Applying the product rule gives
[tex]\displaystyle \frac{d}{dx}\int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \frac{d}{dx}\int_1^{\ln(x)}\frac{dt}{(1+t)^2}[/tex]
Use the fundamental theorem of calculus to compute the remaining derivatives.
[tex]\displaystyle \frac{4x^3}{1+x^4} \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \frac{1}{x(1+\ln(x))^2}\int_1^{x^2}\frac{2t}{1+t^2}\,dt[/tex]
The remaining integrals are
[tex]\displaystyle \int_1^{\ln(x)}\frac{dt}{(1+t)^2} = -\frac1{1+t}\bigg|_1^{\ln(x)} = \frac12-\frac1{1+\ln(x)}[/tex]
[tex]\displaystyle \int_1^{x^2}\frac{2t}{1+t^2}\,dt=\int_1^{x^2}\frac{d(1+t^2)}{1+t^2}=\ln|1+t^2|\bigg|_1^{x^2}=\ln(1+x^4)-\ln(2) = \ln\left(\frac{1+x^4}2\right)[/tex]
and so the overall derivative is
[tex]\displaystyle \frac{4x^3}{1+x^4} \left(\frac12-\frac1{1+\ln(x)}\right) + \frac{1}{x(1+\ln(x))^2} \ln\left(\frac{1+x^4}2\right)[/tex]
which could be simplified further.
Is this scientific notation
42,060=4.206 x 10 to the 4th
Answer:
yes it is scientific notation
The area in square feet of a rectangular field is
x2 – 120x + 3500. The width, in feet, is x-50. What is the
length, in feet?
Answer:
Length in feet: x-70
Step-by-step explanation:
Use factorization to find the length
Area = X^2-120x+3500
Area= length x width.
Area= L x (x-50)= (x-___) (x-50)
To find L we know that in factoring the quadratic equation 50 x __ must be equal to 3500.
(x-70)(x-50) = x^2-120x+3500.
rearrange so u Rearrange the equation so www is the independent variable.
−2u+6w=9
Answer:
w=9+2u/6
Step-by-step explanation:
-2u+6w=9
+2u on both sides
6w=9+2u
/6 on both sides
w=9+2u/6
Please help. I’ll mark you as brainliest if correct!
Answer:
y=1/3x +16/3
Step-by-step explanation:
m=(y2-y1) / (x2-x1)
=(6-5) (2- -1)
=1/3
Substitute in m and either point into the point slope form
y=m(x-x1) + y
y=1/3(x- -1) +5
y=1/3(x+1) +5
Now lets distribute the 1/3 to and combine the constants to put the answer in standard form
y=1/3x + 1/3 + 5
y=1/3x +1/3 + 15/3
y=1/3x +16/3
[tex] \tan(x) [/tex]
integrate ...
x2-30x+81
Answer (x-27)(x-3)
Four years ago, you invested $1000 in an account that returns 5.1% annually. The table shows the value of your investment
at the end of each year.
Time (in years)
1
2
Value (in dollars)
$1051.00
$1104.60
$1160.94
$1220.14
3
4
Does the data represent a linear function? Why or why not?
a. Yes, it appears on a straight line.
C. Yes, the average rate of change is constant.
b. No, it does not appear on a straight line.
d. There is not enough information to determine
whether this is a linear function,
Please coloct the boot
Answer:
It B
Step-by-step explanation:
The data provided in the table does not represent a linear pattern option (b) No, it does not appear on a straight line correct.
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
It is given that:
Four years ago, you invested $1000 in an account that returns 5.1% annually.
The table represents the value of your investment at the end of each year.
Time (in years) Value (in dollars)
1 $1051.00
2 $1104.60
3 $1160.94
4 $1220.14
Plot the point (x, y) on the coordinate plane:
From the graph, as we can see (1, $1051.00) does not lie on the line.
Thus, the data provided in the table does not represent a linear pattern option (b) No, it does not appear on a straight line correct.
Learn more about the rate of change here:
brainly.com/question/12786410
#SPJ2
A triangle has an area of 35 cm squared. The BASE of the triangle is (x-5) cm and the HEIGHT of the triangle is (x-14) cm. Find the measure of the HEIGHT and BASE.
Try to use this method and see if you get the answer
Step-by-step explanation:
area = b * h / 2 , where b is a base, h - height.
so h = 2 * area / b.
ANSWER QUICKLYYYYYY!!!
Answer:
AC = 16.5
AE = 9
Step-by-step explanation:
Connect AC and BE
Note m∠ACD = m∠ACB, (both face arc BD)
ΔACD ~ ΔABE
AD : AB = AC : AE
6 : 4 = AC : (6 + 5)
3 : 2 = AC : 11
2AC = 3*11 = 33
AC = 16.5
AE = 9
Volume: The base of a pyramid is a rectangle with a length of 3 centimeters and a width of 6 centimeters. If the height of the pyramid is 12 centimeters, what is the volume of the pyramid?
Answer:
72 cm³
Step-by-step explanation:
Volume of a pyramid = Area of base * height / 3
= 3 * 6 * 12/3 = 72 cm³
The value of each expression if x=12
3x
Answer:
3*12=36
hope thats the answer
4) The length of a rectangle is double its width. Its perimeter is 33cm. How long is its
width?
5.5 cm
Step-by-step explanation:
Let x be the width of the rectangle.
Since the length is double the width, the length would be 2x.
x can be found by solving the perimeter equation. The perimeter of the rectangle can be found by the equation:
[tex]p = 2(l + w)[/tex]
[tex]33 = 2(2x + x)[/tex]
[tex]33 \div 2 = (2x + x)[/tex]
[tex]16.5 = 3x[/tex]
[tex]16.5 \div 3 = x[/tex]
[tex]5.5 = x[/tex]
Therefore, the width of the rectangle is 5.5 cm.
The Red Shell's flight path is modeled by the equation:
y = -2x2 + 60x + 350
a) Factor the equation below:
olutions to the equation?
Answer:
Geometric figure: Straight Line
Slope = 120.000/2.000 = 60.000
x-intercept = 346/-60 = 173/-30 = -5.76667
y-intercept = 346/1 = 346.00000
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(-4+60*x+350)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve y-60x-346 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-60x-346 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 346/1 so this line "cuts" the y axis at y=346.00000
y-intercept = 346/1 = 346.00000
Calculate the X-Intercept :
When y = 0 the value of x is 173/-30 Our line therefore "cuts" the x axis at x=-5.76667
x-intercept = 346/-60 = 173/-30 = -5.76667
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 346.000 and for x=2.000, the value of y is 466.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 466.000 - 346.000 = 120.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 120.000/2.000 = 60.000
Geometric figure: Straight Line
Slope = 120.000/2.000 = 60.000
x-intercept = 346/-60 = 173/-30 = -5.76667
y-intercept = 346/1 = 346.00000
The smaller of the two containers has a capacity of 150 gallons. When it is $\frac{4}{5}$ full, its contents are emptied into a larger container, filling exactly $\frac{2}{3}$ of it. What is the capacity, in gallons of the larger container?
Answer:
180 gallons
Step-by-step explanation:
The smaller container has 150 gallons.
Now the large container is filled with the 4/5 of the smaller container.
So if the full volume of the small container is 150 gallons so the 4/5 of it can be calculated as, 4/5*150=120 gallons.
Answer:
hoi
Step-by-step explanation:
b. Convert quarts into gallons
20 quarts= X(1 quart)
= X (1
-
4
= Gallons
= Gallons
Answer:
5 Liquid Gallons
Step-by-step explanation:
To find this answer, divide the volume value of liquid quarts by 4, then you will get 5 as your liquid gallon answer.
Sid Upp is four years younger than his brother Tip. Let x stand for Tip's age . Write an equation stating that Sid's age is 32.
Answer:
x+4=36
Step-by-step explanation:
you would subtract 4 on each side
x+4=36
-4 -4
x=32
Figure ABCD is a parallelogram.What is the value of n?3 5 17 25
Answer:
17
Step-by-step explanation:
∠B = ∠D
2n + 32 = 4n - 2
32 + 2 = 4n - 2n
2n = 34
n = 17
PLEASE HELP ME ASAP
Its not that hard im just tired
Answer:
combine like terms; 15.4z - 12
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLY IF YOU GET IT RIGHT AND EXPLAIN PLEASE
Answer:
48 degrees
Step-by-step explanation:
the angle measure doesn't scale of shrink with the dilation of circles. the angle only just extends.
please help, i did 90 - 10 and I got 80. I’m stuck at 80
Answer:
approx 216
Step-by-step explanation:
well we go to the 10mm mark and we add the columns taht appear before that. Those are two columns : the brown/orangey one and the green one.
if the scale goes up in twenty and each jump has four squares then we can say that one square is equal to 5 up
so we now can read the first two columns
the first one reads 135
the second one reads approximately 81
we add those up and that becomes 216
so the answer is approximately 216
Please help me with this coordinate geometry homework !!!!
Answer:
Step-by-step explanation:
a. Gradient of A = 7/-7 = -1.
b. For line B, m = 3/1.5 = 2 and c = y-intercept = 3.
c. The line parallel to B will have the same gradient m = 2.
It also passes through (1, -1) so we use the point-slope form of the straight line
y - y1 = m(x - x1)
Here m = 2 and (x1, y1) = (1, -1) so
y - (-1) = 2(x - 1)
y = 2x - 2 - 1
y = 2x -3.
PLEASE HELP!!!! Which quadratic equation is part of the solution process for solving this rational equation using the least common denominator?
Answer: for plato users
A is the correct answer
Step-by-step explanation:
I just took the test had 100%
The correct option is A. [tex]x^{2} -x-10=0[/tex].
Given quadratic equation [tex]\frac{2}{3x-6} -\frac{1}{3x+6} =\frac{1}{3}[/tex]
On solving, [tex]\frac{2(3x+6)-1(3x-6)}{(3x-6)(3x+6)} =\frac{1}{3}[/tex]
Further, [tex]\frac{6x+12-3x+6}{9x^{2} -6^{2} } =\frac{1}{3}[/tex]
[tex]\frac{3x+18}{9x^{2} -36} =\frac{1}{3}[/tex]
Taking 3 common from numerator and 9 common from denominator, we have
[tex]\frac{3(x+6)}{9(x^{2} -4)} =\frac{1}{3}[/tex]
[tex]\frac{(x+6)}{3(x^{2} -4)} =\frac{1}{3}[/tex]
[tex]\frac{x+6}{x^{2} -4} =1[/tex]
[tex]x+6=x^{2} -4[/tex]
On rearranging in decreasing powers of x we get,[tex]x^{2} -x-10=0[/tex].
Hence on solving, We get [tex]x^{2} -x-10=0.[/tex]
For more details on Quadratic equation follow the link:
https://brainly.com/question/17177510
is 3 8/33 equivalent to the decimal 3.24 (repeating)
Answer:
Yes it is
Step-by-step explanation:
8 ÷ 33 = .242424( infinite )
Add the beginning 3 to it and you get 3.24 (repeating)
Hope this helps.
Solve the following equation.
25z^2+93 = 100z
Step-by-step explanation:
25z square+93=100z
=25z square+93=10z square
=25z square-10z square=-93
=15z square= -93
please help me ..............
Answer: A, C, E
Step-by-step explanation:
An undefined slope means the line is vertical (and thus the x-coordinates are constant).
g (x) = x2 + 12x-
35
Answer:
not factorable
Step-by-step explanation:
g(x) = x²+12x-35
Not factorable
MATHEMATICAL CONNECTIONS The volume of a cylinder is given by V=pi r^2h, where r is the radius of the base of the cylinder and h is the height of the cylinder. Find the dimensions of the cylinder. the radius is h-3 and the volume is 25h*pi
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=h-3\\ V=25h\pi \end{cases}\implies 25h\pi =\pi (h-3)^2 h \\\\\\ \cfrac{25h\pi }{\pi h }=(h-3)(h-3)h\implies 25=\stackrel{F~O~I~L}{h^2-6h+9}\implies 0=h^2-6h-16 \\\\\\ 0=(h-8)(h+2)\implies \blacktriangleright h= \begin{cases} 8~~\checkmark\\ -2 \end{cases} \blacktriangleleft ~\hfill \blacktriangleright \underset{radius}{\stackrel{8~~ - ~~3}{5}} \blacktriangleleft[/tex]
notice, we didn't use h = -2, because the height cannot be a negative value.
Write and equivalent expression for 88 + 16x + 8.
X = 4
Answer:
88+64+8
Step-by-step explanation:
16*4 =64 and you can just replace that with the x.
Diane walked 4/10 mile x 5 days this week. How far did Diane walk?
answer: 2
(4/10) * 5 = 2
she walk 2 miles per day
help i give brianlyist and 5 star rating whith heart
Answer:
26
Step-by-step explanation:
perimeter is sum of all sides
11+7+4+4=perimeter
26