Answer:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
Step-by-step explanation:
Solve for Q:
T = sqrt((P Q)/R) - Q R^2
T = sqrt((P Q)/R) - Q R^2 is equivalent to sqrt((P Q)/R) - Q R^2 = T:
sqrt((P Q)/R) - Q R^2 = T
Add Q R^2 to both sides:
sqrt((P Q)/R) = Q R^2 + T
Raise both sides to the power of two:
(P Q)/R = (Q R^2 + T)^2
Expand out terms of the right hand side:
(P Q)/R = Q^2 R^4 + 2 Q R^2 T + T^2
Subtract Q^2 R^4 + 2 Q R^2 T + T^2 from both sides:
(P Q)/R - Q^2 R^4 - 2 Q R^2 T - T^2 = 0
Collect in terms of Q:
-Q^2 R^4 - T^2 + Q (P/R - 2 R^2 T) = 0
Divide both sides by -R^4:
Q^2 + T^2/R^4 - (Q (P/R - 2 R^2 T))/R^4 = 0
Subtract T^2/R^4 from both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 = -T^2/R^4
Add (P/R - 2 R^2 T)^2/(4 R^8) to both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 + (P/R - 2 R^2 T)^2/(4 R^8) = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Write the left hand side as a square:
(Q - (P/R - 2 R^2 T)/(2 R^4))^2 = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Take the square root of both sides:
Q - (P/R - 2 R^2 T)/(2 R^4) = sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt((P^2)/(4 R^10) - (P T)/(R^7)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4))
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Answer: Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
HELP PLZ! THIS IS TIMED.
Answer:
[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]
Step-by-step explanation:
Given the geometric sequence
[tex]a_1=\dfrac{2}{3}\\ \\a_n=3a_{n-1},[/tex]
then
[tex]a_1=\dfrac{2}{3}\\ \\a_2=3a_1=3\cdot \dfrac{2}{3}=2\\ \\a_3=3a_2=3\cdot 2=6\\ \\a_4=3a_3=3\cdot 6=18\\ \\a_5=3a_4=3\cdot 18=54\\ \\...[/tex]
Hence,
[tex]b_1=a_1=\dfrac{2}{3}\\ \\b_2=a_3=6=\dfrac{2}{3}\cdot 9\\ \\b_3=a_5=54=\dfrac{2}{3}\cdot 9^2\\ \\...[/tex]
Thus, the explicit formula is
[tex]b_n=\dfrac{2}{3}\cdot (9)^{n-1}[/tex]
sally works 40 hours a week and makes $10 an hour, but her kids are in child care each day, and the day care center charges her $20 per day. If you deduct her childcare expenses, how many dollars per hour does she actually make?
Answer:
She makes $60 per hour
Step-by-step explanation:
There are 5 days in a week and 40 divided by 5 is 8 and 8x10=80 and 80 subtracted by 20 gives you 60.
Final answer:
After deducting childcare expenses, Sally's actual hourly wage is $7.50 per hour.
Explanation:
The original question is about calculating Sally's actual hourly wage after accounting for childcare expenses. Sally works 40 hours a week and earns $10 per hour. However, she incurs a cost of $20 per day for childcare. Assuming she works 5 days a week, her weekly childcare expenses are $20 x 5 = $100. Therefore, her weekly take-home pay after childcare is (40 hours x $10/hour) - $100 = $400 - $100 = $300. Now, to find Sally's actual hourly wage after childcare expenses, divide her take-home pay by the number of hours worked: $300 / 40 hours = $7.50 per hour.
10. Write an equation in slope-intercept form for a line that is perpendicular to the line
y= 2/5x +1
Step-by-step explanation:
Equation of given line is:
[tex]y = \frac{2}{5} x + 1 \\ equating\: it \: with \: y = m_1x + c, \:we\:find \\ slope \: of \: given \: line \: (m_1 )= \frac{2}{5} \\ y - intercept \: (c) = 1 \\ let \: the \: slope \: of \: required \: line \: be \: m_2. \\ \therefore \: m_1 \times m_2 = - 1..( \because \: lines \: are \: \perp) \\ \therefore \: \frac{2}{5} \times m_2 = - 1 \\ \therefore \:m_2 = - \frac{5}{2} \\ \\ equation \: of \: required \: line \: in \: slope \: \\intercept \: form \: is \: given \: as: \\ y = m_2x + c \\ \huge \orange{ \boxed{\therefore \: y =- \frac{5}{2}x + 1}} \\ [/tex]
cotA/tanA simplify each question
[tex]\bf \cfrac{cot(A)}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{tan(A)}\implies \cfrac{~~\frac{1}{tan(A)}~~}{\frac{tan(A)}{1}}\implies \cfrac{1}{tan(A)}\cdot \cfrac{1}{tan(A)} \\\\\\ \cfrac{1}{[tan(A)]^2}\implies \cfrac{1}{tan^2(A)}\implies \cfrac{1^2}{tan^2(A)}\implies \left( \cfrac{1}{tan(A)} \right)^2\implies cot^2(A)[/tex]
Final answer:
To simplify cotA/tanA, we recognize that cotA is the reciprocal of tanA. The expression simplifies to cosA^2/sinA^2, which can also be written as cotA^2.
Explanation:
To simplify the expression cotA/tanA, we can use the fundamental trigonometric identities that relate the cotangent and tangent functions. The cotangent function, cotA, is the reciprocal of the tangent function, tanA, which means cotA = 1/tanA. Therefore, when we simplify cotA/tanA, we are effectively dividing the reciprocal of the tangent function by the tangent function itself.
The simplification would thus be:
cotA/tanA = (1/tanA)/tanA = 1/(tanA^2)Since tanA = sinA/cosA, the expression can be rewritten as[tex]1/((sinA/cosA)^2)[/tex]Therefore, cotA/tanA simplifies to [tex]cosA^2/sinA^2, or cotA^2.[/tex]at sal's carshop the salesman make 15 commission on every car they sell. If the dealership buys a car for $16,235 and the salesman sells the car for $22,245 how much is their commission ?
The salesman's commission for selling a car at Sal's car shop is $901.50.
To calculate the salesman's commission for selling a car at Sal's car shop, we must first determine the sale price's profit margin over the dealership's purchase price. The profit is found by subtracting the purchase price ($16,235) from the selling price ($22,245).
Profit = Selling Price - Purchase Price
Profit = $22,245 - $16,235
Profit = $6,010
Next, we calculate the commission by taking 15% of the profit:
Commission = Profit * Commission Rate
Commission = $6,010 * 0.15
Commission = $901.50
Therefore, the salesman's commission for selling the car is $901.50.
Simplify by combining like terms. -4a + b + 9 + a -b-3 plz help !
Answer:
- 3a + 6
Step-by-step explanation:
subtract and add like items together like
- 4a + a = -3a
b-b= 0
and
9-3 = 6
so the answer is
-3a +6
A volleyball has a surface area of about 227 square inches. Which of these could be the radius of the volleyball
Final answer:
To find the radius of the volleyball given its surface area, use the formula for the surface area of a sphere (4πr²) and solve for r. The approximate radius of the volleyball would be 4.25 inches based on a surface area of 227 square inches.
Explanation:
The surface area of a sphere formula is 4πr², where r is the radius. Given that the volleyball's surface area is about 227 square inches, we can find the radius by rearranging the formula as follows:
4πr² = 227r² = 227/(4π)r ≈ √(227/(4π)) ≈ 4.25 inchesThe dimensions of a box are (x + 1), (4x - 2), and
(3x + 4). What is the volume of the box?
Answer:
Volume of box = 12x³ + 10x² - 14x - 8
Step-by-step explanation:
Volume of box = Length × Width × Height
Volume of box = (x + 1) (4x - 2) (3x + 4)
Volume of box = (4x² - 2x + 4x - 2) (3x + 4)
Volume of box = (4x² - 2x - 2) (3x + 4)
Volume of box = 12x³ + 10x² - 14x - 8
Answer:
12x^3+22x^2-2x-8
Step-by-step explanation:
i took the test ^^
Kara works at a fine jewelry store and earns commission on her total sales for the week. Her weekly paycheck is $6,500 including her salary which is $1,000. Her sales for the week totaled to $45,000. Express her rate of commission as a percent rounded to the nearest whole number.
Answer:12.2%
Step-by-step explanation:
Her total paycheck minus her salary = the commission amount
So
6500 - 1000 = 5500
So....her commission as a percentage of sales = 5500/ 45000 = about 12.2%
add blank to each side of x^2-8x=9
Step-by-step explanation:
To complete the square, take half of the second coefficient, square it, then add the result to both sides.
(-8/2)² = (-4)² = 16
x² − 8x + 16 = 9 + 16
Solving:
(x − 4)² = 25
x − 4 = ±5
x = 4 ± 5
x = -1 or 9
Answer:
part 1: x^2 + -8 x=9
part 2: Add 16 to each side
part 3: (x-4)^2 =25
part 4: -1 and 9
There are 15 vocabulary words in Week I. There are 8 more vocabulary words in Week 2 than in Week I. How many words are there in both weeks?
Answer:
There are 38 vocab. words in both weeks
Step-by-step explanation:
There are a few steps to this problem:
First, we know that there are 15 vocab. words in week 1.
Then, in week 2 there are 8 more words than in week 1. So that means 15+8 which equals 23.
Finally, we know that there were 15 words in the first week, and 23 in the second week. So now how many words were there in both weeks? To answer that, you add the number of words in the first week, to the number of words to the second week.
23 + 15 = 38 words total in both weeks
Sally baked 60 cookies for a bake sale. If 12 of her cookies sold in the first hour. What percent of her cookies sold
What are the solutions to the equation x2 + 4x + 5 = 0?
Answer:
no answer
Step-by-step explanation:
x^2+4x+5=0
(x+2)^2+1=0
(x+2)^2=-1
this is impossible,
so this equation has no answer
Answer:
Step-by-step explanation:
What is the solution to this system of equations?
2x - y = 8
x + y = 4
A. (2, -4)
B. (4, 0)
C. (6, 4)
D. (12, -8)
Answer:
Answer is B. (4,0)
Step-by-step explanation:
2x - y = 8
x + y = 4
solve the equation
2x - y = 8
y = 4 - x
substitute the value of y into the equation
2x - (4 - x) = 8
solve the equation
x = 4
substitute the value of x into an equation
y = 4 - 4
solve the equation
y = 0
answer is (4,0)
Find x, then find the measurement of both angles.
A: x = 20; both angles measure 112 degrees
B: x = 20; both angles measure 110 degrees
C: x = 30; both angles measure 114 degrees
D: x = 30; both angles measure 118 degrees.
Answer:
C:x=30:both angles measure 114 degrees
Step-by-step explanation:
in 2 parallel lines with a transversal, the marked angles are alternate exterior angles, which means that both angles are congruent(equal)
ur equation is: 2x+54=4x-6
60=2x
x=30
we have now eliminated options a and b
CHECK:
2*30+54=60+54=114
4*30-6=120-6=114
114=114
PLEASE MARK BRAINLIESTThe two circles shown above have radii of 2 in. and 6 in.
What is a circum A over b?
Answer:
1/3
Step-by-step explanation:
For the first circle 2 x 2in = 4 to find diameter
4 x 3.14 = 12.56
6in x 2 = 12
12 x 3.14 = 37.68
simplify
12.56/37.68
6.28/18.84
3.14/9.42
So the answer is 1/3 since 3.14 x 3 = 9.42
Also since the radius is 3 times longer
Answer:
1/3
Step-by-step explanation:
Simone has 5 employees in her flower shop. each employee works 6 4/15 hours per day.how many hours in total do the 5 employees work per day
Help please, lots of points! Give explanation!
Yo sup??
To solve the 31st one just imagine and add all the cubes.
Start from the left side and keep on counting in your mind.
You will end with 25 cubes
For the 32nd one you can just draw a chart to know it.
Since this man has no bro or sis he is a single child.
The man in the picture is himself.
He is pointing to his picture and saying that 'that guys dad is my dad' and since he's a single child therefore its him itself.
So the answer is that man itself.
For the last one again try to draw a chart and connect the dots with the information.
So Lakisha had a bull dog. Since she has a bull dog she can't have Paul as her brother because paul is the brother of that girl who has her pet as horse.
This means paul is the brother of either Angela or Jessica. But its given that the brother of Angela is Ken therefore Paul is the brother of Jessica.
So the relations are
Lakisha-Bull dog, Stephen
Angela-Ken,XXXXX
Jessica-horse,Paul
Hope this helps.
Write an equation to solve for h. Check your answer.
__________________
| |
| | h Area = 96 ft
| | A = bh
----------------------------------
8 ft h = __________
A/b= h
h=12 ft
Step-by-step explanation:
The formula for area is given as ;
A=b*h
A/b= h .................equation for h
If Area=96 ft² and b =8 then h=96/8 =12 ft
Learn More
Formula variation ;https://brainly.com/question/10584854
Keywords : equation, solve,
#LearnwithBrainly
There are 32 peanuts in a bag Elliot takes 25% of the peanuts from the bag . Then Zaire takes 50% of the remaining peanuts. How many peanuts are left in the bag
Answer: 8
Step-by-step explanation:
32/2 (50%) = 16
32/4 (25%) = 8
Add these together and you'll get 24. Subtract that from the initial amount and you'll have 8.
Bob drove 30 and one third miles towards his house in one third an hour. About how long will the entire 100 mile trip take at this speed?
It would take [tex]1\frac{9}{91}[/tex] hour to complete the entire trip.
Step-by-step explanation:
Given,
Distance covered = [tex]30\frac{1}{3}[/tex] = [tex]\frac{91}{3}[/tex] miles
Time taken =[tex]\frac{1}{3}[/tex] hour
We know that;
Distance = Speed * Time
[tex]\frac{91}{3} = Speed*\frac{1}{3}[/tex]
Multiplying both sides by 3
[tex]3*\frac{91}{3} = Speed*\frac{1}{3}*3[/tex]
91 = Speed
Bob was driving at 91 miles per hour.
Now,
Distance to cover = 100 miles
Time required = x
Distance = Speed * Time
[tex]100=91x\\91x=100[/tex]
Dividing both sides by 91
[tex]\frac{91x}{91}=\frac{100}{91}\\x=1\frac{9}{91}[/tex]
It would take [tex]1\frac{9}{91}[/tex] hour to complete the entire trip.
Keywords: fraction, distance
Learn more about distance at:
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- Cindy spent $6 on her meal. She spent $4
on a sandwich and the rest on a smoothie.
How many smoothies could be bought
with $124?
Answer:
She can buy 62 smoothies
Step-by-step explanation:
What is 671 divided by 4 with remainders
What is the algebraic expression for b divided by 9
Answer:b/9
Step-by-step explanation: the expression b divided by 9 is b/9
Answer: b ÷ 9
Step-by-step explanation:
Well, since the question is to write an expression for b divided by 9, you just write b divided into 9 parts.
NOTE: Remeber, an expression is an equation but WITHOUT an answer.
Hope this helps! Please feel free to correct me if I'm wrong!
(12) Geographers use negative numbers to represent points below sea level and positive numbers for points above 1
level. A penguin dove 5 meters below sea level to catch fish for his family, who are sitting on an Iceberg 1 meter above
sea level. What is the difference in elevation between the family and the penguin?
Please!
Difference in elevation is 6 meters.
Answer: -4
Step-by-step explanation: -5 + 1= -4
A customer purchased a top that was 16.88 and we have a 50% off sale. What would be the sale price of that top?
The sale price of the top after the 50% off discount is $8.44.
To calculate the sale price of the top with a 50% discount, follow these steps:
Step 1: Find the discount amount. The discount amount is 50% of the original price. To calculate this, multiply the original price by 0.50 (50% as a decimal):
Discount amount = 16.88 * 0.50 = 8.44
Step 2: Subtract the discount amount from the original price to find the sale price:
Sale price = Original price - Discount amount
Sale price = 16.88 - 8.44 = 8.44
When the customer applies the 50% off discount, they will pay $8.44 for the top, which is half of the original price of $16.88. This means they are getting a 50% discount on the original price.
To learn more about price click on,
https://brainly.com/question/31353944
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Tomàs is thinking of a number. Thirteen fewer than three times his number is 305. Of what number is Tomás thinking?
Answer:
106
Step-by-step explanation:
Given:
Thirteen fewer than three times his thinking number is 305.
Question asked:
What number is Tomás thinking ?
Solution:
Let Toma's thinking number be [tex]x[/tex]
As 13 fewer than 3 times his thinking number is 305.
The equation will be:
[tex](3 times of x) - 13 = 305[/tex]
[tex]3x - 13 = 305[/tex]
Adding both side by 13
[tex]3x = 318\\[/tex]
Dividing both side by 3
[tex]x = 106[/tex]
Thus, Tomàs was thinking of a number is 106
Which of the following is a complex number?
-7
2 + StartRoot 3 EndRoot
4 + 9i
Pi
Answer:
4 + 9i
Step-by-step explanation:
a complex number by definition must have a real and imaginary components
imaginary components are denoted by the letter i, where i = √(-1)
the only choice with a real and imaginary components is 4 + 9i
Answer:
4 +9i
Step-by-step explanation:
trust me bro
Gumballs are 2 for 8 cents. How many gumballs can I get for 32 cents
Answer: you can get 8 gum balls
Step-by-step explanation:
2) On a map two points are 7cm apart. The map has a scale of 1:10000. Work out the
actual distance. Give your answer in km.
Answer:
0.7 km
Step-by-step explanation:
Actual distance in cm = 7(10000)
= 70 000 cm
Actual distance in km = 0.7 km
Answer:
0.7
Step-by-step explanation: