0.5 and y= 1.5 in the above;
13(0.5) + 15(1.5)
=6.5 + 22.5
=29
Hence;
13 oranges and 15 grapefruits will weigh 29 pounds
Which list orders the numbers from least to greatest?
O√13, 2.1, 5.4, √/17, T
OT, 3.2, 6.3, √/17, √20
√23, 2.6, 1.3, √30, π
T, √15, 4.1, 4. 85, √30 savvas
The list which orders the numbers from least to greatest is π, √15, 4.1, 4. 85, √30.
To find the list which orders the numbers from smallest to largest we need to find the values of the respective numbers,
In the first list, we have the numbers √13, 2.1, 5.4, √/17, π. The value of √13 = 3.6 and the next term is 2.1. As 2.1 < 3.6, the list does not arrange numbers in increasing order.
In the second list, we have the numbers π, 3.2, 6.3, √17, √20. The value of π is 3.14 and the next terms are 3.2 and 6.3 which are more than the former. But the value of √17 is 4.1 which is less than the previous number 6.3.
In the third list,√23, 2.6, 1.3, √30, π the numbers are not arranged in increasing order as √23's value is 4.8 more than the second number.
In the fourth list, π,√15, 4.1, 4. 85, √30 the numbers are arranged in increasing order when calculated. The value of π is 3.1, of √15 is 3.8, then there are 4.1 and 4.85, and at last, is √30 whose value is 5.5.
Hence, π <√15 < 4.1 < 4. 85 <√30 is the list in the increasing order.
To know more about order of numbers visit:
https://brainly.com/question/19905626
#SPJ13
FACTOR:
b(a+1)^2 - 5(a+1)
Answer:(a+1) (ba+b−5)
Step-by-step explanation:
The length of a rectangle is 19 feet longer than the width. If the perimeter is 46 feet, write an equation for this scenario where "x" represents the width.
*
Perimeter formula: 2l+2w=P
Make sure your final equation is simplified
If the length of a rectangle is 19 feet longer than the width. If the perimeter is 46 feet, The equation for this scenario where "x" represents the width is 2x + 2 (x +19 ) = 46 and the width is 2 feet.
WidthGiven data :
Length of a rectangle = 19 feet
Perimeter = 46 feet
Perimeter formula: 2l+2w=P
Let x represent the width
Hence,
2x + 2 (x +19 ) = 46
2x + 2 x +38 = 46
Collect like terms
4x = 46 -38
4x = 8
Divide both side by 4x
x = 8/4
x = 2 feet
Therefore the equation that was used to find the width is 2x + 2 (x +19 ) = 46 while the width is 2 feet.
Learn more about width here: https://brainly.com/question/25855344
#SPJ1
Error Analysis - Describe the error in a sentence or two. Then, solve the problem
correctly.
13. If f(x)=2x-1, then find the x-value so that f(x) = 21.
A f(21) = 2(21)-1
B
f(21) = 42 - 1
C
f(21) = 41
The error was in line A, B, or C
The correct answer is [ans]
Answer:
The error is in line A. f(x), not x, is equal to 21.
f(x) = 2x - 1 = 21
2x = 20, so x = 10.
Consider the function that is represented by the equation y = 3x + 2. If we had an x-value of 3, what would the corresponding y-value be?
When we have an x-value of 3 the corresponding y-value in the equation is 11.
How to compute the equation?It should be noted that an equation simply shows the relationship between the expression that's illustrated.
In this case, the function that is represented by the equation function that is represented by the equation y = 3x + 2. and we have an x-value of 3,
Therefore, the value of y will be:
y = 3x + 2.
y = 3(3) + 2
y = 9 + 2
y = 11
Learn more about equations on;
brainly.com/question/2972832
#SPJ1
What is the answer to the math question 4+8(9+10)
Answer:
31
Step-by-step explanation:
9+10
19
4+8
12
19+12= 31
find the coordinates
Answer:
C (50, - 40 )
Step-by-step explanation:
C is the midpoint of AB
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (0, - 80 ) and (x₂, y₂ ) = B (100, 0 ) , then
C = ( [tex]\frac{0+100}{2}[/tex] , [tex]\frac{-80+0}{2}[/tex] ) = ( [tex]\frac{100}{2}[/tex] , [tex]\frac{-80}{2}[/tex] ) = (50, - 40 )
500 divided by 2/3 = 500 x _ = _ feet
Answer:
500 divided by 2/3 = 500 * 3/2= 750
Step-by-step explanation:
During their family vacation, marcus took 18 photos on his cell phone. the ratio of the number of photos marcus took to the number of photos his sister maribel took is 3 to 4. how many photos did maribel take?
Given,
No. of photos Marcus took on his cell phone = 18
Ratio of photos took by Marcus and Maribel = 3:4
Let the no. of photos took by Maribel be [tex]x[/tex].
∴ [tex]\frac{18}{x} = \frac{3}{4}[/tex]
⇒[tex]3x = 72[/tex]
⇒ [tex]x = \frac{72}{3} = 24[/tex]
Hence, Maribel took 24 photos.
View more https://brainly.com/question/26974513
#SPJ4
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x − 2)?
A) The graph of y = f(x) will shift left 2 units.
B)The graph of y = f(x) will shift right 2 units.
C) The graph of y = f(x) will shift up 2 units.
D) The graph of y = f(x) will shift down 2 units.
We have a horizontal translation of 2 units to the right, so the correct option is B.
"The graph of y = f(x) will shift right 2 units."
Which effect will have it on the graph?
For any function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.
if N < 0, the translation is to the right.
In this case we have the function written as:
y = f(x - 2)
So we have N = -2, which means that we have a translation of 2 units to the right.
Then the correct option is B.
Learn more about translations:
https://brainly.com/question/24850937
#SPJ1
Sophie has
1
2
cup of chocolate which can make
1
3
of a S’more recipe. How many cups of chocolate are needed to make one whole S’more recipe? EXTRA POINTS FOR A CORRECT ANSWER
Answer:
1 1/2 cups of chocolate
Step-by-step explanation:
Sophie has
1/2
cup of chocolate which can make
1/3
of a S’more recipe. How many cups of chocolate are needed to make one whole S’more recipe? EXTRA POINTS FOR A CORRECT ANSWER
1 1/2 cups of chocolate because 1/3 takes 3 times to get a whole so 1/2x3=
1 1/2