Answers
========================================================
Explanation:
Let's say we had a circle with radius 5
It's area would be
A = pi*r^2
A = pi*5^2
A = 25pi
Now let's increase this by a factor of 4. We'll multiply the area by 4
new area = 4*(old area) = 4*(25pi) = 100pi
Now, we'll use this area value to find what the radius must be
A = pi*r^2
100pi = pi*r^2
100 = r^2
r^2 = 100
r = sqrt(100)
r = 10
The old radius r = 5 jumps to r = 10 so that the area quadruples.
We see that the radius has doubled. This must also mean the perimeter around the circle, aka circumference, must also have doubled.
C = 2*pi*r = 2*pi*5 = 10pi = old circumference
C = 2*pi*r = 2*pi*10 = 20pi = new circumference
This is directly because r has been doubled
-------------
Here's one way to think of why this works:
Consider a square of side lengths 3. It's area is 3*3 = 9.
If we double the sides, then we have a 6 by 6 square of area 6*6 = 36.
Note the jump from 9 to 36 is "times 4". This multiplier 4 is from each side doubling and we have 2*2 = 4.
If you were to triple each side, then the area multiplier would be 3*3 = 9
Multiplying each side by k leads to an area multiplier of k^2.
Related Questions
Evaluate each using the values given.
m-((-3) + p)-q; use m= 10, p=-6, and q = 10
Answers
Answer:
9
Step-by-step explanation:
10-((-3) + -6)-10
10-(-9)-10
10+9-10
9
KBL Ltd. entered into an agreement to lease a vehicle from Morgan Ltd.: Cash price of the vehicle Kshs 20.000 Lease payments: 5 instalments of Kshs 5.142 paid in arrears Required: How much of this finance charge will appear in each year's profit and loss expense in the lessee's books using the actuarial method? (10 Marks)
Answers
Finance charge is the amount it costs of borrowing money
The finance charge that will appear in each year's profit and loss expense in the lessee's books are;
[tex]\begin{array}{|c|cc|}\mathbf{Year}&&\mathbf{Finance \ Charge \ (Kshs)}\\&&\\First&&1.8\\&&\\Second&&1.499\\&&\\Third&&1.171\\&&\\Fourth&&0.814\\&&\\Fifth&&0.424\end{array}\right][/tex]
The total financial charge = 5 × 5.142 - 20.000 = 5.71
The annual percentage rate, APR, of an instalment payment is given as follows;
[tex]\dfrac{(1 - (1 + r)^{-5}}{r} \times 5.142 = 20.000[/tex]
Solving using a graphing calculator gives;
r = APR ≈ 0.09 = 9%
The calculation for charges each year is as follows:
Payment interest for the first instalment = 20 × 9% = 1.8
The principal of the first payment = 5.142 - 1.8 = 3.342
The loan balance = 20 - 3.342 = 16.658
Payment interest for the second instalment = 16.658 × 9% = 1.49922
Second payment principal = 5.142 - 1.49922 = 3.64278
Loan balance = 16.658 - 3.64278 = 13.01522
Payment interest for the third instalment = 13.01522 × 9% = 1.1713698
Third payment principal = 5.142 - 1.1713698 = 3.9706302
Loan balance = 13.01522 - 3.9706302 = 9.0445898
Interest for the fourth payment = 9.0445898 × 9% = 0.814013082
Fourth payment principal = 5.142 - 0.814013082 ≈ 4.327986918
Loan balance = 9.0445898 - 4.327986918 = 4.716602882
Fifth payment interest = 4.716602882 × 9% = 0.42449425938
Fifth payment principal = 5.142 - 0.42449425938 ≈ 4.718
Therefore, we have;
[tex]\begin{array}{|c|cc|}\mathbf{Year}&&\mathbf{Finance \ Charge \ (Kshs)}\\&&\\First&&1.8\\&&\\Second&&1.499\\&&\\Third&&1.171\\&&\\Fourth&&0.814\\&&\\Fifth&&0.424\end{array}\right][/tex]
Learn more about the actuarial method here:
https://brainly.com/question/15504405
What is the volume of the following rectangular prism?
Answers
Answer:
[tex]volume \: of \: rectangular \: prism = base \: area \: \times height \\ \\ = length \times width \times height[/tex]
What is the value of X minus Y if x equals 9 and Y equals -20
Answers
doneeee
to divide fractions invert the second fraction and multiply
True
Flase
Answers
Answer:
TrueStep-by-step explanation:
Example of dividing fraction:Givens: 1/2 and 3/61/2 ÷ 3/6= 1/2 × 6/3= 6/6= 1[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Pedro is helping refill ketchup bottles at his uncle's diner. He has a huge container with 2
gallons of ketchup, which he distributes evenly among 15 bottles.
How much ketchup goes in each bottle?
Write your answer as a proper fraction or miye
mbar
Answers
Answer:
estuvo muy Bien jwjejehebqkwjshhshshshhebwwhwbhwhwuwjwywgegevwhwvwgww
Answer:
Naosei
Step-by-step explanation:
Moly and Lynn both set aside money weekly for their savings. Molly already has $650 set aside and adds $35 each week. Lynn already has $825
set aside but acids only 515 each week. Which inequality could they use to determine how many weeks, it will take for Mollys savings to
exceed Lyon's savings?
Answers
Answer:
650+35w>825+15w
Step-by-step explanation:
if two adjacent sides of rectangle having perimeter 21 cm are in the ratio 3:4 what is the area of the rectangle is ...cm ?
Answers
Given,
l/b=3/4
=> l = 3b/4
We have,
P = 2(l+b)
=> 21 = 2(3b/4 + b)
=> 21*2= 7b
=> b = 6cm
Similarly,
l = 4.5cm
Thus, Area = l*b
=> Area = 4.5*6
=> Area = 27cm^2
On a scatter plot, what is the difference between a positive and a negative correlation
Answers
Answer:
Positive correlation means that as the first variable increases, the second variable increases as well. ... Negative correlation would mean that as one variable increases, the second variable decreases. Negative correlation corresponds to points that move down as you go from left to right on your scatter plot
Hope this helps you!
help me again Scooby do
I got more Scooby snac just for you, Imao
Answers
The correct answer is letter B. V = 141.3cm³
Here's the Solution:
V = π r²hV = (3.14) (3cm)² (5cm)V = (3.14) (9cm²) (5cm)V = (3.24) (45cm³)V = 141.3cm³HOPE THIS HELPS. GOODLUCK:)
पाठशाला
Date
Page
amount of Rs sooo at the
annual Rate or 127.
is as
8ooo, and
find the interest
and time 2
Answers
perimeter is 21cm Length is 7.5cm and the Breadth is not given
Answers
Answer:
The answer is 3cm
Please give branliest!
Step-by-step explanation:
(S1×2)+(S2×2)=21cm
(S1+S2)×2=21cm
S1+S2=21÷2
7.5+S2=10.5
S2=10.5-7.5
S2=3
Breadth=3cm
Step-by-step explanation:
p=2(l+b)
21=2(7.5+b)
21=15+2b
21-15=2b
6=2b
6/2=b
b=3
Find the surface area of a cylinder with a base radius of 2 in and a height of 5 in
Answers
Answer:
[tex]r = 2 \\ h = 5 \\ a = 2\pi \: rh + 2\pi {r}^{2} \\ = 2\pi \times 2 \times 5 + 2\pi {2}^{2} \\ = 20\pi + 8\pi \\ = 28\pi \\ = 28 \times 3.14 \\ = 87.92 {unit}^{2} \\ thank \: you[/tex]
When 1480 is divided into 12 equal parts, the remainder is 4. What is a correct way to write the quotient?
123.4
1234 over 12
123 + 4
1234 over 1480
Answers
Answer:
123.4
Step-by-step explanation:
Find the slope of the straight line that passes through the following pair of points. (-4,1) and (2,6)
Answers
Answer:
5/6
Step-by-step explanation:
(6-1)/(2- -4) --> 5/6
Answer: Slope = 5/6
Concept:
Here, we need to know the idea of a slope.
A slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Slope = (y₂ - y₁) / (x₂ - x₁)
Solve:
Given information
(x₁, y₁) = (-4, 1)
(x₂, y₂) = (2, 6)
Given equation
Slope = (y₂ - y₁) / (x₂ - x₁)
Substitute values into the equation
Slope = (6 - 1) / (2 - (-4))
Simplify values in parentheses
REMEMBER to change signs whenever a [+, -] meets [-] sign
Slope = 5 / (2 + 4)
Slope = 5/6
Hope this helps!! :)
Please let me know if you have any questions
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) {-4, 8/3, -16/9, 32/27, -64/81, . . . } an =
Answers
Step-by-step explanation:
a1 = -4 = -4/1, a2 = 8/3
r = a2/a1 = (8/3) / (-4/1) = -2/3
the formula :
an = a1. r^(n-1)
so,
an = (-4). (-2/3)^(n-1)
Step-by-step explanation:
[tex]-4, \dfrac{8}{3}, -\dfrac{16}{9}, \dfrac{32}{27}, -\dfrac{64}{81},..., (-1)^n\dfrac{2^{n + 1}}{3^{n - 1}}, ...[/tex]
0.6(0.6r +0.5) + 7r
PLS HELP
Answers
Answer:
Answer 7.36r + 0.3
Step-by-step explanation:
0.6 (0.6r + 0.5) + 7r
0.6*0.6r = 0.36r
0.6 * 0.5 = 0.3
0.36r + 0.3 + 7r
7.36r + 0.3
If AB is parallel to DE, then CD is:
Answers
Answer:
4
Step-by-step explanation:
because BC=CD as it is parallel that means all the sides are equal
The value of CD is 20/3.
The correct option is (A).
What is Similarity in Triangles?
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
In ACB and ECD,
angle CAB= angle DEC
angle CBA= angle EDC
angle DCE = angle ACB
By, AA similarity criteria,
ΔACB~ΔECD
Now,
AC/CE= BC/CD
3/5=4/CD
CD= 20/3
Learn more about similarity property here:
https://brainly.com/question/25882965
#SPJ2
∠2= ∠5 , because they are
(I) Corresponding angles
(II) Alternate angles
(III) Co- interior angles
(IV) Linear pair
Answers
[tex] \sf \red {alternate \: angles}[/tex]
[tex] \huge \purple{ \underbrace{ \overbrace{Hope \: it \: helps}}}[/tex]
Please help
Solve the inequality.
|14 – 5x] > 8
[?]
x <
or x >
A
Answers
Answer:
x< -4/1 or x > 6/5
If our answers are different, just say so :)
(18 - 3)2 = ?
show your work
help me pls ty
Answers
Answer: 30
Step-by-step explanation:
18 - 3 is in the parenthesis so you have to solve that first. it’s 15 so the equation would then become (15)2 which is equal to 15 times 2. 15 times 2 equals 30.
HELP I NEED SOMBODEY HELP NOT JUST ANYONE JK HELP ME PLSSSSS
Answers
please help will bark brainliest
Answers
Answer:
A.
Step-by-step explanation:
Find NL. Not sure to to solve this.
Answers
Answer:
NL= 2 × HI
x+24 =2 × (X+16)
x+24=2x + 32
2x-x= 24-32
x= – 8
NL=x+24 = –8 +24= 16
So ; NL= 16
I hope I helped you^_^
X +24 = 2x +32
24-32= 2x-x
X = -8
NL = x+24
NL = -8+24
NL = 16
Help please ASAP!!!!!
Answers
Answer:
answer is c because you gota tranlate it left
Step-by-step explanation:
Which graph represents the function below?
h(x)= {-3x+2, x ≤ 2}
{1/2x -4, x > 2}
Answers
Answer is the third graph it was just an error..
Choose the correct statement. Consider the expression: 6.43
А
The product of one rational number and one irrational number is rational.
B
The product of one rational and one irrational number is irrational.
C
The product of two irrational numbers is irrational.
D
The product of two rational numbers is rational.
Answers
Answer:
D
Step-by-step explanation:
Goky kwiwiwjwjjwiwjwiw
An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center
of the quilt. The dimensions of the rectangle are AB = 10 inches and AC = 14 inches.
Answers
Answer: BX = 7
======================================
Explanation:
For any rectangle, the diagonals are the same length and they cut each other in half (aka bisect each other).
This means diagonal BD = AC = 14 and BX = BD/2 = 14/2 = 7. The value of AB is never used.
Answer:
7
Step-by-step explanation:
If a = 3+2✓2 then find the value of a^2+1/a^2
Pls answer first to answer get the brainliest crown
Pls answer ASAP
Answers
Answer: 34
Step-by-step explanation:
[tex]a=3+2\sqrt{2} \\\\\dfrac{1}{a} =\dfrac{1}{3+2\sqrt{2}} =\dfrac{3-2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})} =\dfrac{3-2\sqrt{2}}{3^2-2^2*2} =3-2\sqrt{2}\\\\\\a+\dfrac{1}{a} =3+2\sqrt{2}+3-2\sqrt{2}=6\\\\(a+\dfrac{1}{a})^2=6^2=36=a^2+\dfrac{1}{a^2}+2\\\\\\a^2+\dfrac{1}{a^2}=36-2=34\\[/tex]
calculate the percentage increase for the price of a book increasing from 250 to 275.50
Answers
Step-by-step explanation:
increase in price=275.50-250
=75 .50
now,in precent
( increase in price÷initial price )×100%
=(75.50÷250) ×100%
= 30.2%
Answer:
250×275.50
68,875
answer is 68,875
