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Ray Of Light [21]
2 years ago
13

Find all numbers that satisfy the given condition. 1. Three less than twice the sum of a number and 6 is at most 13. 2. Five les

s than 3 times the sum of a number and 4 is at most 10. 3. Five times the sum of a number and 3 is at least 5. 4. Three times the difference between a number and 2 is at least 12. 5. The sum of 3 times a number and 8 is between 2 and 20. 6. Eight less than twice a number is between -20 and -8. 7. Four subtracted from three times some number is between -4 and 14. 8. Nine subtracted from 5 times some number is between 1 and 11.​
Mathematics
1 answer:
Dmitriy789 [7]2 years ago
5 0

Number be x

#1

\\ \sf\hookrightarrow 2(x+6)-3\leqslant=13

#2

\\ \sf\hookrightarrow 3(x+4)-5\leqslant 10

#3

\\ \sf\hookrightarrow 5(x+3)\geqslant 5

#4

\\ \sf\hookrightarrow 3(x-2)\leqslant 12

#5

\\ \sf\hookrightarrow 2\leqslant 3x+8\leqslant 20

#6

\\ \sf\hookrightarrow -20\leqslant 2x-8\leqslant -8

#7

\\ \sf\hookrightarrow -4\leqslant 3x-4\leqslant 14

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Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two
In-s [12.5K]
Let the original 2-digit number be xy.
Because 5 times the sum of the digits is 13 less than the number, therefore
5(x + y) = 10x + y - 13 
5x + 5y = 10x + y - 13
-5x + 4y = - 13             (1)

The number with reversed digits is yx.
Because 4 times the sum of the digits is 21 less than the reversed 2-digit number, therefore
4(x + y) = 10y + x - 21
4x + 4y = 10y + x - 21
3x - 6y = -21
x - 2y = -7
x = 2y - 7                 (2)

Substitute (2) into (1).
-5(2y - 7) + 4y = -13
-10y + 35 + 4y = -13
-6y = -48
y = 8

From (3), obtain
x = 2*8 - 7 = 9

Answers:
The original 2-digit number is 98
The reversed 2-digit number is 89
The difference between the original and the reversed 2-digit numbers is
98 - 89 = 9
4 0
3 years ago
Clark's weight is increasing these days if it's weight increases by 2 kg mg every 4 months how many kilograms of weight will he
ycow [4]

Answer:

8kg

Step-by-step explanation:

4m=2kg

16m=?

=16m×2

=32

=32÷4

=8kg

Hope this will help ya!

6 0
3 years ago
Calculus 2
FinnZ [79.3K]

Answer:

See Below.

Step-by-step explanation:

We want to estimate the definite integral:

\displaystyle \int_1^47\sqrt{\ln(x)}\, dx

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

1)

The trapezoidal rule is given by:

\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

\displaystyle \Delta x=\frac{4-1}{6}=\frac{1}{2}

Therefore, the trapezoidal approximation is:

\displaystyle =\frac{1/2}{2}\Big(f(1)+2f(1.5)+2f(2)+2f(2.5)+2f(3)+2f(3.5)+2f(4)\Big)

Evaluate:

\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337

2)

The midpoint rule is given by:

\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x

Thus:

\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)

Simplify:

\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319

3)

Simpson's Rule is given by:

\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)

So:

\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)

Simplify:

\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834

6 0
3 years ago
Seth traveled one mile in 57.1 seconds. About how fast does Seth travel in miles per hour?
ZanzabumX [31]
<span>Since we need to convert “miles per second” to “miles per hour,”  we first need to find out how many seconds there are in a hour.
We know that there are 60 seconds in a minute, and if we wanted to do an hour we would have to do 60 * 60 which is 3600 seconds, therefore, 
</span>1 mi/57.1 sec = (1 mi/ 57.1 sec)(3600 sec/1 hour)

                        = (3600/57.1) mi/hours

<span>                        = 63.047 mi/hours</span>
5 0
3 years ago
Which choices are equivalent to the expression below? Check all that apply.
Gre4nikov [31]

Answer:

A and E

Step-by-step explanation:

Sqrt 3 times sqrt 3 is sqrt 9, which simplified is 3

3 0
2 years ago
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