Answer:
A
Step-by-step explanation:
(f*g)(x) = f(x) * g(x)
=(x2+1)(x4-1)=x6-x2+x4-1
Water is leaking out of an inverted conical tank at a rate of 6800 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 21 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Answer:
1508527.582 cm³/min
Step-by-step explanation:
The net rate of flow dV/dt = flow rate in - flow rate out
Let flow rate in = k. Since flow rate out = 6800 cm³/min,
dV/dt = k - 6800
Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone
dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)
So, dV/dt = (πr²dh/dt)/3
Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min
Now, by similar triangles, h/r = h'/r'
r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm
Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.
The net rate of increase of water is dV/dt = (πr'²dh/dt)/3
dV/dt = (π(262.5 cm)² × 21 cm/min)/3
dV/dt = (π(68906.25 cm²) × 21 cm/min)/3
dV/dt = 1447031.25π/3 cm³
dV/dt = 4545982.745/3 cm³
dV/dt = 1515327.582 cm³/min
Since dV/dt = k - 6800 cm³/min
k = dV/dt - 6800 cm³/min
k = 1515327.582 cm³/min - 6800 cm³/min
k = 1508527.582 cm³/min
So, the rate at which water is pumped in is 1508527.582 cm³/min
Find the length of x. Assume the triangles are similar.
A. 2.5
B. 4.4
C. 4.0
D. 3.5
Answer:
the answer is get to be D-3.5
Number 14 please and thank you so much
Answer:
0.13
Step-by-step explanation:
N(s)=310+276+155+445
=1186
P=155:1186
=0.13
I rlly need help like pleasee
The parallelogram in Quadrant III is the image of the parallelogram in Quadrant II after a counterclockwise rotation about the origin. What is the angle of rotation?
A.) 90 B.) 180 C.) 270 D.) 360
Answer:
A. 90
Step-by-step explanation:
Correct on EDGE
Answer:
maybe 90
Step-by-step explanation:
PLEASE HELP, solve for X
Answer:
27
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(48+x) * 48 = 60^2
(48+x)48=3600
Divide each side by 48
48+x =75
Subtract 48
48+x-48 = 75-48
x =27
Carrie is asked to draw a triangle with the following specification
• at least two angles measuring 60°
Which of the following statements about this triangle is true?
A. One and only one triangle exists with the given condition, and it must be an equilateral triangle
В.
More than one triangle exists with the given condition, and all instances must be equilateral triangles
C
One and only one triangle exists with the given condition, and it must be an isosceles triangle
D
More than one triangle exists with the given condition, and all instances must be isosceles triangles
Answer:
just put in the cheat codes of life its not that hard
Answer:
answers is B
(Study island)
Step-by-step explanation:
Am I suppose to substitute the variables with random numbers in order to answer these questions???
Translation A maps (x, y) to (x + n, y + 1). Translation B maps (x, y) to (x +s, y + m).
1. Translate a point using Translation A, followed by Translation B. Write an algebraic rule for the final image of the point after this composition.
2. Translate a point using Translation B, followed by Translation A. Write an algebraic rule for the final image of the point after this composition.
3. Compare the rules you wrote for parts (a) and (b). Does it matter which translation you do first? Explain your reasoning.
9514 1404 393
Answer:
(x, y) ⇒ (x +n +s, y +1 +m)(x, y) ⇒ (x +s +n, y +m +1)they are identical in effect; order does not matterStep-by-step explanation:
Substitute the expressions.
A then BAfter the first translation, the value of x is (x+n). Put that as the value of x in the second translation.
x ⇒ x +s . . . . . . . . . the definition of the second translation
(x+n) ⇒ (x+n) +s . . . the result after both translations
The same thing goes for y. After the first translation, its new value is (y+1).
y ⇒ y +m . . . . . . . . the definition of the second translation
(y+1) ⇒ (y+1) +m . . . the result of both translations
Then the composition of A followed by B is (x, y) ⇒ (x +n +s, y +1 +m).
__
B then AThe same reasoning applies. After the B translation, the x-coordinate is (x+s) and the y-coordinate is (y+m). Then the A translation changes these to ...
x ⇒ x +n . . . . . . . . . . definition of translation A
(x+s) ⇒ (x+s) +n . . . . translation A operating on point translated by B
y ⇒ y +1 . . . . . . . . . . . definition of translation A
(y+m) ⇒ (y+m) +1 . . . . translation A operating on point translated by B
The composition of B followed by A is (x, y) ⇒ (x + s + n, y + m + 1).
__
You should recognize that the sums (x+n+s) and (x+s+n) are identical. The commutative and associative properties of addition let us rearrange the order of the terms with no effect on the outcome.
The two translations give the same result in either order.
Write an equation, in slope-intercept form, of the line that passes through the given point and satisfies the given condition. (-1, -4); perpendicular to y=2x+5
Answer:
y = -1/2x - 9/2
Step-by-step explanation:
A is the point (0, 8) and R is the point (5, 6). Find the point Con the y-axis such that angle ABC is 90°
Answer:
(0, -13/2) or (0, -6.5)
Step-by-step explanation:
a point on the y-axis means x=0.
so, the solution is a point (0, y).
and I assume (5, 6) is not R but is B.
for the angle at B being 90 degrees, we are looking at a right-angled triangle, and basic Pythagoras has to be true :
c² = a² + b²
with c being the Hypotenuse (the line opposite of the angle with the 90 degrees).
in our case, this c is the connection from A to C.
and a and b are the connections AB and BC.
so,
AC² = AB² + BC²
the distance between two points is again calculated via Pythagoras, where the differences in x and y directions are the sides, and the distance itself is the Hypotenuse.
so, we get
(0-0)² + (8-y)² = (0-5)² + (8-6)² + (5-0)² + (6-y)²
(8-y)² = -5² + 2² + 5² + (6-y)²
64 - 16y + y² = 25 + 4 + 25 + 36 - 12y + y²
64 - 16y + y² = 90 - 12y + y²
64 - 16y = 90 - 12y
-26 = 4y
y = -26/4 = -13/2 = -6.5
A shopkeeper fixed the marked price of his radio to make a profit of 30 %. Allowing 15 % discount on the marked price, the radio was sold. What percent profit did he make?
Answer:
10.5 %
Step-by-step explanation:
Here .
let the Cost Price be 'x'
the..
by the question..
the marked price was fixed to make 30% profit
then..
the marked price will be
x+ 30% of x
= x + 30/100 × x
=x+ 0.3x
=1.3x
soo .. the marked price is 1.3x
now.. after allowing 15% discount..
the selling price will be
1.3x - 15% of 1.3x
= 1.3x - 0.195x
= 1.105x
thank you...
plzz mark me brainliest now
now..
profit made = 1.105x-x
= 0.105x
soo .
in percentage..
profit percent = profit/cp × 100%
= 0.105x/x × 100%
= 10.5 %
I need help ASAP pls
what is x increased by 10 divided by 4 as an expression?
please help need answer, I ask you don't answer if you don't know the answer, thank you!
Answer:
[tex]\displaystyle \frac{x+10}{4}[/tex]
Step-by-step explanation:
We want to write an expression for the phrase: "x increased by 10 divided by 4."
If x is being increased by 10, the expression is:
[tex]x+10[/tex]
And if it is then divided by 4, we can place the entire expression over four. Hence:
[tex]\displaystyle \frac{x+10}{4}[/tex]
Our expression is:
[tex]\displaystyle \frac{x+10}{4}[/tex]
Marcus has $7000 to invest in a savings account for 3 years. The bank offers two investment options. Option A pays 5 % simple interest per year and Option B pays 4% compound interest per year. (a) How much interest would Marcus earn after 3 years with Option A?
Answer:
$ 630
Step-by-step explanation:
One is given the following information:
$7000 was invested in a savings accountOption A: 3% simple interest annuallyOption B: 4% interest compounded annuallyThe problem asks one to find out the amount of interest earned after 3 years of going with option A. The easiest way to do such is to form an equation. The general equation for simple interest is the following:
A * 0.01P(d) = I
Where the parameters indicate the following values,
A = amount invested
P = interest rate
d = time invested (years)
I = amount earned in the form of interest
Substitute the given values into the formula, then simplify to evaluate,
A * 0.01P(d) = I
7000 * 0.01(3)(3) = I
7000 * 0.01(9) = I
7000 * 0.09 = I
630 = I
In an experiment on the effects of caffeine on the alertness of college students, student volunteers are randomly assigned to two groups. One group is given caffeinated coffee while the other group is given decaffeinated coffee. All participants then play a video game to assess their mental acuity, measured as their final score on the video game. In this study, the group that is given caffeinated coffee is called the:
Answer:
Experimental group
Step-by-step explanation:
During the process of a research study whereby the participants or subject are divided into groups such that some are exposed to the independent variable or treatment while the other subjects are used as control for the study, The group of participants which are exposed or given the actual treatment or independent procedure are called the experimental group. In the scenario above, experimental group are the group of students which were given caffeinated coffee which is the independent variable in this case.
the width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer: 80, 40
Step-by-step explanation: I just made an equation which went something along the lines Of 3.1x=248 , then you get 80, then 40.
what is the electrical work done in a circuit
Answer:
a open and close switch and a condentation out put.
math help please help please my parents are going to hit me
Answer:
2.1
Step-by-step explanation:
Angle Q of the triangle, SRQ is 47. Let find Length of RQ of SRQ.
If we apply tangent ratio, we get
[tex]x = 5.9[/tex]
Now let find the measure of RP of Triangle SRP.
If we apply tangent ratio, we get
[tex]x = 3.8[/tex]
We can find PQ by Subtraction Poustulate.
[tex]5.9 - 3.8 = 2.1[/tex]
so
Pq=21
Answer:
PQ ≈ 2 cm
Step-by-step explanation:
We know that SRQ is 47.
Next we apply the tangent ratio. We get x = 5.9
Now we find the measure of RP of the triangle SRP.
If we apply tangent ratio, we get x = 3.8
We can find PQ with this:
5.9 - 3.8 = 2.1 ≈ 2 cm
REPLY ASAP PLEASE!!!
Answer:
The answer is c.
Step-by-step explanation:
1. Why should you plan for retirement now?
2. What are 2 different ways that you can save for retirement and what are the benefits of these methods?
3. Why is it important to make sure your retirement account has compounded interest?
4. What is one example of something you could do in the next 5 years to start saving for retirement?
5. What advice you would give to a friend or family member who is thinking of retiring soon? (Right answer only please) :)
1. Because if you have a plan early then you can start saving early, which increases the amount you will have. The future is also unpredictable
2. Set aside money over a set period (put aside money each month, year). You can set up a plan through your employer ie 401K, or set up an individual retirement plan (IRA). Your employer takes a percentage you choose out of your check each month (commonly 3%, 5%, %10, 15%). The money is taken from your paycheck before taxes therefore it lowers your income and you pay less in taxes. An IRA is similar to a bank account as you choose when and how much you put in over time. Both can be withdrawn at 59 1/2.
3. Compound interest essentially earns you more money for retirement. It can be important because you earn more than with regular interest.
4. Start balancing expenses, make a plan for retirement and practicing saving. It would also be beneficial to start setting aside money for retirement even if you haven't opened an account yet.
5. Make sure you can comfortably live off of your retirement. If you can't it would be best to maximize your retirement and savings, or consider working seasonally or part-time
Write down the nth term of the following sequence
the following pattern are made using small squares
Answer:
a) [tex]n = 4 + 7\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex], b) [tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
Step-by-step explanation:
a) The sequence is representative for an arithmetic sequence, whose key characteristic is that difference is between two consecutive elements is the same. In particular, the sequence has a difference of 7 between any two consecutive elements and the initial element is 4. Hence, we can derive the following formula:
[tex]n = n_{o} + r\cdot i[/tex], [tex]\forall\, i \in \mathbb{N}_O[/tex] (1)
Where:
[tex]n_{o}[/tex] - Initial element.
[tex]r[/tex] - Difference between two consecutive elements.
[tex]i[/tex] - Index.
If we know that [tex]n_{o} = 4[/tex] and [tex]r = 7[/tex], then the expression for the n-th term of the sequence is:
[tex]n = 4 + 7\cdot i[/tex], [tex]\forall \,i\in\mathbb{N}_{O}[/tex]
b) In this case, we have a geometric sequence described by the following equation:
[tex]n = 2 + (i+1)^{2}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex] (2)
The constant element ([tex]2[/tex]) represents the two extreme squares, whereas the second order binomial represents the total of squares in the middle ([tex](i+1)^{2}[/tex]) and emulates the area formula of the square.
Answer:
Step-by-step explanation:
?
GEOEMTRY- PLEASE HELP , solve for x
Answer:
[tex]17x-23=1/2\times81[/tex]
[tex]17x-23=40.5[/tex]
[tex]17x=40.5+23[/tex]
[tex]17x=63.5[/tex]
[tex]x=63.5/17[/tex]
[tex]x=3.73[/tex]
OAmalOHopeO
Simplify : -2a(a-d)+2a(2a-3D) pls help.
-2a(a - d) + 2a(2a - 3d)
(-2a * a) + (-d * -2a) + (2a * 2a) + (2a * -3d)
-2a^2 + 2ad + 4a^2 - 6ad
(4a^2 - 2a^2) + (2ad - 6ad)
2a^2 - 4ad
---The above expression is simplified, though not fully. The below expression is fully simplified.
2a(a - 2d)
Hope this helps!
see attached photo, please help asap, it is due in 30 minutes !!!
Answer:
Answer is 3.398
Step-by-step explanation:
Solve by putting into calculator.
Soledad gana 12 pesos por hora entregando tartas. Trabajó 25 horas la semana pasada pero desafortunadamente se demoró en 5 entregas y le descontaron 15 pesos por cada entrega demorada. a. Expresa la respuesta como una ecuación. b. ¿Cuánto dinero ganó la semana pasada?
Answer:
Total earning last week = 225
Step-by-step explanation:
Given:
Earning per hour = 12 pesos
Deduct per late delivery = 15 pesos
Total number of hour = 25 hour
Total number of late delivery = 5
Find:
Total earning last week
Computation:
Total earning last week = (Total number of hour)(Earning per hour) - (Deduct per late delivery)(Total number of late delivery)
Total earning last week = (12)(25) - (15)(5)
Total earning last week = 300 - 75
Total earning last week = 225
solve this questions
Answer:
a) Sale Price; Rs. 800 Discount rate: 20%
b) Sale Price; Rs. 4000 Discount rate: 20%
c) Sale Price; Rs. 6000 Discount rate: 35%
Step-by-step explanation:
1. Approach
In these problems, one is given a list of original prices and the amount of price taken off during a discount. One has to find the sale price and the rate of discount. The easiest way to find the sale price is to subtract the discount price from the original price. The general train of thought to do this can be found in the following formula:
[tex](original\ price)-(discount\ amount)=(sale\ price)[/tex]
One is also asked to find the rate of discount. Use the following proportion format to do so:
[tex]\frac{discount\ amount}{original\ price}=\frac{percent}{100}[/tex]
Substitute each of the values in the given problem into the equation and solve for the price.
2. Part A
Original price: 1000
Discount: 200
1. Sale price
Formula[tex](original\ price)-(discount\ amount)=(sale\ price)[/tex]Substitute and solve,[tex]1000-200=(sale\ price)[/tex][tex]\\800 = sale\ price[/tex]2. Discount rate
Formula[tex]\frac{discount\ amount}{original\ price}=\frac{percent}{100}[/tex]Substitute, simplify, and solve[tex]\frac{200}{1000}=\frac{percent}{100}[/tex][tex]\frac{1}{5}=\frac{percent}{100}[/tex][tex](5)(percent)=1(100)[/tex][tex]percent=20[/tex]3. Part B
Original price: 5000
Discount: 1000
1. Sale price
Formula,[tex](original\ price)-(discount\ amount)=(sale\ price)[/tex]Substitute and solve[tex]5000-1000=(sale\ price)[/tex][tex]4000=(sale\ price)[/tex]2. Discount rate
Formula[tex]\frac{discount\ amount}{original\ price}=\frac{percent}{100}[/tex]Substitute, simplify, and solve[tex]\frac{1000}{5000}=\frac{percent}{100}[/tex][tex]\frac{1}{5}=\frac{percent}{100}[/tex][tex]5(percent)=1(100)[/tex][tex]percent=20[/tex]4. Part C
Original price: 8000
Discount: 2000
1. Sale price
Formula[tex](original\ price)-(discount\ amount)=(sale\ price)[/tex]Substitute and solve[tex]8000-2000=(sale\ price)[/tex][tex]6000=(sale\ price)[/tex]2. Discount rate
Formula,[tex]\frac{discount}{amount}=\frac{percent}{100}[/tex]Substitute, simplify and solve,[tex]\frac{2000}{8000}=\frac{percent}{100}[/tex][tex]\frac{1}{4}=\frac{percent}{100}[/tex][tex]4(percent)=1(100)[/tex][tex]percent=25[/tex]A giant pie is created in an attempt to break a world record for baking. The pie is shown below:
What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
Answer:
Area of the slice of pie = 22.09 ft²
Step-by-step explanation:
Area of the slice of pie = Area of the sector of the circle with the central angle 45°
Area of the sector = [tex]\frac{\theta}{360^{\circ}}(\pi r^{2} )[/tex] [Here, r = radius of the circle]
= [tex]\frac{45^{\circ}}{360^{\circ}}(\pi )(\frac{15}{2})^2[/tex]
= 22.09 ft²
Area of the slice of pie = 22.09 ft²
Answer:
22.08ft^2
Step-by-step explanation:
A = πr^2(x/360) d = 15
Since r is half of diameter this means that r = 15/2 =7.5
so Lets use the Area of Sector formua
A =3.14(7.5)^2 (45/360)
A =3.14(56.25) (45/360)
A = 176.625 (45/360)
A = 176.625 (0.125)
A = 22.078125
rounded to the nearest 10th would make it 22.08
please answer this!!!
Answer:
C 20
Step-by-step explanation:
use sine law
Answer:
C, 20
Step-by-step explanation:
Angle c= 30
side AC= 40
sin(30)=x/40
40sin(30)=x
x=20
question
Instructions: Determine whether the following polygons are similar. If yes, type in
the similarity statement and scale factor. If no, type 'None' in the blanks.
L
35
M
х
w 18
50°
631
63
10
10
50°
35 N
o
Z
18
Y
Similar:
Answer:
No, the polygons aren't similar since they don't have a constant scale factor.
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
Explanation: I would use the substitution method for this system
because one of the variables, x, is already isolated in the first equation.
Since our first equation states that x = 12 - y, 12 - y can be substituted
in for x in the second equation which becomes 2(12 - y) + 3y = 29.
Now we can solve this equation by first distributing the 2
through the parentheses to get 24 - 2y + 3y = 29 and you
should be able to easily finish solving from here to get y = 5.
Now substitute a 5 back in for the first equation to get
x = 12 - (5) or x = 7 which means that our solution is (7, 5).
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
V10
Answer: 2=
=
Submit Answer
Answer:
x=2*sqrt(5)
Step-by-step explanation:
Since the triangle is isosceles, the other side of the triangle is sqrt(10) too. By using Pythagoras theorem, we have 10+10=x^2, x=2*sqrt(5).
