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3 years ago

A number b increased by 8 is greater than 18

Mathematics

1 answer:

Fed [463]3 years ago

5 0

Answer: b > 10

Step-by-step explanation:

b + 8 > 18

Subtract 8 from both sides

that leaves you with

b > 10

You might be interested in

Given that the product of two positive integers is 44, and their least common multiple is 22, what is their greatest common divi

swat32

Answer:

Step-by-step explanation:

For any positive numbers a,b we always have the following identity:

$a\cdot b=gcd(a,b)\cdot lcm(a,b)$

(gcd(a,b) denotes the greatest common divisor between a and b, and lcm(a,b) denotes the least common multiple between a and b)

In our case, we are given that $a\cdot b = 44$ and that $lcm(a,b)=22$ . Plugging that in into our identity, we get:

$44=gcd(a,b)\cdot 22$

And so solving for $gcd(a,b)$ :

$gcd(a,b)=\frac{44}{22}=2$

5 0

3 years ago

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

{(-5,9),(2, 31), (9, 143), (11, 151),(0, 42),(5, 97)}

wlad13 [49]

The number 7 is the best prediction of the output when the input is 13.

<h3>What is the equation of a line passing through two given points in 2 dimensional plane?</h3>

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)$

The equation of the line is found as;

$\rm y-y_1= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm y-9= \frac{31-9}{2+5} (x+5)\\\\ 7y-63 = \frac{31-9}{2+5} (c+5)\\\\ 7y-63=22x+110\\\\ 7y= 22x+173 \\\\ but ,x=13\\\\ 7y=22 \times 13 +173\\\\ y= \frac{1259}{7} \\\\ y= 179$