Answer:
D(x) = 4000 / x + 2
Step-by-step explanation:
Given:
marginal-demand function = d /dx[D(x )] = D'(x)= -4000/x²
Quantity of product demanded = 1002 units
Price of product per unit = $4
To find:
demand function D(x)
Solution:
D'(x)= -4000/x²
= -4000/x² dx
= -4000 x⁻² dx
D(x) = -4000 x⁻¹ + C
D(x) = -4000/x + C
Since we know that the quantity of product is 1002 and price per unit is $4 so,
D(4) = 1002 = 4000/4 + C
1002 = 4000/4 + C
1002 = 1000 + C
1002 - 1000 = C
C = 2
Hence the demand function is:
D(x) = 4000 / x + 2
1/x - 1/y = 1/4
1/x^2 - 1/y^2 = 3/16
x + y = ...
GIVEN:
1/x - 1/y = ¼.1/x² - 1/y² = 3/16.TO FIND:
The value of x + y.ANSWER:
Firstly let us assume ,
p = 1/x .q = 1/y .Now the equⁿ s becomes ,
=> p - q = 4 . ........(1)
Also , given that:
=> 1/x² - 1/y² = 3/16.
=> p² - q² = 3/16.
=> (p+q)(p-q) = 3/16.
From (1),
=> 4 (p+q) = 13/16.
=> (p+q) = 13/16 × 1/4.
=> p+ q = 13/64.
On adding (1) and (2) ,
=> 2p = 4 + 13/64.
=> 2p = 256+13/64.
=> p = 269/64 × 1/2.
=> p = 269/128.
Now lets find q ,
=> q = 13/64 - 269/128.
=> q = 26-269/128.
=> q = -243/128.
Hence
p = 269/128.q = -243/128..°. x = 128/269 , y = -128/243
What mixed
number represents thirty-eighths?
Answer:
............... 3 6/8
Find the value of 4!.
☺ Hi ☺
Find the value of 4!.
• Let's find the value of 4! :
[tex]4! = 4 × 3 × 2 × 1 = {24}[/tex]
Translate into a variable expression.
the product of a number n and four more than the number
Answer:
(x)n+4
Step-by-step explanation:
x=quantity multiplied by n for a product
n=a number
+4=4 more than the number
HOPE THIS HELPS!!!!!! :)
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the distance from a boy's house to his school is 10km. he left home at 6.30am, cycling at the rate of 4km/h. if he spent 15 minutes on the way waiting for his friend, when did he get to school?
Answer:
9:15 am
Step-by-step explanation:
First you know the speed and you know the distance.
So now we have to find the time it took for him to get to school(ignore the waiting time first)
time=10/4=2.5h
now we add the waiting time,
2.5h+0.25h(15minutes is the same as 0.25h)=2.75h
convert 0.75h to minuts,
0.75*60=45minutes
6.30+2.45=9.15am
The boy arrived at school at 8:15 am after cycling for 2.5 hours and waiting for 15 minutes.
Given Distance from the boy's house to school = 10 km
Cycling speed = 4 km/h
Time spent waiting for his friend = 15 minutes
Now calculate the time it took for the boy to cycle the distance from his house to the meeting point, excluding the waiting time.
Distance = Speed × Time
10 km = 4 km/h × Time
Time = 10 km / 4 km/h
Time = 2.5 hours
Now, we need to convert the waiting time from minutes to hours, so we can add it to the cycling time.
Waiting time = 15 minutes / 60 minutes/hour
Waiting time = 0.25 hours
Add the cycling time and waiting time to determine the total time it took for the boy to reach school.
Total time = Cycling time + Waiting time
= 2.5 hours + 0.25 hours
=2.75 hours
We need to determine the arrival time by adding the total time to the departure time.
Arrival time = Departure time + Total time
Arrival time = 6.30 am + 2.75 hours
To calculate the arrival time, we need to consider the minutes and hours separately:
Minutes: 30 minutes + (0.75 hours × 60 minutes/hour)
= 30 minutes + 45 minutes
= 75 minutes
Since 75 minutes is more than an hour, we need to adjust the hours and minutes accordingly.
Adding the hours: 6 + 2 = 8
So, the boy arrived at school at 8:15 am.
Therefore, the boy arrived at school at 8:15 am.
To learn more on Distance click:
https://brainly.com/question/15172156
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It is known that the birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7. Approximately what proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs? Provide all four decimal places in your answer.
Answer: 0.4419
Step-by-step explanation:
Given: The birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7.
i.e. [tex]\mu=6.8\ \ \ \text{ and }\sigma= 1.7[/tex]
Let X denotes the birth weight.
Then, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is given by :-
[tex]P(6<X<8)=P(\dfrac{6-6.8}{1.7}<\dfrac{X-\mu}{\sigma}<\dfrac{8-6.8}{1.7})\\\\=P(-0.47<Z<0.71)\ \ \ [Z=\dfrac{X-\mu}{\sigma}] \\\\=P(Z<0.71)-(1-P(Z-0.47))\\\\=0.7611-(1-0.6808)\ \ \ [\text{By z-table}]\\\\= 0.4419[/tex]
Hence, the proportion of newborn babies will have a birth weight between 6 lbs and 8 lbs is 0.4419 .
PLZ HELP ME OUT Is 1.3 rational or irrational? Is 36 rational or irrational Is 3.14 or pi rational or irrational Is 2/3 rational or irrational
A rational number can be made by dividing two integers.
An irrational number cannot be made by dividing two integers.
1.3 is rational
36 is rational
2/3 is rational
Pi is not rational
Can someone help me!!!
Answer:
Step-by-step explanation:
[tex]a.\\sin \theta =\frac{12}{13}\\\theta=sin ^{-1}(\frac{12}{13}) \approx 67^\circ\\b.\\cos75=\frac{x}{13}\\x=13 cos ~75 \approx 7.5 ~ft[/tex]
it forms a right angled triangle.
ladder=hypotenuse.
side of house=perpendicular.
from the base of house to the foot of ladder on the ground=base
Round 72.163 to the nearest tens place.
Answer:
72.2 is the correct answer
Step-by-step explanation:
1.) Which of the following is the correct equation for the Pythagorean Theorem, where a and b are the side lengths and c is the length of the hypotenuse?
a.) (a+b)^2=c^2
b.) a^2+b^2=c^2
c.) a^2-b^2=c^2
d.) (a-b)^2=c^2
3.) Find the distance between the points (9, −7) and (5, −4).(1 point)
a.) 5
b.) 25
c.) √7
d.) √137
4.) To find the distance between (17, 3) and (17, −5), Marcia used the following equation. Is Marcia correct? Explain.
D = | 3 − (−5) | = 8
a.) Marcia is not correct. Since the points are in two-dimensions, the distance formula must be used to find the distance.
b.)Marcia is correct. For any pair of points, the distance between the points can be treated as if they are in one-dimension.
c.)Marcia is correct. Since the x-coordinates are the same, the distance between the points can be treated as if they are in one-dimension.
d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=√8
Option d for question 4 should be:
d.)Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8
Answer:
1. (b) a^2+b^2=c^2
3. (a) 5
4. (d) Marcia is not correct. According to the distance formula, the distance should be D=√(17-17)^2+(3-(-5))^2=8
Step-by-step explanation:
(1) From Pythagoras' theorem, the square of the hypotenuse side of a given right-angled triangle, is equal to the sum of the squares of the other two sides. Now, if the other two sides are a and b, and the hypotenuse is c, then using this theorem, the following holds:
c² = a² + b²
(2) The distance D, between two points (a, b) and (c, d) is given by;
D = √(a-c)² + (b-d)² ----------------(i)
From the question, the points given are (9, -7) and (5, -4):
This means that;
a = 9
b = -7
c = 5
d = -4
Substitute these values into equation (i) and get;
D = √(9-5)² + (-7- (-4))²
D = √(4)² + (-3)²
D = √16 + 9
D = √25
D = 5
Therefore, the distance between these points is 5 units
(4) As explained in question 3 above, Maria is not correct. To find the distance between two points, we use the relation shown in the answer to question 3 above. i.e
D = √(a-c)² + (b-d)²
Since the given points are (17, 3) and (17, -5), it implies that;
a = 17
b = 3
c = 17
d = -5
D = √(17-17)² + (3-(-5))²
D = √(0)² + (8)²
D = √8²
D = 8
witch is the simplified form of x-12
A solid aluminum cube has sides each of length L . A second cube of the same material has sides four times the length of the first cube; i.e., 4 L . Compared to the first cube, the total surface area of the second cube is
Answer:
Compared to the first cube, the total surface are of the second cube is 16 times larger.
Step-by-step explanation:
The first cube has L*L*6=6L²
The second cube has 4L*4L*6=14L²*6=84L²
Compared to the first cube, the total surface are of the second cube is 16 times larger. (6*16=84)
If a=8 and b=5 and x=4 and y=6m -2 what is the value of m ?
Answer:
m = 2
Step-by-step explanation:
Given:
x = 4
y = 6m - 2
a = 8
b = 5
Required:
Value of m
SOLUTION:
x and y are segments of a chord divided when it intersects another chord that also has segments a and b.
According to the Intersecting chords theorem, [tex] a*b = x*y [/tex]
Thus:
[tex] 8*5 = 4*(6m - 2) [/tex]
Solve for m
[tex] 40 = 24m - 8 [/tex]
[tex] 40 + 8 = 24m - 8 + 8 [/tex]
[tex] 48 = 24m [/tex]
[tex] \frac{48}{24} = \frac{24m}{24} [/tex]
[tex] 2 = m [/tex]
The value of m = 2
Please help me with this
Answer:
7^-3+5 (5 goes up and becomes+5)
so ans is 7^2
Answer:
7^2[tex] \frac{ {7}^{ - 3} }{ {7}^{ - 5} } = {7}^{ - 3 + 5} = {7}^{2} [/tex]
What’s 4/10i simply ?
Answer:
= 2i / 5
Step-by-step explanation:
4 / 10 i
= 2² / (2 * 5) i
= 2i / 5
Answer:
2i / 5 is the answer.
plot the x-intercept of the function f(x)=(x+4)squared
Answer:
(-4,0)
Step-by-step explanation:
Hello, we need to find the points so that f(x)=0 as this is the intersection between y = f(x) and y = 0.
[tex](x+4)^2=0<=> x+4=0<=> x =-4[/tex]
Thank you
Geometry: Find the value of x.
X = [?]°
Answer:
x = 25°
Step-by-step explanation:
The secant- secant angle DGB is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] ( BD - FE) = 55
[tex]\frac{1}{2}[/tex](135 - x) = 55 ( multiply both sides by 2 )
135 - x = 110 ( subtract 135 from both sides )
- x = -25 ( multiply both sides by - 1 )
x = 25°
Solve this equation 7- 4=7 +:
Answer:
what is after the plus sign
Determine if ΔABC and ΔFHG are similar. If so, write the similarity statement.
options:
A) The triangles are not similar
B) ΔABC ∼ ΔHFG
C) Impossible to determine.
D) ΔABC ∼ ΔFHG
Answer:
[tex]\Large \boxed{\mathrm{D) \ \triangle ABC \sim \triangle FHG }}[/tex]
Step-by-step explanation:
The two triangles are similar.
The corresponding sides are proportional.
AB ∼ FH
[tex]\displaystyle \frac{72}{12} =6[/tex]
AC ∼ FG
[tex]\displaystyle \frac{48}{8} =6[/tex]
BC ∼ GH
[tex]\displaystyle \frac{84}{14} =6[/tex]
What is the x-intercept of the graph -4x=20
Answer:
-4x=20
x=20/-4
x=-5
maybe not sure
what is the probability that the card drawn from a stack of 52 cards is a face card or a black card?
Answer: 8/13
Step-by-step explanation:
There are 52 cards in a deck.
26 cards are black --> P(Black) = 26/52
Face cards are J, Q, K. There are 12 face cards --> P(Face) = 12/52
6 Face cards are black --> P(both) = 6/52
Face card or Black card - both Face card & Black
[tex]\dfrac{26}{52}[/tex] + [tex]\dfrac{12}{52}[/tex] - [tex]\dfrac{6}{52}[/tex] [tex]=\dfrac{32}{52}[/tex]
[tex]\dfrac{32}{52}\div \dfrac{4}{4}=\dfrac{8}{13}[/tex]
What is the prime factorization of 315?
Johanna rode her bike 7 miles to a lake . She rode 3/4 of distance to the lake before lunch. How many miles did johanna ride before lunch?
Answer:
5.25 miles
Step-by-step explanation:
Total distance = 7 miles
Distance she rode before lunch = 3/4 of the total distance
=> 3/4 of 7
=> 21/4
=> 5.25 miles
So, she drove 5.25 miles before lunch.
a ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answer:
(a) The new angle the ladder makes with the ground = 32.66°
(b) The distance the ladder slipped back on the ground from it's original position = 5 m
Step-by-step explanation:
The given parameters are;
The length of the ladder = 10 m
Angle of inclination of the ladder = 70°
Length to which the ladder slips down the wall = 4 m
(a) The height of the wall adjacent to the ladder = 10×sin(70°) ≈ 9.4 m
The new height of the wall adjacent to the ladder after the ladder slips down 4 m = 9.4 - 4 = 5.4 m
Therefore, the new angle of inclination of the ladder = sin⁻¹(5.4/10) = 32.66°
The new angle the ladder makes with the ground = 32.66°
(b) The distance the ladder slipped back on the ground from its original position is found as follows
The initial distance of the base of the ladder from the wall = 10 × cos(70°) = 3.42 m
The distance of the base of the ladder from the wall after slipping 4 m down the wall = 10 × cos(32.66°) ≈ 8.42 m.
Therefore, the amount by which the ladder slip back on the ground from its original position = 8.42 - 3.42 = 5 m.
The distance the ladder slipped back on the ground from it's original position = 5 m.
What does a “3-mile” radius mean? What does it look like, and how large is it?
Answer:
the radius is halfway across the circle, while diameter is all the way across. for reference, a three mile radius would be equivalent to 52.8 football fields
Step-by-step explanation:
Y=4x-3; A(5,17) Use substitution to determine whether the point is on the line.
Answer:
the point is on the line
Step-by-step explanation:
The ordered pair gives the values of (x, y). Put those values in the equation and see if it is true:
y = 4x -3
17 = 4(5) -3 = 20 -3 . . . . . . for (x, y) = (5, 17)
17 = 17 . . . . true, the point is on the line
Can Someone please help me with this?
Answer:
9^18
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)^c = a^(bc)
__
[tex](9^3)^6=9^{3\cdot 6}=\boxed{9^{18}}[/tex]
what is simplifying?
what is simplifying in math?
Answer:
Simplifying means making (something) simpler or easier to do or understand.
Simplification in math is the process of replacing a mathematical expression by resolving it or making it shorter.
Step-by-step explanation:
hope it will help :)
Convert 330 meters per second (m/s) to kilometers per minute (km/min). A) 1.98 x 10^1 km/min B) 1.98 x 10^-1 km/min C) 1.98 x 10^2 km/min D) 1.98 x 10^-2 km/min
Answer:
A
Step-by-step explanation:
330 m/s=330×60 m/min=19800/1000 km/min=198 km/min=1.98×10^1 km/min
Write the equation of a line with a slope of −1 and a y-intercept of −6. (2 points)
Answer:
y = -1x - 6
Step-by-step explanation:
Hi!
The format of the equation of a line is y = mx + b
m is the slope and b is the y-intercept
We just need to substitute in the values you gave for the variables and we get the answer,