The demand is decreasing at the rate of 2units per week.
Given the price p (in dollars) and the demand x (in thousands of units) of a commodity satisfy the demand equation 6p+x+xp=94
Differentiating the function with respect to time will result in;
[tex]6\frac{dp}{dt}+\frac{dx}{dt} + x \frac{dp}{dt} + p\frac{dx}{dt} = 0[/tex]
Given the following paramters
p = $6
dp/dt = $2/wk
Substitute the given parameters into the formula to have:
[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0[/tex]
To get the demand x, we will simply substitute p = 9 into the expression to have:
6(9)+x+9x=94
10x+54 = 94
10x = 94 - 54
10x = 40
x = 4
Substitute x = 4 into the derivative to have:
[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 2(4) + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 8 + 9\frac{dx}{dt} = 0\\20 + 10\frac{dx}{dt} =0\\10\frac{dx}{dt} =-20\\\frac{dx}{dt} =\frac{-20}{10}\\\frac{dx}{dt} =-\$2/wk[/tex]
Hence the demand is decreasing at the rate of 2units per week.
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Flying against the wind, a jet travels 3780 miles in 6 hours. Flying with the wind, the same jet travels 5950miles in 7 hours. What is the rate of the jet in still air and what is the rate of the wind? 1111 Rate of the jet in still air:
The rate of the jet in still air is 740 mph and the rate of the wind is 110 mph.
The given parameters;
distance traveled against the wind, d₁ = 3780 milestime of motion, t₁ = 6 hoursdistance traveled with wind, d₂ = 5950 milestime of motion, t₂ = 7 hoursLet the rate of the jet in still air = R₁
Let the rate of the wind = R₂
The rate of the jet against the wind:
[tex]R_1 - R_2 = \frac{3780}{6} \\\\R_1 - R_2 = 630[/tex]
The rate of the jet with the wind:
[tex]R_1 + R_2 = \frac{5950}{7} \\\\R_1 + R_2 = 850\\\\[/tex]
The rate of the jet in still air is calculated as follows;
[tex]R_1 = \frac{630 + 850}{2} \\\\R_1 = 740 \ mph[/tex]
The rate of the wind is calculated as follows;
[tex]R_1 - R_2 = 630\\\\R_2 = R_1 - 630\\\\R_2 = 740 - 630 \\\\R_2 = 110 \ mph[/tex]
Thus, the rate of the jet in still air is 740 mph and the rate of the wind is 110 mph.
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Pizza Palace sells cheese pepperoni, sausage and mushroom pizzas. Caleb noticed that for every 10 orders of cheese pizza, there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushrooms pizza. If there were 35 pepperoni pizzas ordered, how many total pizzas were ordered?
Step-by-step explanation:
cheese : pepperoni : sausage : mushroom =
10 : 7 : 5 : 8
so, in total there are 10+7+5+8 = 30 "business pieces".
to get the total number of pizzas, we need to see how many pizzas are sold per "business piece" ?
we get this from the 35 orders of pepperoni pizzas.
these 35 orders represent 7 "business pieces".
that means 1 "business piece" = 35/7 = 5 pizzas.
that means that 30 "business pieces" are 5×30 = 150
so, in total, 150 pizzas were ordered.
Solve for k.
14k+3k–16k=5
k=
Answer:
5Step-by-step explanation:
Solve for k.
14k+3k–16k=5
17k - 16k = 5
k = 5
HELP ME OUT PLEASE
Use the data to create a scatter plot.
C D
Given: r is inversely proportional to s. If r = 16 when s = 3, then write the formula for the relation between r and s.
a. r=s/48
C. r=s/16
b. r= 48/s
d. r= 16/s
Please select the best answer from the choices provided
A
B
ОООО
Submit
Next
Save and Exit
Mark this and retum
Answer:
You choose but it looks like what you have labeled B
Step-by-step explanation:
R = K / S INVERSE PROPORTION
16 = K / 3 VALUES GIVEN: MULTIPLY BY 3 ON BOTH SIDES
16*3 = k
K = 48
Answer: R = 48/S
elijan un lugar de su escuela o de su localidad y elaboren un croquis a escala muestren su trabajo a la clase e indiquen que escala utilizaron
Answer:
pls ask the question in english pls i don't understand it
lisa's father gave her $1032 to buy a present. this covered 3/5 of the cost. How many did the present cost?
Answer:
$1720
Step-by-step explanation:
1032 is 3/5 of the cost.
Divide 1032 by 3/5, which is 1720.
Thus, the answer is $1720.
The cost of the present day will be $1,720.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Lisa's father gave her $1032 to buy a present. This covered 3/5 of the cost.
The cost of the present day will be given by the division of the numbers 1032 and 3/5.
⇒ 1032 / (3/5)
⇒ 1032 x 5 / 3
⇒ $1,720
The cost of the present day will be $1,720.
More about the Algebra link is given below.
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does 17/10 and 12/5 form a proportion?
Answer:
No
Step-by-step explanation:
17/10 is not proportional to 12/5. Proportional relationships are relationships between two variables where their ratios are equivalent. 17/10 as a ratio is 17:10 and 12/5 as a ratio would be 12:5. A proportional relationship for 12/5 would be 24/10.
Hope this helps :)
No, 17/10 and 12/5 do not form a proportion.
What is a proportion?A proportion is an equation that sets two ratios at the same value.
We have two fractions,
17/10 and 12/5.
That means,
17/10 = 1.7
And 12/5 = 2.4
And 1.7 is not equals to 2.4.
So, the fraction does not show the proportional relationship.
Therefore, the fraction does not show the proportional relationship.
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The sum of two numbers is 48. One numner is 3 times the other. Find the numbers.
Answer:
16 and 3?
Step-by-step explanation:
48÷3=16
hope this helps
Answer:
12 & 36
Step-by-step explanation:
According to the statement:
[tex]x+y=48[/tex]
[tex]x=3y[/tex]
Replace x= 3y:
[tex]3y+y=48[/tex]
[tex]4y=48[/tex]
[tex]y=48/4=12[/tex]
Then:
[tex]x=3y=3(12)=36[/tex]
Hope this helps
(2,-6); m= -1/4
(Write an equation in point-slope form of the line that passes through the given point and has the given slope)
Answer:
y + 6 = -1/4(x - 2)
Step-by-step explanation:
Point slope form: [tex]y - y_{1} = m(x - x_{1} )[/tex]
[tex]y - y_{1} = m(x - x_{1} )[/tex] Substitute slope = -1/4 and point (2, -6)
[tex]y - (-6) =\frac{-1}4} (x - 2)\\[/tex]
y + 6 = -1/4(x - 2)
Use this data set to answer the following question: 5, 10, 12, 4, 6, 11, 13, 5. Remember to show your work.
Calculate the median.
Question 8 options:
Part A: Solve −mk − 90 > 85 for m. Show your work. (4 points) Part B: Solve 3c − 5f = 55 for f. Show your work. (6 points) (10 points)
Answer:
m < -175/k
f = -11 + [tex]\frac{3}{5}[/tex]c
Step-by-step explanation:
Part A:
-mk - 90 > 85
add 90 to each side to get:
-mk > 175
divide each side by -k to get:
m < -175/k
(inequality symbol switched because we divided by a negative)
Part B:
3c - 5f = 55
subtract 3c from each side to get:
-5f = 55 - 3c
divide each side by -5 to get:
f = -(55 - 3c) / 5 or -11 + [tex]\frac{3}{5}[/tex]c
what is 1 1/2 of 150 and what is 1/2 of 180
Answer:
1 1/2 of 150 is 225 and 1/2 of 180 is 90
Step-by-step explanation:
1 1/2 of 150 basically means 1 1/2 x 150, which equals to 225. 1/2 of 180 means 1/2 x 180 which is 90.
Answer:
1 1/2 of 150 is "225" and
1/2 of 180 is "90"
Step-by-step explanation:
1 1/2 of 150 basically means 1 1/2 x 150, which equals to 225. 1/2 of 180 means 1/2 x 180 which is 90.
Hope this helps :)
5 divided by 325 what is the strategy to this question and answer
Answer: 65
Step-by-step explanation: divided the 2
Suppose all counting numbers are arranged in columns as shown below. Under what letter will the number 2019 appear?
Answer: b
Step-by-step explanation:
Solve |x – 4| + 6 = 17.
A. x = 15 and x = -7
B. x = 15 and x = -15
C. x =-15 and x = -7
D. x = -15 and x = 7
Answer:
A
Step-by-step explanation:
15 and -7
|x-4|=17-6
|x-4|=11
x-4=11
x-4=-11
x=11+4
x=15
x=-11+4
x=-7
HELPPP LAST ATTEMPT!!
Answer:
(0,4) is the answer hope it helps
There are 25 students in a class, and 6 of them will be chosen to go on a field
trip. How many ways can these students be chosen?
5^-x = 6
Help ASAP
STEPS MUST.
We have to Find:
The value of x[tex] \sf \longmapsto5^{ - x }= 6[/tex]
Let's start.
Take Logarithm of both sides[tex] \sf \longmapsto log(5^{-x}) = log(6) [/tex]
Solving Further[tex] \sf \longmapsto - x \: log(5) = log(6)[/tex]
[tex] \sf \longmapsto - x = \dfrac{ log(6) }{ log(5) } [/tex]
Take the minus from (-x) and put in on log(6)[tex] \sf \longmapsto \: x = \dfrac{ -log(6) }{ + log(5)} [/tex]
Done
Solve for x
(x+16) over 3 = 3x
a. X=-7
b. X=-13
c.x= 8
d. X= 2
Answer:
X=8
Step-by-step explanation:
8+16=24
and 3(8)=24
What is the value of 1027
A. 100
B. 1,000
C. 10,000
D. 100,000
Answer:
huh? this doesn't even make sense or I'm just tripib
Step-by-step explanation:
-xoxo
4-3/7. Can u pls help me out
Answer:
1/7
Step-by-step explanation:
4-3/7
1/7
Hope This Helps You.
Answer:
3 4/7
Step-by-step explanation:
Regroup 4 as 3 7/7.
Subtract 3 7/7 - 3/7 = 3 4/7
There's your answer!
please mark brainliest!
A grocery store has five different packages of bottled water.Which is the best deal available on bottled water at this grocery store?
Answer:
Step-by-step explanation:
First, check the amount of water in each one and the price. Which ever one has the lowest price for more water has the best deal.
:) Hope this helps
can somebody tell me the answer to this?
Answer:
∠AFB is adjacent
What is the answer to this problem?
Answer:
infinitely many solutions
Step-by-step explanation:
If you can do your homework at a rate of 2.6 minutes for every problem, how many problems could be done after 1.78 hours? Round to a whole number.
Answer:
41
Step-by-step explanation:
help me with number 9 please!!
Answer:
10
Step-by-step explanation:
just guessed
plsssssss answerrrrrr
Answer:
Step-by-step explanation:
Angle C and angle with 120 degrees measure are alternate and their measurement is equal so C = 120
angle C and angle B are supplementary and so their sum is equal to 180
B = 180 - 120
B = 60
angle D and angle B are also alternate so their measure is also equal to each other therefore
D = 60
These points are linear.
Find the slope.
M=?
Answer:
Step-by-step explanation:
(5, 0) (6, 8)
(8 - 0)/(6 - 5) = 8/1 = 8
pls help with khan academy
Answer:
c
Step-by-step explanation:
because the rest are just way off
Answer:
The answer is C, bro
Step-by-step explanation:
hope this helped.