Write a general formula to describe each variation.
The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3
Answer:T² = [tex]\frac{18a^3}{d^2}[/tex]
Step-by-step explanation:Few things to note:
i. direct variation: When a variable x varies directly with another variable y, we write it in this form;
x ∝ y.
This can then be written as;
x = ky
Where;
k = constant of proportionality variation.
ii. inverse variation: When a variable x varies inversely with another variable y, we write it in this form;
x ∝ [tex]\frac{1}{y}[/tex]
This can then be written as;
x = k([tex]\frac{1}{y}[/tex])
Where;
k = constant of proportionality or variation
iii. combined variation: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;
x ∝ ([tex]\frac{y}{z}[/tex])
This can then be written as;
x = k ([tex]\frac{y}{z}[/tex])
Where;
k = constant of proportionality or variation
From the question;
The square of T varies directly with the cube of a and inversely with the square of d.
Note that
square of T = T²
cube of a = a³
square of d = d²
Therefore, we can write;
T² ∝ [tex]\frac{a^3}{d^2}[/tex]
=> T² = k ([tex]\frac{a^3}{d^2}[/tex]) -------------------(i)
Since;
T = 4 when a = 2 and d = 3
We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;
(4)² = k ([tex]\frac{2^3}{3^2}[/tex])
16 = k ([tex]\frac{8}{9}[/tex])
8k = 16 x 9
8k = 144
k = [tex]\frac{144}{8}[/tex]
k = 18
Now substitute the value of k back into equation (i);
T² = 18 ([tex]\frac{a^3}{d^2}[/tex])
T² = [tex]\frac{18a^3}{d^2}[/tex]
Therefore, the general formula that describes the variation is;
T² = [tex]\frac{18a^3}{d^2}[/tex]
Why are unit fractions important?
Answer:
Unit fractions play an important role in modular arithmetic, as they may be used to reduce modular division to the calculation of greatest common divisors. Specifically, suppose that we wish to perform divisions by a value x, modulo y. In order for division by x to be well defined modulo y, x and y must be relatively prime.
Step-by-step explanation:
Two angles are complementary ( the sum of the two angles is 90°). The sum of the first angle plus twice the second angle is 150°. Find the measures of the angles.
Answer:
30 and 60
Step-by-step explanation:
Let x represent the first angle
(x) the sum of the first angle plus twice of the second angle 2(90 - x)
x + 180 - 2x = 150
180 - 150 = 2x - x (we export like terms to the same side of the equation)
30 = x is the measure of the first angle and since the second angle is complementary to this the measure of the second angle is 90 - 30 = 60
What is the y-intercept of the graph of the line whose equation is y = -2/5x + 4?
1) - 5/2
2) - 2/5
3) 0
4) 4
I’ve been stuck on this question for so long I need help with it.
Answer:
4
Step-by-step explanation:
in y=mx+b, the "b" is the y-intercept
Answer:
4
it's in y = mx + b form, where b is the y-intercept
Please answer and explain.
Answer:
x = 13
Step-by-step explanation:
The sum of the exterior angles of a 4 sided polygon is 360
139+ 6x+9x+2x = 360
Combine like terms
139+17x=360
Subtract 139 from each side
17x = 360-139
17x = 221
Divide each side by 17
17x/17 = 221/17
x = 13
determine the value of a in the figure shown
Answer:
d
Step-by-step explanation:
180-149= 31.
31+ 122= 153
180-153= 27
a= 27
ou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required
Answer: the required sample size =1658944
Step-by-step explanation:
When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]
z-value for 99% confidence = 2.576
[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]
Hence, the required sample size =1658944
Paul signs up for a new cell phone plan. He is offered a discount for the first five months. After this period, his rate increases by $8.50 per month. His total cost at the end of the year is $245.50. Paul wrote the following equation to represent his plan. 5x + 7(x + 8.50) = 245.50
Answer:
The first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
Step-by-step explanation:
Since Paul signs up for a new cell phone plan, and he is offered a discount for the first five months, and after this period, his rate increases by $ 8.50 per month, and his total cost at the end of the year is $ 245.50, and Paul wrote the following equation to represent his plan: 5x + 7 (x + 8.50) = 245.50; To determine the value of X, the following calculation must be performed:
5X + 7 x (X + 8.50) = 245.50
5X + 7X + 59.50 = 245.50
12X + 59.50 = 245.50
12X = 245.50 - 59.50
12X = 186
X = 186/12
X = 15.50
Therefore, the first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
Select the points that are solutions to the system of inequalities. Select all that apply A. (-12, 0) B. (1, 2) C. (0, 0) D. (-10, 1)
Answer:
B. (1, 2)
D. (-10, 1)
Step-by-step explanation:
Both points land in the highlighted area.
Hope this helps! :)
Answer:
The correct answer would be
A. (–12, 0) & D. (–10, 1)
In angle ABC, AB = 2.5 m, BC = 3.2 m and AC = 2.9 m. Use the Cosine Law to find
, to the nearest degree.
9514 1404 393
Answer:
∠A ≈ 72°
Step-by-step explanation:
Fill in the given numbers and do the arithmetic.
cos A = (2.9² +2.5² -3.2²)/(2(2.9)(2.5)) = 4.42/14.5
The inverse cosine function is used to find the angle, given its cosine.
A = arccos(4.42/14.5)
∠A ≈ 72°
14. Anna, Bella, Claire, Dora and Erika meet at a party. Each pair who know each other shake hands exactly once.
Anna shakes hands only once, Bella twice, Claire three times and Dora four times. How many people does Erika
shake hands with?
(A) 1
(B)2
(C) 3
(D) 4
(E) 5
Answer:
(B) part is the answer which means he shook hands with 2.
Step-by-step explanation:
Since Dora shook hands four time with: Alan, Bella, Claire, Erik. Then Erik shook hands only with Dora. Claire shook hands three times with Bella, Claire and Dora. Then Bella shook hands with two people Claire and Dora. Now Erik would shook hands only with those who shook hands with him. 2 people Claire and Dora
The required handshake Erika had is given as 2. Option B is correct.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
According to the question,
Dora shake hands 4 times,
So Dora shakes hands with Anna, Bella, Claire, and Erika.
Anna shake hands 1 time,
From the above combination.
Dora shakes hands with Anna,
Implies Anna does not shake hands with Erika,
Clair shakes hands 3 times,
So Clair shakes hands with Bella, Claire, and Erika.
Bella shake hands 2 times,
So Bella shakes hands with Bella and Claire.
From the above reasoning, Erika shakes hands with Dora and Clair.
Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ2
factorise fully 16c^4p^2+20cp^3
Answer:
4cp^2 ( 4c^3+5p
Step-by-step explanation:
See image below:)
The factored form of the expression will be [tex]4cp^2 (4c^3+5p)[/tex]
Factorization:Given the expression 16c^4p^2+20cp^3
Get the factor for each term
[tex]16c^4p^2 = 4 * 4 * c^3 * c * p^2 \\20cp^3= 4 * 5 * c * p^2 * p[/tex]From the factors, you can see that 4cp^2 is common to both terms. Hence the factored form of the expression will be:
[tex]4cp^2 (4c^3+5p)[/tex]
Learn more on factored form here: https://brainly.com/question/25948667
If each 2 cm on the scale drawing below equals 9 feet, what is the actual area of the shape in square units?
Answer: 18 cm
Step-by-step explanation: 9 feet x 2
The length of a rectangle is 4 meters more than the width of the rectangle. The perimeter of the rectangle is 40 meters. What are the length and the width of the rectangle? *
Answer:
Length = 12 m, Width = 8 m
Step-by-step explanation:
Let the width of the rectangle is b.
Length, l = 4+b
The perimeter of the rectangle = 40 m
We know that,
Perimeter of rectangle = 2(l+b)
2(4+b+b) = 40
4+2b = 20
Subtract 2 from boths sides,
2b = 16
b = 8
Width = 8 m
Length = 4+8 = 12 m
Hence, the length and the width of the rectangle is 12 m and 8 m respectively.
which statement is true?
Answer:
The y-intercept of function a is greater than the y intercept of function b
Step-by-step explanation:
function a:
y = 4x + 2
function b:
y = 2x + 1
answer 1 or answer 2?
Answer:
2 Function B
Step-by-step explanation:
Answer:
Function B is greater
Step-by-step explanation:
The gradient of Function B is of 3 = m
Though the gradient of Function A is of 1 = m, obviously being of the smaller size
If you didn't know, gradient is the same as the slope
Hope this helps
What is the slope of the line through (-5, -10) and (-1, 5)
Answer:
Slope = 15/4
Step-by-step explanation:
Use the slope formula and you'll get the same answer.
Hope this helps:)
1 ÷ 7
pls help me
hi)
Answer:
7 lol
Step-by-step explanation:
self explanatory-
but you divide 1 by 7 you get 7
Question 6,7 I needed the answer
Answer:
6.n/4
7.3/4time G or 0.75G
Step-by-step explanation:
6.3m+n/12-m-n/4=3m-3m+n+3n=4n/12=n/4
7.G=0.9a/1.2b G=3/4*a/b
Which of the following figures has reflectional symmetry?
Help !!
Answer:
Figure D. (A)
When you flip the figure across like a mirror, it remains the same shape as the other side. An easy way to determine this is by cutting a line down the middle.
Reflectional symmetry states that if there exists at least one line that divides a figure into two halves such that one-half is the mirror image of the other half.
Edit: Typo!
11
Akhtar gets a bonus of 20% of £70
Karl gets a bonus of £26
Work out the difference between the bonus Akhtar gets and the bonus Karl gets.
help
Answer:
8.8
Step-by-step explanation:
Akhtar's bonus = 20% × £70 = £14
karl's bonus = 20% × £26 = £5.2
Difference = £14 - £5.2 = 8.8
**I'm not sure about the answer sorry, please get it checked.
If 50% of the students in your class are men and 20% of the men have blond hair, which of the following describes the percentage of students in your class who are men with blond hair?
Answer:
10%
Step-by-step explanation:
10% of the Male students have blonde hair
A cone-shaped paper drinking cup is to be made to hold 24 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.)
Answer:
I. Radius, r = 2.90 cm
II. Height, h = 4.10 cm
Step-by-step explanation:
Given the following data;
Volume of cone = 24 cm³
To find the height and radius of the cup that will use the smallest amount of paper;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex] ......equation 1
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the formula, we have;
[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]
Multiplying both sides by 3, we have;
[tex] 108 = \pi r^{2}h[/tex]
Making radius, r the subject of formula, we have;
[tex] r^{2} = \frac {108}{ \pi h} [/tex]
Taking the square root of both sides, we have;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
Mathematically, the lateral surface area of a cone is given by the formula;
[tex] LSA = \pi rl [/tex] ......equation 2
Where;
r is the radius of a cone
l is the slant height of a cone.
To find the slant height, we would apply the Pythagorean' theorem;
[tex] l = \sqrt {r^{2} + h^{2}} [/tex]
Substituting r into the above equation, we have;
[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Substituting the values of r and l into eqn 2, we have;
[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Simplifying further, we have;
[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]
[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]
Next, to find the value of h, we differentiate the above mathematical equation with respect to h;
[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]
Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;
[tex] \frac {dS}{dh} = 0 [/tex]
[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]
Rearranging the equation, we have;
[tex] \pi = \frac {216}{h^{3}} [/tex]
We know that π = 3.142
[tex] 3.142 = \frac {216}{h^{3}} [/tex]
Cross-multiplying, we have;
[tex] 3.142h^{3} = 216 [/tex]
[tex] h^{3} = \frac {216}{3.142} [/tex]
[tex] h^{3} = 68.75 [/tex]
Taking the cube root of both sides, we have;
Height, h = 4.10 cm
Lastly, we find the value of r;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]
[tex] r = \sqrt { \frac {108}{12.88}} [/tex]
[tex] r = \sqrt {8.39} [/tex]
Radius, r = 2.90 cm
The height and radius of the cup that will use the smallest amount of paper is;
Radius = 2.52 cm
Radius = 2.52 cmHeight = 3.58 cm
Let us first state some relevant formulas;
Volume of a cone is;
V = ⅓πr²h
Surface area of a cone is;
S = πrL
Where L is Slant height and has a formula;
L = √(h² + r²)
We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³
24 = ⅓πr²h
πr²h = 72
r = √(72/πh)
Putting √(72/πh) for r in the Slant height equation gives;
L = √(h² + (72/πh))
Thus;
S = π × √(72/πh) × √(h² + (72/πh))
Differentiating with respect to h gives;
dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)
At dS/dh = 0,we will have;
(π - 144/h³) = 0
Thus;
h³ = 144/π
h = 3.58 cm
Thus, from r = √(72/πh);
r = √(72/(π × 3.58))
r = 2.52 cm
Read more at; https://brainly.com/question/4405937
Use the given values to complete each table.
PLEASE HELP.
PLEASE HELP !!! WILL MARK WHOEVER GETS IT RIGHT AS BRAINLIEST !!
Answer:
Last one (x + 4, y - 1).
Step-by-step explanation:
From the point, you go right 4 (going right on a graph is positive).
From there, you go down 1 (going down on a graph is negative).
on an eight-question true-false quiz, a student guesses each answer. What is the proability that the student gets at least one of the answers correct
Answer:
0.9961
Step-by-step explanation:
Number of options per question = 2
P(success), p = 0.5
q = 1 - p = 0.5
Number of trials, n = 8
P(x ≥ 1) = p(x= 1) + p(x=2) +... + p(x = 8)
P(x = x) = nCx * p^x * q^(n-x)
Using a calculator to save computation time :
p(x ≥ 8) = 0.9961
I am one of Jehovah's Witnesses reply if you are to
Answer:
I am
Step-by-step explanation:
What is the slope of the line described by the equation below?
y-5=-3(x - 17)
O A. -3
O B. 3
O c. 5
O D. -5
PLEASE HELP ME
Answer:
A
Step-by-step explanation:
Hi there!
The given equation of the line is in slope-point form, which is y-y1=m(x-x1), where (x1,y1) is a point and m is the slope
the given equation is y-5=-3(x - 17)
-3 is in the place of where m is, so -3 is the slope. Remember that the sign is part of the slope, so it can't be B (3). Therefore, the answer is A
Hope this helps!
Can y’all help me on question 1?! Have a good day everyone!
Answer:
54 square inches
Step-by-step explanation:
9 times 12 is 108. That is the area of a rectangle with the same length and width/height. A right triangle is half of that. So 108/2=54
Hi there!
»»————- ★ ————-««
I believe your answer is:
Option B
»»————- ★ ————-««
Here’s why:
An area of a triangle is half the value of the product of the triangle's base and height.⸻⸻⸻⸻
[tex]\boxed{\text{Area of A Triangle:}}\\\\---------\\\frac{b*h}{2}\\\\\boxed{\text{Key:}}\\\\\text{b - base}\\\text{h - height}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Finding the area of the Triangle:}}\\\\-------------\\\ \frac{9*12}{2}\\\\\rightarrow\frac{108}{2}\\\\\rightarrow \boxed{54}\\\\\text{The area should be 54 square inches.}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Trig how do you do I do not know
9514 1404 393
Answer:
a) 2π radians
b) 10π inches
c) 5/4π inches per minute
Step-by-step explanation:
The formulas are fairly straightforward. Use the given values in each.
a) θ = ωt
θ = (π/4 radians/min)(8 min) = 2π radians
__
b) s = rθ
s = (5 in)(2π radians) = 10π in
__
c) v = s/t
v = (10π in)/(8 min) = 5/4π in/min
Use the net to find the surface area of the regular pyramid.
Answer:
D
Step-by-step explanation:
Base perimeter = side x 5 = 8 x 5 = 40 cm
LA = (base perimeter x slant height)/2 = (40 x 9)/2 = 180 cm^2
SA = base area + lateral area = 110.1 + 180 = 290.1 cm^2