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2 years ago

How do you solve the first one

Mathematics

1 answer:

Dominik [7]2 years ago

6 0

Answer:

x= -2 x=-2

Step-by-step explanation:

move over the leading coefficient and you get

3x²+12x+12

the pull out a 3 because that's your gcf and 3 cannot equal zero so you can just do without id and you get

x²+4x+4

and when you factor that you get

(x+2)(x+2)

and when you set those equal to zero you get x= -2 and x= -2

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The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th

Fantom [35]

Answer:

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C$

Step-by-step explanation:

To find:

∫ $6x^5(x^6-2)\,dx$

Solution:

Method of substitution:

Let $x^6-2=t$

Differentiate both sides with respect to $t$

$6x^5\,dx=dt$

[use $(x^n)'=nx^{n-1}$ ]

So,

∫ $6x^5(x^6-2)\,dx$ = ∫ $t\,dt$ = $\frac{t^2}{2}+C_1$ where $C_1$ is a variable.

(Use ∫ $t^n\,dt=\frac{t^{n+1} }{n+1}$ )

Put $t=x^6-2$

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1$

Use $(a-b)^2=a^2+b^2-2ab$

So,

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C$

where $C=2+C_1$

Without using substitution:

∫ $6x^5(x^6-2)\,dx$ = ∫ $6x^{11}-12x^5\,dx$ = $\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C$

So, same answer is obtained in both the cases.

7 0

2 years ago

Express in the form <br> 1<br> :<br> n<br> .<br> Give <br> n<br> as a decimal.<br> 10<br> :<br> 4

Brut [27]

Answer:

n=0.4

Step-by-step explanation:

10:4=5:2

to make 5 as 1, we will divide both 5 and 2 by 5

<h3> $\frac{5}{5}$ : $\frac{2}{5}$ =1:n</h3><h3>therefore, n= $\frac{2}{5}$ = 0.4</h3><h3 /><h3> </h3>

5 0

3 years ago

Maya says that value of the 6 in 0.006 is 1/10 of the value of the 6 in 0.6 . Is she correct? Explain

Nikolay [14]

Answer:

Maya is NOT correct as

$\frac{1}{1000}$ is 1/100 of the value $\frac{1}{10}$

Step-by-step explanation:

The value of 6 in 0.006 = $\frac{1}{1000}$

Also, the value of 6 in 0.6 = $\frac{1}{10}$

But, $\frac{1}{1000}$ is not 1/10 of the value $\frac{1}{10}$

as 1/10 of the value $\frac{1}{10}$ = $\frac{1}{100}$

Hence,Maya is NOT correct.

$\frac{1}{1000}$ is 1/100 of the value $\frac{1}{10}$

8 0

3 years ago

What is x in 7x-17=18

Evgen [1.6K]

Answer:

x=5

Step-by-step explanation:

7x-17=18

7x=18+17

7x=35

x=35/7

x=5

5 0

3 years ago

Extra points!! A candle is 17 in tall after burning for 3 hours. After 5

PIT_PIT [208]

Answer:

1) $h=-t+20$

2) 12 inches tall.

Step-by-step explanation:

1) The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

In this case:

$y=h$ (The height of the candle in inches)

$x=t$ (The time in hours)

Then, we can rewrite it:

$h=mt+b$

Based on the information provided in the exercise, the line passes through these points:

$(3,17)$ and $(5,15)$

Then, we can find the slope of the line with the formula $m=\frac{y_2-y_1}{x_2-x_1}$ :

$m=\frac{15-17}{5-3}=-1$

Now we need to substitute the slope and one of the points into $h=mt+b$ and then solve for "b":

$17=(-1)(3)+b\\\\b=17+3\\\\b=20$

Substituting values, we get that the a linear equation that models the relationship between the heigth of the candle and the time, is:

$h=-t+20$

2) We must substitute $t=8$ into the linear equation $h=-t+20$ in order to find the height of the candle after burning 8 hours:

$h=-(8)+20\\\\h=12$

4 0

3 years ago