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Vesnalui [34]
2 years ago
13

Solve the Antiderivative.​

Mathematics
1 answer:
Black_prince [1.1K]2 years ago
3 0
1
∫ -------------------- dx
x² + 6x + 10


1
∫ -------------------- dx
(x+3)² + 1

Let t = x + 3
dt = dx

1
∫ -------------------- dt
t²+1

1/1 arctan(t/1)

1/1 arctan (x+3 / 1)


=arctan(x+3) + C
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Find the gradient of the line passing through (6,8) and (4,10)
Mariulka [41]

Question:

Find the gradient of the line passing through (6,8) and (4,10).

Answer:

-1 is the right answer.

Step-by-step explanation:

Slope of the line = The gradient of the line

Gradient of the line is known as change in the value of y-axis by change in the value of x-axis

Gradient = ∆y\∆x

Gradient = \frac{y_ 2 - y_1}{x_2 - x_1}  =  \frac{(10 - 8)}{(4 - 6)}  =  \frac{(2)}{(- 2)} =\boxed{- 1}\\

7 0
2 years ago
How many gallons of a 80​% antifreeze solution must be mixed with 100 gallons of 20​% antifreeze to get a mixture that is 70​% a
Blababa [14]

To Find :

How many gallons of a 80​% antifreeze solution must be mixed with 100 gallons of 20​% antifreeze to get a mixture that is 70​% antifreeze.

Solution :

Let, x gallons of 80​% antifreeze solution is required :

So,

(x \times 80) + ( 100 \times 20 ) = (x + 100 )\times 70\\\\8x + 200 = 7( x + 100)\\\\x = 500

Therefore, 500 gallons of 80% antifreeze solution is required.

6 0
2 years ago
3x + 5= -1 <br> Ayuda xddddd
bija089 [108]

Answer: x = -2

Step-by-step explanation:

8 0
2 years ago
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Estimate 307% of 29.
aleksley [76]

Answer:

89.03

Step-by-step explanation:

29x3.07=89.03

6 0
2 years ago
Find the length of the arc and express your answer as a fraction times pie
Elina [12.6K]

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}

To find the length of the arc, s, the formula is

\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}

Substitute the variables into the formula to find the length of an arc, s above

\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}

Hence, the length of the arc, s, is 3π units.

4 0
10 months ago
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