Answer:
[tex]\displaystyle AL = 2sinh(10)[/tex]
General Formulas and Concepts:
Pre-Calculus
Hyperbolic FunctionsCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Exponential Differentiation
Integration
IntegralsIntegration Constant CDefinite IntegralsParametric Integration
Vector Value Functions
Vector IntegrationArc Length Formula [Vector]: [tex]\displaystyle AL = \int\limits^b_a {\sqrt{[i'(t)]^2 + [j'(t)]^2 + [k'(t)]^2}} \, dt[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \vec{r}(t) = <10\sqrt{2}t , e^{10t} , e^{-10t} >[/tex]
Interval [0, 1]
Step 2: Find Arclength
Rewrite vector value function: [tex]\displaystyle r(t) = 10\sqrt{2}t \textbf i + e^{10t} \textbf j + e^{-10t} \textbf k[/tex]Substitute in variables [Arc Length Formula - Vector]: [tex]\displaystyle AL = \int\limits^1_0 {\sqrt{\bigg[\frac{d}{dt}[10\sqrt{2}t \textbf i]\bigg]^2 + \bigg[\frac{d}{dt}[e^{10t} \textbf j]\bigg]^2 + \bigg[\frac{d}{dt}[e^{-10t} \textbf k ]\bigg]^2}} \, dt[/tex][Integrand] Differentiate [Respective Differentiation Rules]: [tex]\displaystyle AL = \int\limits^1_0 {\sqrt{[10\sqrt{2} \textbf i]^2 + [10e^{10t} \textbf j]^2 + [-10e^{-10t} \textbf k]^2}} \, dt[/tex][Integrand] Simplify: [tex]\displaystyle AL = \int\limits^1_0 {\sqrt{200 \textbf i + 100e^{20x} \textbf j + 100e^{-20x} \textbf k}} \, dt[/tex][Integral] Evaluate: [tex]\displaystyle AL = 2sinh(10)[/tex]Topic: AP Calculus BC (Calculus I + II)
Unit: Vector Value Functions
Book: College Calculus 10e
Find the area of the figure. (Sides meet at right angles.)
Answer:
[tex]9 \times 2 = 18 \: \: \\ 4 \times 5 = 20 \\ 20 + 18 = 38 \\ 38 {in}^{2} [/tex]
hi please give brainly
Can somebody help me find the answer to this problem please ?
Answer:
Step-by-step explanation:
Answer:
D. x = -2y + 4
Step-by-step explanation:
4x + 8y = 16
Solve for x
Our objective here is to isolate x ( in other words we want to get x by itself ) using inverse operations.
So let's begin
4x + 8y = 16
First we want to get rid of 8y
Notice how 8y is being added to 4x
Well we can get rid of it by applying it's inverse operation. The opposite of addition is subtraction. So to get rid of 8y we would simply subtract 8y.
Important note! Whatever we do to one side we must do to the other
So we would subtract 8y from both sides
4x + 8y - 8y = 16 - 8y
The 8y on the left hand side cancels out and the 8y on the right side stays as it is as you can't subtract 8y from 16
We then have 4x = 16 - 8y
Next we want to get rid of 4 from 4x.
4x is the same as 4*x which is multiplication
The inverse of multiplication is division so to get rid of the 4 we divide both sides by 4
4x/4 = (16-8y)/4
4x/4 = x
16-8y/4 ( simply divide 16 by 4 and -8y by 4 )
16-8y/4 = 4 - 2y
We're left with x = 4 - 2y which can also be written as x = -2y + 4
Find two positive numbers whose difference is 28 and whose product is 1653
Answer:
Step-by-skfmckfmkfkfkfkfkkfkfkfkfkfkfoftep explanation:
Cl
Translate and solve: fife less than z is 4
Answer:
z=9
Step-by-step explanation:
z-5=4. /+5
z=4+5
z=9
Answer:
z<-1
Step-by-step explanation:
5<z=4
collect like terms
z=<4-5
z<-1
Q3) He decorated the path in his garden with LED bulbs in three rows so that the bulbs in the first row blink at every 4 min, the bulbs in the second row blink at every 6 min and the bulbs in the third row blink at every 8 min. When will they blink together for the first time if he switches the lights on together at 6pm?
6.24 pm
6.30 pm
6.40 pm
They will not blink together at any time
Q4) If so, which is the next time they blink together?
6.28 pm
6.48 pm
6.50 pm
None of these.
Answer:
They will blink together at 24minutes
Step-by-step explanation:
Using product of primes
4 = 2²
6 = 2 × 3
8 = 2³
Prime numbers with highest power
2³ × 3
8 x 3
24 minutes.
Simplify: −4(b+6)−2b(1−4b
Step-by-step explanation:
-4b-24-2b+8b2
8b2-6b-24=0
I need help this is confusing to me
Answer:i think it is b not really sure
Step-by-step explanation:
how do i find the area of a cone when all i get is radius and theta? radius = 5 theta = 52°
Answer:
11.34464...
Step-by-step explanation:
it is not a 3-dimensional cone, it is a 2-dimensional segment of a circle. and you need to find its area.
which is also why you are asked to find the area, because for a 3-dimensional object you would have been asked about the volume of the surface.
now, about a circle and its segments.
you know how to get the area of a circle ?
it is pi×r²
that is for the full circle.
you know how many degrees it is to go "full circle" ?
360 degrees.
so, here we have only a segment of 52 degrees out of the full 360 degrees.
in other words we are dealing with 52/360 = 13/90 of the full circle.
all we have to do is therefore multiply the area of the full circle with that fraction, and we have our result.
pi×r²×13/90 = pi×5²×13/90 = pi×5×13/18 = 11.34464...
Consider the following. fourteen less than the total of a number and three Translate into a variable expression. (Use x for your variable. Do not simplify.)
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Answer:
(x +3) -14
Step-by-step explanation:
The total of a number and 3 will be represented by (x +3). Fourteen less than that is ...
(x +3) -14 or -14 +(x +3)
A train leaves the station and has to travel 486km. The train maintains a speed of 120km. After travelling for 3 hours and 15 minutes, how much further does the train have to travel to reach its destination?
Answer:
I think its 2 hours 30 minutes
Step-by-step explanation:
The number of patients treated at Dr. Frank's dentist office each day was recorded for ten days: 11, 4, 6, 7, 5, 10, 9, 21, 3, 0. Using the given data, find the mean for this sample.
Answer:
7.6
Step-by-step explanation:
Mean = (sum of numbers)/amount of numbers
11 + 4 + 6 + 7 + 5 +10 +9 + 21 + 3 + 0 = 76
76/10 = 7.6
Help me this question
Answer:
(a) 218.6 N
(b) 97.14 N
Step-by-step explanation:
When the system is in equilibrium, the net torque on the system is zero.
AC = 1.5 m, CD = 2.3 m, DB = 5 - 1.5 - 2.3 = 1.2 m
Let the centre of gravity of plank is at G.
AG = 2.5 m, CG = 2.5 - 1.5 = 1 m, GB = 2.5 m
(a) Let the reaction at C is R and at D is R'.
R + R' = 29 x 9.8 = 284.2 N ... (1)
Take the torque about C.
29 x 9.8 x CG = R' x GD
29 x 9.8 x 1 = R' x 1.3
R' = 218.6 N
(b) Take the torque about D.
6 x 9.8 x AD = R x CD
6 x 9.8 x (1.5 + 2.3) = R x 2.3
R = 97.14 N
Is the relationship shown by the data linear? If so, model the data with an equation.
Answer:
The relation is linear
Step-by-step explanation:
Answer:
Yes, the relationship shown is linear. The equation of the line is y=-1.25x-13.25.
Step-by-step explanation:
This data is linear as y decreases at a constant rate. The equation of a line is y=mx+b, where m=slope and b=y intercept
To find m:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{(-2)-(-7)}{(-9)-(-5)}[/tex]
m=[tex]\frac{5}{-4}[/tex]
m=[tex]-\frac{5}{4}[/tex]=-1.25
To find b, you can use any of the given points:
(-9,-2)
(-2)=-1.25(-9)+b
-2=11.25+b
-2-11.25=b
b=-13.25
Therefore, using the calculated values for m and b:
y=mx+b
y=-1.25x-13.25
Which of the following choices is equivalent to -6x > -42?
Answer:
Where is the rest?
Step-by-step explanation:
%7"7:7;9
A chef is going to use a mixture two different brands of Italian dressing the first spring and days 5% vinegar the second brain contains 15% vinegar the sheriff wants to make 390$ ml addressing that is 9% vinegar how much of each brand should she use
I guess the chef is making the mixture for the sheriff... Let x be the amount of dressing with 5% vinegar that is required, and y the amount of 15% vinegar dressing (both amounts in mL).
The sheriff wants 390 mL of the mixed dressing, so that
x + y = 390
x mL of the 5% dressing contains 0.05x mL of vinegar, while y mL of the 15% dressing contains 0.15y mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means
0.05x + 0.15y = 35.1
Solve for x and y :
y = 390 - x
0.05x + 0.15 (390 - x) = 35.1
0.05x + 58.5 - 0.15x = 35.1
23.4 = 0.10x
x = 234
y = 156
Given h(x) = -x + 1, find h(0).
Answer:
Answer:
1
Step-by-step explanation:
Given,
h ( x ) = - x + 1
To find : h ( 0 ) = ?
h ( 0 )
= - ( 0 ) + 1
= 1
Answer: 1
Step-by-step explanation:
h(x) = -x + 1
To Find = h(0)
= -(0) + 1
= 1
Answered by GauthMath if you like pls heart it and comment thanks
Which of the following algebraic steps will solve the equation 5p= -35 and what is the solution
Answer:
p=-7
Step-by-step explanation:
5p=-35
Divide both sides by 5
5p/5 =-35/5
therefore p=-7
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{5p= -35}\\\\\underline{\huge\text{DIVIDE 5 BOTH SIDES}}\\\\\mathsf{\dfrac{5p}{5p}= \dfrac{-35}{5}}\\\\\large\text{CANCEL out: }\dfrac{5}{5}\large\text{ because that gives you 1}\\\large\text{KEEP: }\dfrac{-35}{5}\large\text{ because that gives you the value of p.}\\\\\large\textsf{p = }\mathsf{\dfrac{-35}{5}}\\\\\mathsf{-35\div5= p}\\\\\large\text{Simplify above and you have your result to the p-value.}\\\\\boxed{\boxed{\huge\text{Therefore your answer is: \textsf{p = -7}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer??? I need it in under 5 mins
Answer:
The answer is 5 units.
Step-by-step explanation:
A circle has a radius of 10 units and is centered at (-9,9). What is the equation of this circle? \sqrt{9
square root of, 98, end square write the equation of this circle.
A circle has an equation of a form,
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Where [tex](a, b)[/tex] is the center and [tex]r[/tex] is the radius.
The coordinates of your circle center are [tex](a,b)=(-9,9)[/tex] and the radius is [tex]r=\sqrt{98}[/tex], so plug that in,
[tex](x-(-9))^2+(y-9)^2=\sqrt{98}^2[/tex]
and simplify to get the equation,
[tex](x+9)^2+(y-9)^2=98[/tex]
Hope this helps :)
A bicycle with 24-inch diameter wheels is traveling at 12 mi/h.
What is the exact angular speed of the wheels in rad/min?
Number rad/min:
How many revolutions per minute do the wheels make?
The answer must be rounded to three decimal places by the way.
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Answer:
1056.000 radians per minute168.068 revolutions per minuteStep-by-step explanation:
The linear speed 12 mi/h translates to inches per minute as follows:
(12 mi/h) × (5820 ft/mi) × (12 in/ft) ÷ (60 min/h) = 12,672 in/min
The relationship between arc length and angle is ...
s = rθ
For a constant radius, the relationship between linear speed and angular speed is ...
s' = rθ'
θ' = s'/r = (12,672 in/min)/(12 in) = 1056 rad/min
There are 2π radians in one revolution, so this is ...
(1056 rad/min) ÷ (2π rad/rev) = 168.068 rev/min
ABCD is rectangle with diagonals AC and BD meeting at point O. Find x if OA = 5x-7 and OD=4x-5
A 13-ounce can of coffee costs $2.73. What is the unit price per pound (1 pound=16 ounces)?
Supervisor: "I need you to increase the number of customers you talk to daily by
20%."
Employee: "I talk to an average of 8 customers per hour during an 8 hour shift so
now I'll need to talk to customers per day."
68
77
85
97
160
NEXT
Answer:
77
Step-by-step explanation:
Currently:
Talk to 8 customers per hour, work 8 hours, so:
Talk to 8*8 = 64 customers.
With the increase:
Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then
64*1.2 = 76.8
Rounding up, 77 is the answer.
can anybody help me with this?
Answer:
Option (a)
Step-by-step explanation:
[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]
Write the piecewise defined function for the total cost of parking in the garage. That is, state the function C(x), where x is the number of hours a car is parked in the garage.
Answer:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
Step-by-step explanation:
Given
See attachment for question
Required
The piece-wise function
From the attachment, we have:
(1) $4/hr for first 2 hours
This is represented as:
[tex]C(x) = 4x[/tex]
The domain is: [tex]0 \le x \le 2[/tex]
(2) $2/hr for next 4 hours
Here, we have:
[tex]Rate = 2[/tex]
The total cost in the first 2 hours is:
[tex]C(x) = 4x[/tex]
[tex]C(2) = 4*2 = 8[/tex]
So, this function is represented as:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex] ----- 2 represents the first 2 hours
So, we have:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex]
[tex]C(x) =8 + 2(x - 2)[/tex]
Open brackets
[tex]C(x) =8 + 2x - 4[/tex]
Collect like terms
[tex]C(x) =8 - 4+ 2x[/tex]
[tex]C(x) =4+ 2x[/tex]
The domain is:
[tex]2 < x \le 2 + 4[/tex]
[tex]2 <x \le 6[/tex]
(3) 0 charges for the last 2 hours
The maximum charge from (2) is:
[tex]C(x) =4+ 2x[/tex]
[tex]C(6) = 4 + 2*6[/tex]
[tex]C(6) = 4 + 12[/tex]
[tex]C(6) = 16[/tex]
Since there will be no additional charges, then:
[tex]C(x) = 16[/tex]
And the domain is:
[tex]6 < x \le 8[/tex] --- 8 represents the limit
So, we have:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
You need a 75% alcohol solution. On hand, you have a 60 mL of a 55% alcohol mixture. You also have 85% alcohol mixture. How much of the 85% mixture will you need to add to obtain the desired solution?
You will need_____ mL of the 85% solution
60 mL=55% alcohol
?mL=85% alcohol
85×60÷55
=92.727 mL
I think do like this....I'm not sure
Hope this help you
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Answer:
120 mL
Step-by-step explanation:
Let x represent the amount of 85% solution needed. Then the total amount of alcohol in the mix is ...
0.55(60) +0.85(x) = 0.75(60 +x)
33 + 0.85x = 45 +0.75x . . . . . . . eliminate parentheses
0.85x = 12 +0.75x . . . . . . . . . .subtract 33
0.10x = 12 . . . . . . . . . . . . . . subtract 0.75x
x = 120 . . . . . . . . . . . . . . multiply by 10
You will need 120 mL of the 85% solution.
write the number 16, 107, 320 in expanded
form.
398383i4irujidifififif
How to multiply
(c+7)(3x-2)
Answer:
3cx - 2c + 21x - 14
Step-by-step explanation:
( c + 7 ) ( 3x - 2 )
= c ( 3x - 2 ) + 7 ( 3x - 2 )
= c ( 3x ) - c ( 2 ) + 7 ( 3x ) - 7 ( 2 )
= 3cx - 2c + 21x - 14
Answer:
3cx-2c+21x-14
Step-by-step explanation:
try to expand it by multiplying everything in the first brackets by every thing in the second brackets.
c(3x-2)+7(3x-2)
3cx-2c+21x-14
I hope this helps
The tree diagram below shows the possible combinations of juice and snack that can be offered at the school fair.
A tree diagram. Orange branches to popcorn and pretzels. Grape branches to popcorn and pretzels. Apple branches to popcorn and pretzels. Grapefruit branches to popcorn and pretzels.
How many different combinations are modeled by the diagram?
6
8
12
32
Answer:
B. 8Step-by-step explanation:
The combinations are:
Orange - 2 (with popcorn and pretzels)Grape - 2 (with popcorn and pretzels)Apple - 2 (with popcorn and pretzels)Grapefruit - 2 (with popcorn and pretzels)Total number of combinations:
4*2 = 8Correct choice is B
there are 8different combinations are modeled by the diagram.
Answer:
Solution given:
orange:2
grape:2
apple:2
grapefruit:2
no of term:4
now
total no. of combination ia 4*2=8
Find the inequality represented by the graph
I'm using khan academy btw
Answer:
Step-by-step explanation:
slope of line through (0,0) and (4,3) =(3-0)/(4-0)=3/4
eq. of line is y-0=3/4(x-0)
y=3/4 x
put x=4
y=2
2=3/4×4
2=3
which is true if 2<3
2<3
so y<3/4 x
