Two fifths of a number is 64. What is three eighths of a number

Two fifths of a number is 64. What is three eighths of a number

Xx2／5＝64
X＝160
160X3／8＝60

On the calculation of percentage
1) Suppose that the price of an article increases by 5.4% in the first year and 30% in the second year, and find out the average growth rate in these two years
2) Suppose the world population tripled from 1960 to 2000. What is the average annual growth
3) The population of a city is decreasing at the rate of 2% every year. How many years later will the population be reduced to half of the original population
I know the answer to the first question is 17,1% and the second one is 1,75%. So it seems that the second one on the first floor is wrong. Can you calculate the second one

1) Square of (1 + a) = (1 + 5.4%) (1 + 30%) → a = 0.1706 = 17.06%
2) The 40th power of (1 + a) = 3 → a = 0.0278 = 2.78%
3) (1-2%) n power = 0.5 → n = 34.3, take 35
Landlord, I've read your supplementary. Maybe the answer is wrong,
First of all, we should understand two concepts
① The population of 2000 was twice that of 1960;
② The population in 2000 was twice as large as that in 1960;
These two are different,
The former (1 + a) to the 40th power = 2, the result is 1.75%, which is your answer
The 40th power of the latter (1 + a) is 3, which is 2.78%, which is my answer
I thought about the meaning of the question, should be in line with the latter one. I don't know if the landlord can agree?

Equation log2 (2 ^ x + 1) log2 [2 ^ (x + 1) + 2] = 2
Find X. - -

log2(2^x+1)log2[2^(x+1)+2]=2
log2(2^x+1)[log2（2^x+1）+1]=2
Log2 (2 ^ x + 1) = 1, because 2 ^ x + 1 > 1, the negative value is omitted
We get 2 ^ x + 1 = 2
We get x = 0

How to find the maximum area and perimeter of the inscribed rectangle of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) without solving the parametric equation

1) Let 1 Vertex be (m, n)
m^2/a^2+n^2/b^2=1
Mn can be obtained from the basic inequality m ^ 2 / A ^ 2 + n ^ 2 / b ^ 2 > = 2Mn / ab

hiop

Bob's mother is crazy
His room is a mess!
She said, "clean your room!"
Bob put the toy under the bed
Bob put the dirty clothes under the bed
Bob put the book under the bed
He said, "my room is clean now."

The square of polynomial 2 / 1 x | n | - (n + 2) x + 7 is a quadratic binomial about X, and the value of N can be obtained

The square of polynomial 2 / 1 x | n | - (n + 2) x + 7 is a quadratic binomial about X
So | n | = 2 and N + 2 is not equal to 0
So n = 2

The function f (x) = root sign 2 sin (2x + π / 4) Let G (x) = f (x + π / 8) - A, if G (x) has two zeros when x ∈ [- π / 6, π / 3],
Find the value range of a

Function f (x) = root 2 sin (2x + π / 4) g (x) = f (x + π / 8) - a = root 2 sin (2 (x + π / 8) + π / 4) - a = root 2 sin (2x + π / 2) - A = root 2 cos (2x) - ax ∈ [- π / 6, π / 3] 2x ∈ [- π / 3,2 π / 3] root 2 cos (2x) ∈ [- √ 2 / 2, √ 2] from the image, we can see that G (x) is in X ∈

There are 64 simple calculation questions in primary school,

Case 1: 1.24 + 0.78 + 8.76
The original formula = (1.24 + 8.76) + 0.78
=10+0.78
=10.78
[key to problem solving and tips]
Use the commutative and associative laws of addition, because 1.24 is combined with 8.76, and the sum is exactly the integer 10
Case 2 933-157-43
The original formula is 933 - (157 + 43) = 933-200 = 733
[key to problem solving and tips]
According to the nature of subtraction to remove brackets, the sum of several numbers can be subtracted by subtracting several numbers continuously from a number. Therefore, the sum of questions 157 and 43 is exactly 200
Case 3 4821-998
=4821-1000+2=3823
[key to problem solving and tips]
The subtraction 998 in this question is close to 1000, so we will change it into 1000-2. According to the nature of subtraction, the original formula is 4821-1000 + 2, which is delicious. After skilled calculation, the step of 998 becoming 1000-2 can be omitted
Case 40.4 × 125 × 25 × 0.8
The original formula = (0.4 × 25) × (125 × 0.8) = 10 × 100 = 1000
[key to problem solving and tips]
Using commutative law and associative law of multiplication, because 0.4 × 25 is exactly 10, and 125 × 0.8 is exactly 100
Case 5 1.25 × (8 + 10)
The original formula is 1.25 × 8 + 1.25 × 10 = 10 + 12.5 = 22.5
[key to problem solving and tips]
According to the law of multiplicative distribution, the sum of two addends is multiplied by a number. Each addend can be multiplied by the number respectively, and then the product is added
Case 6 9123 - (123 + 8.8)
The original formula = 9123-123-8.8 = 9000-8.8 = 8991.2
[key to problem solving and tips]
According to the nature of subtraction to remove brackets, subtracting the sum of several numbers from a number can continuously subtract these numbers, because 9123 minus 123 is exactly 9000. It should be noted that after subtraction to remove brackets, the original addition of 8.8 has become the subtraction of 8.8
Cases 7 1.24 × 8.3 + 8.3 × 1.76
The original formula is 8.3 × (1.24 + 1.76) = 8.3 × 3 = 24.9
[key to problem solving and tips]
This solution is the inverse application of the law of distribution by multiplication, that is, the sum of several numbers multiplied by a number can be multiplied by the number
Case 8 9999 × 1001
Solution formula = 9999 × (1000 + 1) = 9999 × 1000 + 9999 × 1
=10008999
[key to problem solving and tips]
In this problem, 1001 is regarded as 1000 + 1, and then simplified according to the distributive law of multiplication
[key to problem solving and tips]
In this problem, we use twice multiplication distribution law, so we can't only satisfy the first simple calculation success, we should continue to find a reasonable and flexible algorithm until the end
[key to problem solving and tips]
According to the needs of the problem, the use of two subtraction to the nature of brackets
Cases 11 14.8 × 6.3-6.3 × 6.5 + 8.3 × 3.7
The original formula = (14.8-6.5) × 6.3 + 8.3 × 3.7
=8.3×6.3+8.3×3.7
=8.3×（6.3＋3.7）
=8.3×10
=83
[key to problem solving and tips]
The 8.3 × 3.7 in this question can't be mistaken as 6.3 × 3.7 in the first simple calculation. If it can't participate in the simple calculation for the first time, copy it down to see if there is a chance later. The result of the first simple calculation happens to be 8.3 × 6.3, so that we can carry out the second simple calculation
Case 12 32 × 125 × 25
The original formula is 4 × 8 × 125 × 25
=（4×25）×（8×125）
=100×1000
=100000
[key to problem solving and tips]
By decomposing 32 into 4 × 8, 125 × 8 and 25 × 4 can get the whole number of hundreds and thousands

Given the curve C: y = x ^ 3.1, find the tangent equation of the point on the curve C whose abscissa is 1. 2. Whether there are other common points between the tangent in question 1 and the curve C

1) Y '= 3x ^ 2Y' (1) = 3Y (1) = 1 the tangent at point (1,1) is: y = 3 (x-1) + 1 = 3x-22) substitute y = 3x-2 into y = x ^ 3 to get: x ^ 3 = 3x-2x ^ 3-3x + 2 = 0x ^ 3-x-2x + 2 = 0x (x ^ 2-1) - 2 (x-1) = 0 (x-1) (x ^ 2 + X-2) = 0 (x-1) (x + 2) (x-1) = 0, so it has zero point x = 1, - 2, so it has another relation with the curve

Optional questions: if P is a point on the plane where △ ABC is located, and ∠ APB = ∠ BPC = ∠ CPA = 120 °, then point P is called the Fermat point of △ ABC. (1) if point P is the Fermat point of △ ABC with acute angle, and ∠ ABC = 60 °, PA = 3, PC = 4, then the value of Pb is___ (2) as shown in the figure, make an equilateral △ ACB 'outside the acute angle △ ABC to connect BB'