Given that p varies directly as q and
[tex] \sqrt{q} [/tex]
varies inversely with t², show how p varies with t.
Answers
Answer:
Above is the step-by-step solution
![Given That P Varies Directly As Q And [tex] \sqrt{q} [/tex]varies Inversely With T, Show How P Varies](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/bkqFIgLAgyqByMtai47MyZFa4QGAYYyy.jpeg)
[tex]\\ \sf\longmapsto p\propto q [/tex]
[tex]\\ \sf\longmapsto p=kq[/tex]
Divide both sides by q[tex]\\ \sf\longmapsto \dfrac{p}{q}=k[/tex]
[tex]\\ \sf\longmapsto q=\dfrac{p}{k}[/tex]
Now
[tex]\\ \sf\longmapsto p\propto \sqrt{q}[/tex]
[tex]\\ \sf\longmapsto p\propto \dfrac{1}{t^2}[/tex]
[tex]\\ \sf\longmapsto p=\dfrac{k}{t^2}[/tex]
Substitute√q[tex]\\ \sf\longmapsto \sqrt{q}=\dfrac{k}{t^2}[/tex]
[tex]\\ \sf\longmapsto q=\dfrac{k^2}{t^4}[/tex]
Substitute q=p/k[tex]\\ \sf\longmapsto \dfrac{p}{k}=\dfrac{k^2}{t^4}[/tex]
[tex]\\ \sf\longmapsto p=\dfrac{k}{t^4}[/tex]
[tex]\\ \sf\longmapsto p\propto \dfrac{1}{t^4}[/tex]
Done
Related Questions
Tangela bought 12 cans of sodas for $5.40
Answers
Answer:
324
Step-by-step explanation:
Answer:
0.45 for one can of soda
Step-by-step explanation:
If you want to know the price for one soda all you have to do is divde.
12 ÷ 5.40 = 0.45
So, one soda can is $0.45! Have a great day friend! :D
if i get 1 pack of pepsi bottles 8-pack how much would it be if it i can get 3 for $12.88?
Answers
Answer:
38.64
Step-by-step explanation:
If 3 = 12.88
Then Just do 12.88+12.88=25.76 which also equal 6. Then 12.88/2=6.44
so 25.76+6.44+6.44=38.64
Therefore it would be 38.64.
I'm not sure but base on the math above I think the answer is 38.64
4(x + 3) + 3x = 24
Step by step please
Answers
Answer: 12/7
Step-by-step explanation: steps in pic, hope this helps!
witch points has have a distance of 3 units from point S
Answers
a path forms a diagonal of a rectangular city park. a bench is placed along the path at a point that is closest to the fountain. this point is 30 yards from one end of the path and 50 yards from the other end of the path what is the distance from the bench to the fountain to the nearest yard
Answers
The answer: 39 yards
Sorry, ignore the other question I had on here, that was a typo. How do you find the positive/negative intervals of f(x) = 3/(x + 5) ? Please show in full detail!!
Answers
Answer:
Positive interval: x is in (-5, infty)
Negative interval: x is in (-infty, -5)
Step-by-step explanation:
A fraction is positive when the numerator and denominator have the same sign. Since the numerator is positive in this case, the fraction will be positive when it's denominator is also positive. Thus, we need to solve x+5>0. Subtracting 5 on both sides gives x>-5.
Positive interval: x is in (-5, infty)
A fraction is is negative when the numerator and denominator have the different signs. Since the numerator is positive in this case, the fraction will be negative when it's denominator is negative. Thus, we need to solve x+5<0. Subtracting 5 on both sides gives x<-5.
Negative interval: x is in (-infty, -5)
A fraction doesn't have an output when it's denominator is 0. That is, in this case when x+5=0 which is when x is -5.
decrease £67 by 26% give your answer in pounds
Answers
Answer:
£ 49.58
Step-by-step explanation:
26% of 67 = 0.26 * 67 = £17.42
67 - 17.42 = £49.58
Now, you multiply
.74x67
The answer will be
£49.58
Hope this helps!!
2. Three vertices of a parallelogram are
given as coordinates (-4, 2), (-2, 4), and
(1, -3) in the graph. Which coordinates
best represent the location of the fourth
vertex of the parallelogram?
o
F. (3, 1)
G. (3, -1)
H. (1, -3)
1. (-1,3
HELPP MEEE PLSSS
Answers
Answer:
I think g would be correct
14. Write an equation for the line in slope-intercept form.
Answers
Answer:
y equals -2x plus 8
Step-by-step explanation:
if a woman sells bitcoins for £42000 which is 12%more than she originally bought them for then calculate the original value of her bitcoins
Answers
136-284=37
136%
I have no clue how to do any of this please help
Answers
Answer:
help with what there nothing there?
what do u need help with?
Hey if someone can help me I'd appreciate it please show your work.
Answers
Answer:
Step-by-step explanation:
Umm what is your question u did not add it?
16. The measures of the acute angles of a right triangle have a ratio of 2 :7.
What is the measure of the smaller angle?
Answers
Answer:
The smaller angle is 20 degrees.
Step-by-step explanation:
A triangle's interior angles must have a sum of 180 degrees. Hence the two acute angles must have a sum of 180-90=90 degrees.
Say that the angles have 2x and 7x length:
2x+7x=90
9x=90
x=10
Hence the acute angles have degrees 2*10=20, 7*10=70.
The smaller angle is 20 degrees.
Hope this was helpful!
Translate the sentence into an inequality.
Twice the difference of a number and 7 is at most 30.
Use the variable w for the unknown number.
Answers
Answer:
[tex]2(w-7) < 30[/tex]
Step-by-step explanation:
Twice is translate as multiply by 2The different is the subtraction between [tex]w[/tex] and 7at most 30 is equal to say that can't be greater than 30Combine each step give us the next expression: [tex]2(w-7) < 30[/tex]
Answer:
2w+14<(with the line under the <)30
Step-by-step explanation:
5 (m - 3) = 40
What do 5m and m represent?
(Quick Question I NEED REAL QUICK!)
(Thanks)
Answers
[tex]5(m -3 ) = 40 \\ = > 5m - 15 = 40 \\ = > 5m = 40 + 15 \\ = > 5m = 55 \\ = > m = 11[/tex]
Therefore, m = 11
5m = 5 × 11 = 55
Answers5m is 55, m is 11.
Hope it helps.
Do comment if you have any query.
Answer:
m=11
5m=55
Step-by-step explanation:
To find the answer to this question, isolate m. Do this by using the properties of equality.
First, distribute the 5 to the terms within the parentheses
5m-15=40Then, add 15 to both sides
5m=55Next, divide both sides by 5
m=11This gives you the solution to both questions. If you want to check the answer, simply plug the variable back in. This gives you, 5(11-3)=40. Once solved this equals 40=40. Therefore, 11 is correct.
Consider a graph of the equation y = −3x + 4. What is the y-intercept? 4 −4 3 −3
Answers
Answer:
The y-intercept is 4
Step-by-step explanation:
in y=mx+b, the b will always be your y-intercept
Determine whether the lines are parallel, perpendicular, or neither.
2x+y=6
y=1/2x−7
Answers
Answer:
Step-by-step explanation:
2x + y = 6
y = -2x + 6
Comparing this with y = 1/2x - 7
Multiplying the 2 slopes:
-2 * 1/2
= -2/2
= -1
- this means that the 2 lines are perpendicular.
help me!
A
B
C
D
E
F
Answers
Answer: g
Step-by-step explanation:
solve pls brainliest
Answers
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
How many classes would Gina need to take for the total cost to be the same at both dance studios?
10
15
100
150
Answers
Answer:
The correct answer is A: 10
Step-by-step explanation:
Same Question : https://brainly.com/question/17110602
1. Nancy works at a Dunkin Donut. The coffee maker has the ability to make 64oz of coffee. If
one coffee maker is half full, and coffee is brewed at a rate of 2oz per minute.
a. Write an equation to represent the total amount of coffee, c, in the coffee makers after t
minutes of brewing. (2 points)
b. How much coffee is there after 10 minutes of brewing? (2 points)
Answers
a = 2t+32=c
b= 2*10=20+32=52oz of coffee
I think this is right
a
What is the equation of the line that passes through the point (3, 2) and has a slope
of 2/3?
Answers
Answer:
y=2/3x
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (3,2) and has a slope of 2/3
We can write the equation of the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
Since we are already given the slope, we can substitute it into the equation as m
y=2/3x+b
Now we need to find b
Since the equation passes through the point (3,2), we can plug its values into the equation to solve for b
Substitute 3 as x and 2 as y into the equation:
2=2/3(3)+b
Multiply
2=2+b
Subtract 2 from both sides
0=b
Substitute 0 as b into the equation
y=2/3x+0
Simplify:
y=2/3x
Hope this helps!
I need help with this please! It’s due tonight and I don’t know.
Answers
Answer:
b
Step-by-step explanation:
Which list shows all the factors of 72?
A. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
B. 1, 2, 3, 4, 6, 9, 12, 18, 24, 36, 72
C. 1, 2, 3, 4, 5, 6, 8, 9, 12, 18, 24, 36, 72
D. 1, 2, 3, 4, 6, 7, 8, 9, 12, 18, 24, 36, 72
PLS HELPP :)
Answers
( xy-1 )^ 2 - ( y-1 ) ^2
help pleaseeeeeeeeeeee
Answers
[tex](xy-1)^2-(y-1)^2\\\\=(xy - 1 - y+1)(xy-1+y-1)~~~~~~;[a^2-b^2 = (a-b)(a+b)]\\\\=(xy-y)(xy+y-2)\\\\=y(x-1)(xy+y-2)[/tex]
Someone please help me. I will give Brainliest. No links, please.
Answers
Answer:
SAS - If a two sides and the angle between them are congruent to another two sides and the angle between them, the triangles are congruent
two sets of congruent sides, a set of congruent angles between the sides
ASA - If two angles and the side between them are congruent to another two angles and the side between them, the triangles are congruent
two sets of congruent angles, a set of congruent sides between the angles
AAS - If two angles and a side next to them are congruent to another two angles and the side next to them, the triangles are congruent
two sets of congruent corresponding angles, a pair of congruent sides next to the angles
HL - If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the two triangles are congruent, and the other leg of the two right triangles are congruent.
two congruent hypotenuses and two congruent legs of a right triangle
Step-by-step explanation:
(pls help quick and explain how you got the answers for brainliest)
Answers
You only have to apply the theorem of Pythagoras here. Remember the square on the hypotenuse (the longest side) is equal to the sum of the squares on the other two sides :
1. AB is the hypotenuse, so, according to the theorem we can write :
AB² = AC² + CB²
c² = 5² + 4²
c²= 25 + 16
c² = 41
applying the square root of 41 we get :
c ≈ 6.40 rounded to the hundred
The next cases are exactly the same thing so there is no need for explanation :
2.
AB is the hypotenuse here because it is the biggest side clearl :
AB² = AC² + CB²
25² = 15² + b²
Thus
b² = 25² - 15²
we just subtracted 15² on each side of the equation
b² = 625 - 225
b² = 400
applying the square root of 400 we get
b = √400 = 20
So AC = 20
3. The longest side is clearly AB = 60
So
AB² = AC² + CB²
60² = 40² + a²
subtracting 40² on each side of the equation we get :
a² = 60² - 40²
I let you finish this using your calculator and doing exactly like the previous cases
4.
AB is the hypotenuse,
AB² = AC² + CB²
23² = b² + 14²
Subtracting 14² from each side of the equation we get
b² = 23² - 14²
5.
AB is the biggest side :
AB² = AC² + CB²
29² = 23² + a²
We subtract 23² on each sides of the equation :
a² = 29² - 23²
You can finish with your calculator
6.
AB² = AC² + BC²
78² = b² + 30²
subtraction...
b² = 78² - 30²
Good luck :)
Need help on this! Please help
Answers
Answer:
PDR= 127
Step-by-step explanation:
10-(-x)=-5
How do I find out what x is
Answers
Answer:
x=-15
Step-by-step explanation:
10-(-x)=-5
10+x=-5
x=-5-10
Answer:
x = -15
Step-by-step explanation:
A negative times a negative equals a positive, so it's just positive x. After that, isolate the variable.
AYUDAAA PORFAVOOOOOOR!!
Answers
Answer:
4
Step-by-step explanation:
Answer:
La respuesta seria 3 espero que esto ayude
Step-by-step explanation: