Answers
Answer:
[tex]\frac{9x^{2}}{y^{2}}[/tex]
Step-by-step explanation:
First you need to do what is inside the parenthesis
Dividing by a variable with the same base means the powers subtract so if we do this for x we get.
[tex]\frac{x^{\frac{1}{2}}}{x^{-\frac{1}{2}}}=x^{\frac{1}{2}-(-\frac{1}{2})}=x^{1}=x[/tex]
That brings us to
[tex](\frac{3xy^{-\frac{1}{2}}}{y^{-\frac{1}{2}}})^2[/tex]
Then we need to do a similar process for the y variable.
[tex]\frac{y^{-\frac{1}{2}}}{y^{\frac{1}{2}}}=y^{-\frac{1}{2}-(\frac{1}{2})}=y^{-1}=\frac{1}{y}[/tex]
Which brings us to
[tex](\frac{3x}{y})^2[/tex]
From here we just need to square the top and the bottom of the fraction which brings us back to our final answer with
[tex]\frac{9x^2}{y^2}[/tex]
Answer:
[tex]\dfrac{9x^2}{y^2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(\dfrac{3x^{\frac{1}{2}}y^{-\frac{1}{2}}}{x^{-\frac{1}{2}}y^{\frac{1}{2}}} \right)^2[/tex]
Separate the variables inside the parentheses:
[tex]\implies \left( 3 \cdot \dfrac{x^{\frac{1}{2}}}{x^{-\frac{1}{2}}} \cdot \dfrac{y^{-\frac{1}{2}}}{y^{\frac{1}{2}}}\right)^2[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \left( 3 \cdot x^{(\frac{1}{2}-(-\frac{1}{2}))} \cdot y^{(-\frac{1}{2}-\frac{1}{2})}\right)^2[/tex]
[tex]\implies \left( 3 \cdot x^{1} \cdot y^{-1}\right)^2[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^2 \cdot x^{(1 \cdot 2)} \cdot y^{(-1 \cdot 2)}[/tex]
[tex]\implies 9x^2y^{-2}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{9x^2}{y^2}[/tex]
Learn more about exponent laws here:
https://brainly.com/question/28515230
https://brainly.com/question/28211147
Related Questions
b^2=48, how do you answer a question like this? (also the words have nothing to do with the equation, i'm just confused)
Answers
The solution of the equation b² = 48 is b = 4√3
How to solve equation?The equation can be solved as follows;
b² = 48
Therefore, we are to find the value of b in the equation.
The value of b comes with a square sign, so we have to remove the square to make b stand alone in the equation.
By removing the square sign we have to square root both sides.
Hence,
b² = 48
square root both sides of the equation
b² = 48
√b² = √48
Therefore,
b = √16 × 3
b = 4√3
learn more on equation here: https://brainly.com/question/1333242
#SPJ1
Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
m arcQS
Answers
Answer:
m arcRP = 125°
m arcQS = 125°
m arcSP = 55°
m arcQR = 55°
Step-by-step explanation:
An arc is the curve between two points on the circumference of a circle.
An arc measure equals its corresponding central angle measure.
Vertical Angles Theorem: When two straight lines intersect, the opposite vertical angles are congruent.
Angles on a Straight Line Theorem: The sum of angles formed on a straight line is equal to 180°.
Arc RPAs m∠ROP = 125°
Therefore, m arcRP = 125°
Given the measure of angle ROP is 125°, and an arc measure equals its corresponding central angle measure, the measure of arc RP is 125°.
Arc QSUsing the Vertical Angles Theorem:
⇒ m∠QOS = 125°
Therefore, m arcQS = 125°
Using the Vertical Angles Theorem, the measure of angle QOS is equal to the measure of angle ROP, so the measure of angle QOS is 125°. As an arc measure equals its corresponding central angle measure, the measure of arc QS is 125°.
Arc SPUsing the Angles on a Straight Line Theorem:
⇒ m∠SOP = 180° - 125° = 55°
Therefore, m arcSP = 55°
Using the Angles on a Straight Line Theorem, the measure of angle SOP is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc SP is 55°.
Arc QRUsing the Angles on a Straight Line Theorem:
⇒ m∠QOR = 180° - 125° = 55°
Therefore, m arcQR = 55°
Using the Angles on a Straight Line Theorem, the measure of angle QOR is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc QR is 55°.
Please help me. Thank you!
Answers
Only height, because when you have an expression that relies only on multiplication (not addition or subtraction), we'll say:
cb = a
Tripling either c or b will also triple a. For example:
(8)(3) = 24
(8 + 8 + 8)(3) = 24(3)
(24)(3) = 24(3)
This will be true even if you multiply c by any other number.
So, in the expression v = πr²h, any term except r can be tripled with the result of tripling v. We exclude r because r has an exponent, which means tripling r will more than triple v.
according to a survey of adults, 64% have money in a regular savings account. if we plan on surveying 50 randomly selected adults, find the mean number of adults who would have regular savings accounts.
Answers
By using Binomial probability distribution, the mean number of adults who would have bank savings accounts is 32.
For every survey, there are only two possible outcomes.
First- they have bank savings accounts,
second- they do not.
So, by using the binomial probability distribution we can solve this problem.
Probability of exactly Y successes in ‘n’ repeated trials, with ‘p’ probability.
Probability = p
Successes repeated = n times
The value of the binomial distribution is:
E(Y) = n x p
In this problem, we have that:
p = 0.64
If we were to survey among 50 randomly selected adults, the mean number of adults who would have bank savings accounts is,
E(Y) when, n = 50
So,
E(Y)= n x p
= 50 x 0.64
= 32
Hence ,our required answer is 32 adults who would have bank savings accounts
To learn more about Binomial probability distribution, visit here: https://brainly.com/question/9325204
#SPJ4
If f(x) = x² + 5, then what is the remainder when f(x) is divided by x + 5?
Answers
Step-by-step explanation:
you can ask questions for clarification
Answer:
3
Please refer to the photo below:
if there are 36 apples and 6 bananas for a fruit basket, fill out all the possible ratios of apples to banana that could be made
Answers
36:6
30:5
24:4
18:3
12:2
6:1
EXPLANATION
For every 6 apples there is 1 banana. You can use this information to use your multiples of 6 starting from 36 going down to 6 changing banana side by 1 each time.
Write as fraction
4. 6.025
Answers
Answer: In simplest form it would be 6 1/40
Step-by-step explanation:
[tex] \frac{241}{40} [/tex]
but in mixed number
[tex]6\frac{1}{4} [/tex]
a cell phone battery is rated at 3.85 v and can store 10.78 watt-hours of energy. (a) how much average current can it deliver over a period of 3 hours if it is fully discharged at the end of that time? (b) how much average power is delivered in part (a)? (c) what is the ampere-hour rating of the battery?
Answers
The 10.78 watt–hour battery with a voltage rating of 3.85 V gives;
(a) The average current delivered in 3 hours is approximately 0.93 A
(b) The average power delivered at 0.93–A is approximately 3.593 watts
(c) The ampere hour rating of the battery is 2.8 Ah
What is the relationship between power and energy?Power is the rate at which energy is given out or expended.
The rating of the phone battery = 3.85–VThe power stored in the battery = 10.78 watt–hoursRequired;
(a) The amount of average current that can be delivered in 3 hours
Solution;
The power in the battery is given by the equation;
P = I²•R = I•V
10.78 watt–hour = 10.78 J/s × 60 × 60 s = 38,808 J
In 3 hours, the energy per second, which is the power is given by the equation;
P = 38,808 J/(3×60×60 s) ≈ 3.593 watts
I = P/V
Therefore;
I = 3.593 watts/(3.85 V) ≈ 0.93 A
The average current it can discharge in 3 hours is approximately 0.93 A(b) The average power delivered is given by the equation;
P = Energy/Time
Therefore;
P = 38,808 J/(3×60×60 s) ≈ 3.593 watts(c) An equation that can be used to find the ampere hour, Ah is as follows;
Ah = Watt hour ÷ Voltage
The ampere hour rating of the battery is therefore;
Ah = 10.78 watt–hour ÷ 3.85 V = 2.8 AhLearn more about electric power and energy here:
https://brainly.com/question/15296808
#SPJ1
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Use the Pythagorean theorem to solve for c using the lesser two sides.
The answer is A.
the given family of functions is the general solution of the differential equation on the indicated interval. find a member of the family that is a solution of the initial-value problem. y
Answers
the given family of functions is the general solution of the differential equation on the indicated interval y=[tex]7/2e^{x} -7/2e^{-x}[/tex]
What is differential equation?
Equations which involves functions and its derivative is known as differential equation. these equations are highly used to model behaviour of complex system.
How to solve?
y(x) = [tex]C_{1} e^{x}+C_{2}e^{-x}[/tex]
y(0) = [tex]C_{1} +C_{2}[/tex]
0 =[tex]C_{1} +C_{2}[/tex] --------------------------------------------------(1)
y'(x) = [tex]C_{1}e^{x} -C_{2}e^{-x}[/tex]
y'(0) = [tex]C_1- C_{2} }[/tex]
7 = [tex]C_{1}-C_{2}[/tex] -------------------------------------------------(2)
From Equation 1 and 2
[tex]C_{1} +C_{2}[/tex] = 0
[tex]C_{1} -C_{2}[/tex] = 7
[tex]C_{1}[/tex] = 7/2
[tex]C_{2}[/tex] = -7/2
y=[tex]7/2e^{x} -7/2e^{-x}[/tex]
the complete question is
The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−∞, ∞); y'' − y = 0, y(0) = 0, y'(0) = 7
learn more about of differential here
https://brainly.com/question/13008235
#SPJ4
What is the image of (-8,6) after a reflection over the line y=-x
Answers
The image of (-8,6) after a reflection over the line y = -x is (-6, 8).
What is reflection transformation?In geometry, a reflection is referred to as a flip. A reflection is the shape's mirror image. A line, called the line of reflection, is where an image will reflect. Changes in position during reflection may also result in translation. The coordinate system may be referred to by the reflection transformation(X and Y-axis).Given:
The image of (-8,6) after a reflection over the line y = -x.
The x-coordinate and y-coordinate of a point change positions and are negated when it is reflected across the line y = -x.
So, the reflection of the point (-8, 6) across the line y = -x is (-6, 8).
To know more about reflection of a point over a line visit:
https://brainly.com/question/12676179
#SPJ9
PLEASE HELP WILL GIVE BRAIBNLIEST!
Answers
We determine the scale factor by comparing the lengths of corresponding sides of the square.
The length of O’N’=15 and the length of the corresponding segment ON =9.
Then, we compute the scale factor:
O’N’=kON
15=9k
k=15/9=5/3.
The scale factor is k=5/3.
A force of 40.0 N accelerates a 5.0-kg block at 6.0 m/s2 along a horizontal surface. what is the net force acting on the block
Answers
The value of the net force acting on the block will be equal to 79N.
Force may be defined as the product of mass and acceleration, and it acts on the body in order to move the body. Since, the external force is acting on the block there will be a frictional force which opposes the block to move. The frictional force may be represented by f(k) and is given by
f(k) = external force - (ma)
f(k) = 40N - (5×6)
f(k) = 40N - 30N
f(k) = 10N and since it opposes the external force then the sign will be negative that is f(k) = -10N.
Also, there is a force of gravity acting on the body which will be equal to mg where 'g' is the acceleration due to gravity.
Now, force of gravity = mg
= 5×9.8 = 49N
Now, net force acting on the block = 40N - 10N + 49N
Learn more about Force at:
brainly.com/question/27777011
#SPJ1
Lines b and c are parallel. What is the measure of Angle6? Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: (13 x + 9) degrees, 2, 4, 3. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, (5 x + 9) degrees, 8.
Answers
Using the angle theorems, the measure of angle 6, m ∠6, is 54°
Calculating the measure of anglesFrom the question, we are to determine the measure of angle 6
From the given diagram, we can write that
(13x + 9)° = m ∠5 (Corresponding angles theorem)
and
m ∠5 + (5x + 9)° = 180° (Linear pair theorem)
Thus,
(13x + 9)° + (5x + 9)° = 180°
Now, we will solve for x
13x + 9 + 5x + 9 = 180
18x + 18 = 180
Subtract 18 from both sides of the equation
18x + 18 - 18 = 180 - 18
18x = 162
x = 162/18
x = 9
Now, to determine the measure of angle 6
m ∠6 = (5x + 9)° (Vertical angles theorem)
Substitute the value of x
m ∠6 = (5(9) + 9)°
m ∠6 = (45 + 9)°
m ∠6 = 54°
Hence, measure of ∠6 is 54°
Learn more on Calculating measures of angles here: https://brainly.com/question/24607467
#SPJ1
HELP PLEASEEEEEEEEEEEEE!!!!!!
Answers
∠1 and ∠4 are supplementary angle in transversal line .
What is a transversal angle?
When a transversal splits two parallel lines, the two intersections create a number of angles. Transversal angles are what those are.A transversal is a line that crosses a network of lines, according to the definition. Transversals include, for instance, a line that crosses a set of two parallel lines.A transversal line is one that crosses two other lines at two different locations. Line l meets a and b in the picture below at two different locations, P and Q. Line l is the transversal line as an outcome.1) ∠6 ≅ ∠8 congruent angle.
2) ∠6 = ∠1 and ∠8 = ∠3 are Verical angles.
3) ∠1 and ∠4 are supplementary angle.
Learn more about Transversal angles
brainly.com/question/9610896
#SPJ13
#16 23.8 divided by 5.6
Answers
Answer:
23.8/5.6=4.25
Step-by-step explanation:
Answer:
4.25
Step-by-step explanation:
[tex] \sf \: 23.8 / 5.6 =4.25[/tex]
[tex] \sf----------------------------------[/tex]
30 kilograms of beans cost $5 how many beans can you buy for $1
Answers
Answer:
6kg
Step-by-step explanation:
5 to 30 ratio
1 to 6 ratio
Answer:
30/5=6
6 kg beans for $1
Plsmark as brainliest
Which graph shows the solution to the system of linear inequalities?
2x – 3y <12
y < –3
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.
Answers
The solution for the system of linear inequalities is y <-3 and x < 10.5
What are linear inequalities?Linear inequalities are inequalities that have constant average rates of change.
How to determine the graph of the linear inequalities?A system of linear inequalities is a collection of at least two linear inequalities
In this case, the system of inequalities is given as
2x - 3y < 12
y < -3
Substitute y < -3 in 2x - 3y < 12
2x - 3(3) < 12
Evaluate the like terms
2x - 9 < 12
This gives
2x < 21
Divide by 2
x < 10.5
Hence, the solution is y <-3 and x < 10.5
See attachment for the graph where the green line represents y <-3 and the other represents 2x - 3y < 12
Read more about inequality at
https://brainly.com/question/25275758
#SPJ1
What rules of exponents do you use to solve 10^3*10^-7*10^2? Choose all answers that apply.
Product Rule
Negative Rule
Quotient Rule
Power Rule
Answers
The rules of exponents which can be used to solve the expression as given in the task content are; Product rule, Negative rule and Quotient rule.
What rules of exponents do you use to solve 10³ * 10-⁷ * 10² as given in the task content?It follows from the task content that the rules which can be used to correctly solve the expression as given in the task content be determined.
Since the expression given is;
10³ * 10-⁷ * 10²
We can therefore have rewrite 10-⁷ using the negative rule so that we have; 1/10⁷.
Also, the product rule can be used on; 10³ * 10² so that we have; 10⁵.
Ultimately, the quotient rule can be used on the resulting expression; 10⁵/10⁷ so that we have; 10-².
Read more on exponent rules;
https://brainly.com/question/847241
#SPJ1
A field has width x and and length 2x+1 the area of the field is 600m^2 find the width and the length of the field
Answers
The length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.
What is termed as the rectangle?A rectangle is indeed a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal as well as parallel. Because a rectangle is a two dimensional shape, it has two dimensions: length and width. The length of the rectangle is the longer side, and the width seems to be the shorter side.The given values in the question are-
The width of the field = w.
The length of the field = 2x+1
The area of the field = 600 m².
The formula of area of rectangular field;
A = length×width
Put the values;
600 = (2x+1)x
Simplifying the equation;
600 = 2x² + x
2x² + x - 600 = 0.
Find the factors of the above quadratic equation using quadratic formula.
x = 2.08, neglecting negative value.
Thus, the width is x = 2.08 m.
length = 2x + 1
length = 5.16 m.
Thus, the length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.
To know more about rectangle, here
https://brainly.com/question/25292087
#SPJ10
URGENT!!!!!
math assignment(not to be confused with assessment) that I need help with
Answers
The statements that are true in the lines of construction of the straightedge and compass construction which makes use of congruent circles, are;
Line EF is the perpendicular bisector of segment BD
Line EF is the bisector of angle BAC
How are a compass and straightedge used to construct geometric figures?Geometric figures are constructed using a compass and a straightedge, by using outlined steps or procedures.
From the diagram, given that the circumference of the circle with center B passes through the center of the circle with center D, and vice versa, we have;
Circle B is congruent to circle D
Construction of Perpendicular Bisector to Line BDThe steps to construct a perpendicular bisector to the segment BD includes;
Placing the compass at point B and draw an arc above and below segment BC then place the compass at point D then draw arcs above and below the segment BD to intersect the previous arcs drawn from point B. at points E and FJoin the point of intersection of the two arcs which are the points E and F to complete the the construction of the perpendicular bisector of segment BDTherefore;
Line EF is the perpendicular bisector of segment BDThe steps to construct the angle bisector of angle BAC
The angle bisector can be constructed by using the following steps
Place the compass at point A which is the vertex of the angle, and draw arcs to intersect the arms of the angle at B and D Place the compass at points B and D and draw arcs above BD to intersect at point F which is on the of BD away from point AJoin FAV to complete the construction of the bisector of angle BACWhich gives;
Line EF is the bisector of angle BACLearn more about construction of geometric figures here:
https://brainly.com/question/17834363
#SPJ1
Factorise fully 3x² -75
Answers
Answer : 3(x - 5)(x + 5)
example 3(x 2 - 25)
3x2 - 75
sorry about what happened but I hope this helps have a great day
a farmer grew 8,914 bushels of corn. he delivered corn to different stores using his truck. his truck can carry 336 bushels of corn in one load. what was the least number of loads the farmer made to deliver all the corn to the stores?
Answers
Answer:
The farmer had to do 27 loads.
Step-by-step explanation:
Basically the easy way to do this is to grab a calculator (or the paper and pen way) and keep adding 336 until you get to 8914.
Once you add it all you will see there is a remainder of his corn left (that has not been delivered):178
Even though it isn't a full 336, the farmer would still have to make another trip.
336*26=8,736
So, adding the remainder into it's own load, we would get:
27.
on a popular fictional game show, contestants are given the opportunity to win money by reaching into a bag after being blindfolded and selecting a chip with a dollar amount written on it. assume all chips are identical. the bag contains four chips with a $0 amount, six chips with $1, five chips with $5, two chips with $10, and one chip with $100. the chips are mixed in the bag before the contestant draws their chip. a. construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game. b. what is the expected value for x?
Answers
Construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game is 1/18.
What is a probability math example?
Probability is the measurement of how likely something is to happen. As an example, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head. We write P(heads) = 12 here. The four most popular approaches to probability are axiomatic, classical, empirical, and subjective.from above total number of chips =4+6+5+2+1 =18
hence Probabilty of win 0 P(0)=4/18
P(1) =6/18
P(5) =5/18
P(10) =2/18
P(100)=1/18
x P(x) xP(x)
0 0.22 0.00
1 0.33 0.33
5 0.28 1.39
10 0.11 1.11
100 0.06 5.56
8.39
therefore expeted value =8.39
Learn more about probability
brainly.com/question/11234923
#SPJ9
I need help on number 10! asap!!
Answers
Answer:
6
Step-by-step explanation:
match the metric measurements below
a. 2.4 meters
b. 0.4 kilometers
c. 0.04 hectometers
d. 240 decimeters
_ 40 dekameters
_ 0.24 hectometers
_400 centimeters
_ 2400 millimeters
Answers
Metric measurement are given below:
What is metric measurement?The meter, liter, and gram are the corresponding base units for length (distance), capacity (volume), and weight (mass) in the metric system. To measure smaller or larger amounts, we use units that are derived from metric units.
The three most used base units in the metric system are the meter, gram, and liter. The liter is a unit of volume equal to 1.05 quarts, the meter is a unit of length equal to 3.28 feet, and the gram is a unit of mass about equivalent to 0.0022 pounds (or roughly the mass of a paper clip).
Given Data
a) 2.4 meters
b. 0.4 kilometers
c. 0.04 hectometers
d. 240 decimeters
_ 40 dekameters
_ 0.24 hectometers
_400 centimeters
_ 2400 millimeters
a) 2.4 meters = 2400 millimeters
b) 0.4 kilometers = 400 centimeters
c) 0.04 hectometers = 40 dekameters
d) 240 decimeters = 0.24 hectometers
To learn more about metric, visit:
https://brainly.com/question/24248807
#SPJ13
Help plhyhrfdhfgtsgf
Answers
Answer:
60000
Step-by-step explanation:
Answer:
60000
Step-by-step explanation:
6 × [tex]10^{4}[/tex] =
6 × 10000 =
60000
I need to work out these answers. If u can provide working that would be helpful
Answers
===================================================
Explanation:
The car is initially worth 44000 pounds.
It loses 25% of its value after the first year, but keeps the remaining 75% of it.
75% of 44000 = 0.75*44000 = 33000
The car is worth 33000 pounds at the end of year 1. This is effectively the "starting" value when we change the rate of depreciation.
------------------
The new percentage of the depreciation rate is x%
The car loses x% of its value each year
But it keeps the remaining (100-x)% of the value from year to year. Refer to the previous section.
x% = x/100
(100-x)% = (100-x)/100 = 100/100 - x/100 = 1 - 0.01x
The 1 - 0.01x is the value of b in the exponential equation y = a*b^t
The value of 'a' is the "starting" value of 33000 pounds.
The t represents the number of years after that first year (so that means we have t+1 years total).
The equation we have is
y = a*b^t
y = 33000(1 - 0.01x)^t
The teacher mentions "after 3 years" which means we'll have t+1 = 3 solve to t = 2 which is what we'll plug in along with y = 25555
Let's solve for x.
y = 33000(1 - 0.01x)^t
25555 = 33000(1 - 0.01x)^2
25555/33000 = (1 - 0.01x)^2
0.77439393939393 = (1 - 0.01x)^2
(1 - 0.01x)^2 = 0.77439393939393
1 - 0.01x = sqrt(0.77439393939393)
1 - 0.01x = 0.87999655646709
-0.01x = 0.87999655646709-1
-0.01x = -0.1200034435329
x = -0.1200034435329/(-0.01)
x = 12.00034435329
Due to rounding error, it appears that it should be x = 12 since your teacher mentions x is an integer.
Also, 12.00034435329 is pretty close to 12.
If it decays at 12% per year, then the car keeps the remaining 88% since 100-12 = 88
Therefore 0.88 is the base of the exponential, it's the value of b.
Computing 33000(0.88)^2 gets us 25,555.2 which isn't too far from the goal of 25,555 pounds.
------------------
We found the exponential decay equation to be
y = 33000(0.88)^t
where t is the number of years after that first year. We have t+1 years total.
Your teacher asks how much the car will be worth after 4 years, so we'll plug in t = 3 because it's the solution to t+1 = 4.
In other words, we're working 3 years after that first year is up, so 3+1 = 4 total years.
Plug in t = 3 to find the following
y = 33000(0.88)^t
y = 33000(0.88)^3
y = 22,488.576
Rounding to the nearest pence gets us 22,489.58 which is the value of the car after 4 years. You can verify this with a spreadsheet table as I have shown in the diagram below. The highlighted rows mention values on your screenshot.
I'll round to the nearest pound since the other car values mentioned were whole numbers rather than decimal ones.
The 22489.58 rounds to 22490
------------------
For the final part, we'll need logarithms to solve the equation. Logarithms are useful to isolate the exponent.
We'll plug in y = 14520 and solve for t
y = 33000(0.88)^t
14520 = 33000(0.88)^t
14520/33000 = (0.88)^t
0.44 = (0.88)^t
Log[ 0.88^t ] = Log[ 0.44 ]
t*Log[ 0.88 ] = Log[ 0.44 ]
t = Log[ 0.44 ]/Log[ 0.88 ]
t = 6.42227097958021
This rounds up to t = 7
Round up instead of down because we want to clear the hurdle of passing the 14520 marker.
Recall once again that t is the number of years after the first year.
So t = 7 represents t+1 = 7+1 = 8 years in total that have passed by. Therefore, after 8 years is when the car's value is below 14520 pounds. Refer to the table diagram below.
2üssü15 artı 2 üssü 14
Answers
Answer:
What is this, give context and I'll help you.
Step-by-step explanation:
Need more context.
determine the body mass index of a person 65 inches tall with a weight of 175 pounds
Answers
The body mass index of a person 65 inches tall with a weight of 175 pounds is 29.12
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The body mass index (BMI) is given by:
BMI = [mass in pounds / (height in inches)²] * 703
Given mass = 175 pounds, height = 65 in, hence:
BMI = [175/65²] * 703 = 29.12
BMI = 29.12
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1