The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.
Given:
radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.
we are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.
we have dr/dt = 6 in/min and dh/dt = -4 in/min
Volume, V = πr²h
Differentiate the above expression to get:
dV/dt = 2πrh dr/dt + πr² dh/dt
SUbstitute the value we get:
dV/dt = 2π(6)(18)(6) + π(6)²(-4)
= 4069.44 - 452.16
= 3617.28 in³ per minute.
The volume is increasing at a rate of 3617.28 in³ per minute.
Area = 2πr(h+r)
Differentiate the above expression:
dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}
dA/dt = 2π {(18+6)(6) + 6(-4+6)}
= 2π(144 + 12)
= 312π
= 979.68 in² per minute.
The area is increasing at a rate of 979.68 in² per minute.
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The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.
Given:
The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.
We are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.
We have dr/dt = 6 in/min and dh/dt = -4 in/min
In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
Volume, V = πr²h
Differentiate the above expression to get:
dV/dt = 2πrh dr/dt + πr² dh/dt
Substitute the value we get:
dV/dt = 2π*6*18*6 + π*6² * -4
= 4069.44 - 452.16
= 3617.28 in³ per minute.
The volume is increasing at a rate of 3617.28 in³ per minute.
Area = 2πr(h+r)
Differentiate the above expression:
dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}
dA/dt = 2π {(18+6)(6) + 6(-4+6)}
= 2π(144 + 12)
= 312π
= 979.68 in² per minute.
The area is increasing at a rate of 979.68 in² per minute.
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Jane bought 3 shirts and returned 2 pairs of pants. Her friend Laura bought 4 shirts and 3 pairs of pants. Jane’s bill was $5 and Laura’s bill was $120. Write a systems of equations to determine the cost of a shirt, s, and the cost of a pair of pants, p.
The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120
Define System of Equation
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Jane bought 3 shirts and returned 2 pairs of pants
Laura bought 4 shirt and 3 pairs of pants.
Let, s = cost of shirt
and, p = cost of a pair of pants
The equation for Jane is
3s - 2p = $5
Here, -ve sign because Jane returned 2 pairs of pants and then bill was $5.
Now, the equation for Laura is
4s + 3p = $120
Here, +ve sign because Laura bought 4 shirt and 3 pairs of pants and then bill was $120.
So, the system of equation we get
3s - 2p = $5
4s + 3p = $120
After solving simultaneously we get the values s = 15 and p = 20.
Now, if you want to cross check then put the values of s and p in equations and it should be equal to RHS value like this,
for 1st equation,
3 * 15 - 2 * 20 ⇒ 45 - 40 = 5 (which is correct)
for 2nd equation,
4 * 15 + 3 * 20 ⇒ 60 + 60 = 120 (which is correct)
Hence, The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120.
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Jacob makes lemonade to sell at a carnival. He makes 20 cups of lemonade in 120 minutes. Working at this rate, how many cups of lemonade can Jacob make in 1 hour?
Answer:
10 cups
Step-by-step explanation:
120minutes divided into 60minutes = 2 hours
20 divided by 2 = 10 cups
If 5 dollars can be exchanged for 7.7095 units of some foreign currency, how much of that currency can be obtained for 6 dollars?
If 5 dollars can be exchanged for 7.7095 units of some foreign currency, the unit of that currency that can be obtained for 6 dollars will be
How do we calculate how much currency can be obtained for 6 dollars?5 dollars can be exchanged for 7.7095 units. This means that 1 dollar equals to:
5 dollars / 5 = 7.7095 units / 5
1 dollar = 7.7095 units / 5
1 dollar = 1.5419 units.
Now, for 6 dollars, the foreign currency that can be obtained is:
= 6 * 1.5419 units
= 9.2514 units. Therefore, 9.2514 unit of the foreign currency can be obtained for 6 dollars.
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A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after
another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. Finally, the
thief leaves the nursery with 0 plants. How many plants were originally stolen?
Answer:
28 plant were stolen------------------------------------
Calculate it from end to start.
Before guard 3 he had:
(0 + 2)*2 = 4 plantsBefore guard 2 he had:
(4 + 2)*2 = 12 plantsBefore guard 1 he had:
(12 + 2)*2 = 28 plantsThis is the number of plants stolen.
What is the common ratio of the sequence below?
2/3, 1/6, 1/24, 1/96,…
1/9
1/4
4
9
How do you simplify 24 ⋅ 2^ − 2 ?
Answer:
Step-by-step explanation:
We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:24⋅2−2=24⋅12+2=244=6
Answer:
We can use one of the properties of exponents to change the −2 into +2 by sending the base to the denominator as:
24⋅2−2= 24⋅1/2 OVER +2= 24/4= 6
Step-by-step explanation:
At the beginning of a population study, a city had 230,000 people. Each year since, the population has grown by 2.8%. Let t be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t.
Answer:
y = 0.028t + 230,000
Step-by-step explanation:
We know
t = number of years since the start of the study
y = be the city's population
Each year the population has grown by 2.8%, this is the slope
The city had 230,000 people, this is the y-intercept
2.8% = 0.028
The equation is y= mx + b
So, our equation in this case is
y = 0.028t + 230,000
If you can please give me a Brainliest, thank you, and have a good day!
Which equation could represent the situation described and how long does it take for the bacteria to reach 16,000?
The equation to represent the given situation is [tex]500(2)^x=16000[/tex] after 5 hours. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a bacteria has an initial population of 500 and is doubling every hour.
Let x be the number of hour bacteria population to reach 16,000
The bacteria reaches a population of 16,000 bacteria.
So, the equation is [tex]500(2)^x=16000[/tex]
⇒ [tex]2^x[/tex]=16000/500
⇒ [tex]2^x[/tex]=160/5
⇒ [tex]2^x=2^5[/tex]
⇒ x=5
Therefore, after 5 hours the bacteria population reaches 16,000.
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Two hikers set out from camp. the first hikes 4 miles due west then turns 40° south and hikes 1.8 miles. second hikes 4 miles to East then turns 52° north toward North in Heights 1.8 miles which hiker is farther from the camp explain
Answer:
The second hiker is farther away from the visitor center as all things being equal cos 128 < cos 140
from distance^2 = 4^2 + 1.8^2 -- 2*4*1.8 cos (angle turned).
Step-by-step explanation:
brainliest pls
Answer:
The first hiker is the farthest from camp since 140° > 128°.
Step-by-step explanation:
The journeys of both hikers can be modelled as triangles (see attachment).
Even though they hike the same distance of 4 miles plus 1.8 miles, as the angles of their turns between the two legs of their journeys are different, the final distance they are from camp is also different.
The first hiker turns 40° south so the included angle of the triangle is 140°.
The second hiker turns 52° north, so the included angle of the triangle is 128°.
As 140° > 128°, the distance between the first hiker and camp is farther than the distance between the second hiker and camp.
To prove this, use the cosine rule to find the missing length of each triangle.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Cosine Rule} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
First hiker:
[tex]\implies c^2=4^2+1.8^2-2(4)(1.8) \cos 140^{\circ}[/tex]
[tex]\implies c^2=19.24-14.4\cos 140^{\circ}[/tex]
[tex]\implies c=\sqrt{19.24-14.4\cos 140^{\circ}}[/tex]
[tex]\implies c=5.501912393[/tex]
Second hiker:
[tex]\implies c^2=4^2+1.8^2-2(4)(1.8) \cos 128^{\circ}[/tex]
[tex]\implies c^2=19.24-14.4\cos 128^{\circ}[/tex]
[tex]\implies c=\sqrt{19.24-14.4\cos 128^{\circ}}[/tex]
[tex]\implies c=5.301464443[/tex]
As 5.50 > 5.30, this proves that the first hiker is farthest from the camp.
A satellite orbiting the earth uses radar to communicate with two control stations on the earth’s surface. The satellite’s orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth’s radius is 3,963 miles, answer the following questions. Round all answers to the nearest whole number.
1. Is there a right angle in the triangle shown by connecting the center of the earth, the satellite, and Station 1? How do you know? *Assume that the line connecting the satellite and Station 1 is tangent to the earth.
The number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48135 miles
How to find the distance of separation?Let us first find the distance from Station 1 to the satellite:
Using trigonometric ratio, we have;
tan 8.7 = length of longest leg/length of shortest leg
Thus;
tan 8.7 = 3963/length of longest leg
Length of longest leg = 3963/tan8.7°
Length of longest leg = 3963/0.15302150298
Length of longest leg = 25,898 miles
Distance from Station 2 to satellite:
Using trigonometric ratio again, we have;
sin 8.7 = length of longest leg/ length of hypotenuse
sin 8.7 = 3963/length of hypotenuse
Length of hypotenuse =3963/ sin 8.7
Length of hypotenuse =3963/0.1526082024
Length of hypotenuse = 26, 200 miles
Thus, the difference is;
26200 - 3,963 = 22237 miles
Total distance will calculated as;
25898 miles + 22237 miles = 48135 miles
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The complete question is:
A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.
How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?
solve by applying the counting principle.
A car dealership has five exterior color choices, six interior color choices, and two model choices. How many different ways could you choose a car?
There are 60 different ways could you choose a car and this can be determined by using arithmetic operations.
What are arithmetic operations?
For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-") Multiplication ("×") Finding the quotient in division ("÷").
Given :
A car dealership has five exterior color choices.
A car dealership has six interior color choices.
A car dealership has two model choices.
The following steps can be used to determine the different ways could you choose a car:
Multiply 5 and 6 that is multiply five exterior color choices and six interior color choices.
= 5 * 6
Multiply the above expression by 2 which is with two model choices.
= 30 * 2
Further, simplify the above expression.
= 60
Hence, There are 60 different ways could you choose a car.
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Will give big points
Answer: 6 and 7
Step-by-step explanation: The square root of 41 is 6.4. Since you multiply it by itself, it’s the nearest square root to 41.
Need help understanding how to Solve EBF = 6x+4 and CBF = 7x-2 find EBF
The measure of angle EBF is 40 degrees
How to determine the measure of angle EBF?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
EBF = 6x + 4
CBF = 7x - 2
Also from the question, we understand that the measures of angle EBF and the measure of angle CBF are congruent
This can be represented mathematically as follows
EBF = CBF
Substitute the known values in the above equation, so, we have the following representation
6x + 4 = 7x - 2
Multiply through by 1
6x + 4 = 7x - 2
Collect the like terms
7x - 6x = 4 + 2
Evaluate the like terms
x = 6
Recall that
EBF = 6x + 4
Substitute the known values in the above equation, so, we have the following representation
EBF = 6 x 6 + 4
Evaluate
EBF = 40
Hence, the measure is 40 degrees
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Complete question
If the measures of angle EBF and the measure of angle CBF are congruent and EBF = 6x+4 and CBF = 7x-2 find EBF
how many solutions does 4(1/2x + 3) = 3x + 12 - x have?
please answer ASAP
Answer:
Infinite
Step-by-step explanation:
2x + 12 = 2x + 12
they both are equal
(d) at the 0.05 level of significance, is there evidence of a linear relationship between the number of cases delivered and the delivery time?
Yes, there is evidence that the level of significance is taken at 0.05 or 5% when the p-value is low.
Level of significance: The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the level of significance, which is set by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. It is anticipated to determine whether the outcome is statistically significant enough to reject or prove the null hypothesis wrong.
The significance level is set at 0.05 or 5%. Low p-values indicate that the observed values differ significantly from the population value that was initially hypothesized. If the p-value is as small as possible, it is said to be more significant. Additionally, if the p-value is very low, the outcome would be highly significant. However, since obtaining a p-value below 0.05 is quite uncommon, p-values less than 0.05 are typically considered significant.
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evaluate the integral by interpreting it in terms of areas. 0 36 − x2 dx −6
The value of the original integral is 42, as expected.
What must an answer about a indefinite integral of a function include?
A definite integral is an infinitesimal sum derived from a integrable function, that is, a function that exist for all value x within the range of integration.
To evaluate this integral, we can interpret it in terms of the area of a region. To do this, we can rewrite the integral as:
∫0 36 − x2 dx −6
= ∫0 36 x2 dx + ∫0 36 dx
= ∫x2 dx + ∫dx
The first integral on the right-hand side represents the area under the curve y = x^2 from x = 0 to x = 6.
The second integral on the right-hand side represents the area of the rectangle with base 6 and height 1, which is just 6.
Therefore, the original integral can be interpreted as the sum of the area under the curve y = x^2 from x = 0 to x = 6 and the area of the rectangle with base 6 and height 1. This area is equal to 36 + 6 = 42. Thus, the value of the original integral is 42.
We can also verify this result using the formula for the area under a curve:
∫x2 dx = (1/3) x3 + C
Substituting the limits of integration, we get:
∫0 6 x2 dx = (1/3) * 6^3 - (1/3) * 0^3
= (1/3) * 216
= 72
Therefore, The value of the original integral is 42, as expected.
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Describe fully the single transformation that takes shape P to shape Q.
Answer: Shape P is similar to shape Q, however, shape P, is smaller than shape Q.
A single transformation that takes shape P to shape Q is; a dilation by a scale factor of 3 with a center of dilation at .
Reasons:
The give figure shows;
The preimage figure = P
The image figure = Q
The image P is larger than the preimage Q, therefore, the figure, Q is a
dilation of the preimage P
(x₁, y₁) = A point on the preimage, P = (2, 3)
(x₂, y₂) = The corresponding point on the dilated image, Q = (4, 9)
k = The scale factor = 3
Therefore;
The center of dilation, (x₀, y₀) = (1, 0)
Therefore;
The single transformation that takes shape P to shape Q is a dilation by a scale factor of 3 with a center of dilation at (1, 0).
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Step-by-step explanation:
for each 7-subset of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, give the next largest 7-subset or indicate that the 7-subset is the last one in lexicographic order. (a) {1, 2, 3, 4, 5, 6, 7} (b) {2, 4, 5, 9, 11, 12, 13} (c) {2, 4, 5, 11, 12, 13, 14} (d) {2, 4, 5, 6, 11, 12, 14} (e) {7, 8, 10, 11, 12, 13, 14}
(a) {2, 3, 4, 5, 6, 7, 8}
(b) {2, 4, 5, 9, 11, 12, 14}
(c) No next largest 7-subset; this is the last one in lexicographic order.
(d) {2, 4, 5, 6, 11, 12, 13}
(e) No next largest 7-subset; this is the last one in lexicographic order.
What in math is a subset?If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.
Subset example: What is it?For instance, if A represents the set of natural numbers and B represents the set of all whole numbers, then B is a subset of A since the set of whole numbers contains all natural numbers. This is how we may comprehend it: Natural numbers 1, 2, 3, and so on make up the set A. B = A collection of whole numbers, such as "0, 1, 2, 3,..."
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Can someone help me with making the x the subject of the formula100 point up for grabs pls helpppp I will make brainliest
y =xa+ b
y =xa− b
y =x + 2 divided by two
Answer:
x = [tex]\frac{y-b}{a}[/tex]
Step-by-step explanation:
y = xa + b ( subtract b from both sides )
y - b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y-b}{a}[/tex] = x , that is
x = [tex]\frac{y-b}{a}[/tex]
-------------------------------------
y = xa - b ( add b to both sides )
y + b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y+b}{a}[/tex] = x , that is
x = [tex]\frac{y+b}{a}[/tex]
--------------------------------------------
assuming you mean
y = [tex]\frac{x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
2y = x + 2 ( subtract 2 from both sides )
2y - 2 = x , that is
x = 2y - 2
A line has a slope of 1 and passes through the point (–3, –13)What is its equation in slope intercept form?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is
y = x - 10.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The line has,
Slope = 1
Passes through = (-3, -13)
Now,
The equation of a line is given as,
y = mx + c
Put (-3, -13) = (x, y)
-13 = 1 x (-3) + c
-13 = -3 + c
c = -13 + 3
c = -10
Now,
The equation of the line.
y = 1x - 10
y = x - 10
Thus,
The equation of the line is
y = x - 10.
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(d)
Most of the kinetic energy of the diver is transferred to the water.
How does this affect the thermal energy of the water?
Tick (✓) one box.
The thermal energy decreases.
The thermal energy stays the same.
The thermal energy increases.
Most of the kinetic energy of the water is transferred into the water, then the thermal energy will increase. Hence, option C is correct.
What is kinetic energy?Kinetic energy is the term used in physics to describe the force that a moving item has. It is described as the amount of effort necessary to accelerate anybody with a particular mass from rest to a given velocity. Except variations in speed, the body retains the kinetic energy it gains during acceleration.
The body uses exactly the same amount of energy when slowing down from its current rate to a state of rest. Formally, kinetic energy refers to any term in a system's Lagrangian that has a derivative with respect to time.
As per the given information in the question,
When the kinetic energy of the diver is transferred into the water, the thermal energy will increase.
The entity's thermal energy grows as the average kinetic energies of its particles rise. As a result, an object's thermal energy rises as its temperature does.
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HELP PLEASEJG
Problem: What is the actual distance between two cities if it is drawn to scale of 1:3,000,000 and it is 3 cm on the map?
Answer:
distance between two cities will be 9 000 000 km
Answer:
Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km
The vertices of a cube or cuboid is suppposed to be V, side is E and surface is F, then which of the following is the relation between them? Write it.
1) V+E+F=2
2)V+E-F=2
3) V-E+F=2
4)V-E-F=2
The relation between the vertices of a cube or cuboid is V, the side is E, and the surface, F is V - E + F = 2. Option 3) is the correct answer.
What is the relationship between the vertice, face and side of a cube or cuboid?The vertice, face, and side of a cube or cuboid are related by Euler's Theorem. This theorem states that the number of faces, vertices, and edges of any polyhedron are related by Euler's formula.
Euler's formula can be stated as:
F + V = E + 2.
or
F + V - E = 2
where,
F = equal to the number of faces,
V = equal to the number of vertices
E = equal to the number of edges.
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In the figure, quadrilaterals ABHI, BCDE, and EFGH are squares. Which statement can be concluded from the fact that the area of square ABHI plus the area of square BCDE is equal to the area of square EFGH?
The statement that can be concluded from the fact that the area of square ABHI plus the area of square BCDE is equal to the area of square EFGH is of:
D. BE² + BH² = EH².
How to obtain the areas?The area of a square of side length s is given by the side length squared, as follows:
A = s².
Hence the areas of each square on the image given at the end of the answer are given as follows:
Area of ABHI = AB² = BH² = HI² = AI² (all these side lengths are equal).Area of BCDE = BC² = CD² = DE² = EB².Area of EFGH = EH² = HG² = GF² = FE².Hence the correct statement regarding the areas is given as follows:
BE² + BH² = EH².
Meaning that statement D is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
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a better understanding of how I can solve for 1/2d-3/4d+3f-2f
The simplified form of the given expression is, 1/4d + f.
What is simplified form of the expression?
To simplify an expression, create an equivalent expression without any terms that are similar.
The expression will then be rewritten using the fewest terms possible.
Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.
Consider the given expression,
1/2d - 3/4d + 3f - 2f
Here the like terms are '1/2d and 3/4d' and '3f and 2f'.
To simplify the expression,
1/4d + f
Hence, the simplified form of the given expression is, 1/4d + f.
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The maker of an automobile advertises that it takes 11 seconds to accelerate from 25 kilometers per hour to 75 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 11 seconds. Round your answer to two decimal places. 168.06 m 152.78 m 305.56 m 76.39 m 32.73 m
The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
Explain the equation of motion?motion is shift in a body's orientation or position over time. Translation is defined as movement across a line or a curve. Rotation is a motion that modifies a body's orientation.Time t = 11 sec
Initial velocity u = 25 kmph
u = (25 × 1000)/(60 × 60) = 6.9 m/s
final velocity v = 75 kmph
v = (75 × 1000)/(60 × 60) = 20.83 m/s
From the first equation of motion;
v = u + at
Put the values;
20.83 = 6.9 + 11a
20.83 - 6.9 = 13a
11a = 13.93
a = 13.93 / 11
a = 1.26 m/s²
Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
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Help. (4x + 7)°
51°
please help asap! theres a picture below to help
The coefficient and constant in the system of linear equations are identified below
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
In this question, we are given two equations to define the variables.
3x + 7y = 18 ...eq(i)
2x - 4y = 9 ..eq(ii)
In the equations above;
3 = The coefficient of x in the first equation7 = The coefficient of y in the first equation2 = The coefficient of x in the second equation-4 = The coefficient of y in the second equation18 = The constant in the first equation9 = The constant in the second equationLearn more on system of linear equation here;
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Which of the following is a factor of (x+y)3−(x3+y3)? · x2+y2+2xy · x2+y2−xy · xy2 · 3xy ·
We know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.
What is algebraic identity?An identity element, also known as a neutral element, in a binary operation on a set is a set element that, when the operation is applied, leaves each element of the set untouched.
In algebraic structures like groups and rings, this idea is applied.
The left side of the equation equals the right side of the equation in an algebraic identity.
As an illustration, (a+b)2 = a2+2ab+b2 is true for all values of and b.
So, we have the equation:
(x + y)³ - (x³ + y³)
Now, get factors as follows:
Use the algebraic identity: (a + b)³ = a³ + b³ + 3ab (a + b)
x³ + y³ + 3xy (x + y) - x³ - y³
Simplify one more step to obtain:
3xy (x + y)
Therefore, we know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.
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Correct question:
Which of the following is a factor of (x + y)3 - (x3 + y3 )
a. x² + y² + 2xy
b. x² + y² - xy
c. xy²
d. 3xy
Tom is buying a home for $144,000. He will make a 10% down payment and borrow the remaining balance for 30 years at 4.5%. His monthly mortgage payments will be $985.24. What total amount of interest will he pay over the 30 year loan?
PLEASE SHOW WORK
Answer:
Tom will pay a total of $58,064 in interest over the 30 year loan.
Step-by-step explanation:
The purchase price of the home is $144,000, and Tom will make a down payment of 10%, or $144,000 * 10/100 = $14,400.
Therefore, Tom borrows $144,000 - $14,400 = $129,600.
Next, we need to calculate the total number of payments he will make over the 30 year loan. Since the loan is for 30 years and the payments are made monthly, there will be 30 years * 12 months/year = <<30*12=360>>360 payments.
Finally, we can use the mortgage formula to calculate the total amount of interest Tom will pay over the loan:
I = P * r * t
Where:
I is the total interest
P is the principal (the amount borrowed)
r is the annual interest rate (in decimal form)
t is the number of payments
Plugging in the values, we get:
I = $129,600 * 0.045 * 360 payments
= $58,064
