how to solve derivative of (sin3x)/x using first principle
Answers
[tex]\dfrac{d}{dx}(\dfrac{\sin(3x)}{x})[/tex]
First we must apply the Quotient rule that states,
[tex](\dfrac{f}{g})'=\dfrac{f'g-g'f}{g^2}[/tex]
This means that our derivative becomes,
[tex]\dfrac{\dfrac{d}{dx}(\sin(3x))x-\dfrac{d}{dx}(x)\sin(3x)}{x^2}[/tex]
Now we need to calculate [tex]\dfrac{d}{dx}(\sin(3x))[/tex] and [tex]\dfrac{d}{dx}(x)[/tex]
[tex]\dfrac{d}{dx}(\sin(3x))=\cos(3x)\cdot3[/tex]
[tex]\dfrac{d}{dx}(x)=1[/tex]
From here the new equation looks like,
[tex]\dfrac{3x\cos(3x)-\sin(3x)}{x^2}[/tex]
And that is the final result.
Hope this helps.
r3t40
Answer:
[tex]\frac{3\cos(3x)}{x}-\frac{\sin(3x)}{x^2}[/tex]
Step-by-step explanation:
If [tex]f(x)=\frac{\sin(3x)}{x}[/tex], then
[tex]f(x+h)=\frac{\sin(3(x+h)}{x+h}=\frac{\sin(3x+3h)}{x+h}[/tex].
To find this all I did was replace old input, x, with new input, x+h.
Now we will need this for our definition of derivative which is:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]
Before we go there I want to expand [tex]sin(3x+3h)[/tex] using the sum identity for sine:
[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]
[tex]\sin(3x+3h)=\sin(3x)\cos(3h)+\cos(3x)\sin(3h)[/tex]
So we could write f(x+h) as:
[tex]f(x+h)=\frac{\sin(3x)\cos(3h)+\cos(3x)\sin(3h)}{x+h}[/tex].
There are some important trigonometric limits we might need before proceeding with the definition for derivative:
[tex]\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1[/tex]
[tex]\lim_{u \rightarrow 0}\frac{\cos(u)-1}{u}=0[/tex]
Now let's go to the definition:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{\frac{\sin(3x)\cos(3h)+\cos(3x)\sin(3h)}{x+h}-\frac{\sin(3x)}{x}}{h}[/tex]
I'm going to clear the mini-fractions by multiplying top and bottom by a common multiple of the denominators which is x(x+h).
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x(\sin(3x)\cos(3h)+\cos(3x)\sin(3h))-(x+h)\sin(3x)}{x(x+h)h}[/tex]
I'm going to distribute:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)\cos(3h)+x\cos(3x)\sin(3h)-x\sin(3x)-h\sin(3x)}{x(x+h)h}[/tex]
Now I’m going to group xsin(3x)cos(3h) with –xsin(3x) because I see when I factor this I might be able to use the second trigonometric limit I mentioned. That is xsin(3x)cos(3h)-xsin(3x) can be factored as xsin(3x)[cos(3h)-1].
Now the limit I mentioned:
[tex]\lim_{u \rightarrow 0}\frac{\cos(u)-1}{u}=0[/tex]
If I let u=3h then we have:
[tex]\lim_{3h \rightarrow 0}\frac{\cos(3h)-1}{3h}=0[/tex]
If 3h goes to 0, then h goes to 0:
[tex]\lim_{h \rightarrow 0}\frac{\cos(3h)-1}{3h}=0[/tex]
If I multiply both sides by 3 I get:
[tex]\lim_{h \rightarrow 0}\frac{\cos(3h)-1}{h}=0[/tex]
I’m going to apply this definition after I break my limit using the factored form I mentioned for those two terms:
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)\cos(3h)-x\sin(3x)+x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)(\cos(3h)-1)+x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
[tex]f'(x)=\lim_{h \rightarrow 0}\frac{x\sin(3x)(\cos(3h)-1)}{x(x+h)h}+\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
So the first limit I’m going to write as a product of limits so I can apply the limit I have above:
[tex]f’(x)=\lim_{h \rightarrow 0}\frac{\cos(3h)-1}{h} \cdot \lim_{h \rightarrow 0}\frac{x\sin(3x)}{x(x+h)}+\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
The first limit in that product of limits goes to 0 using our limit from above.
The second limit goes to sin(3x)/(x+h) which goes to sin(3x)/x since h goes to 0.
Since both limits exist we are good to proceed with that product.
Let’s look at the second limit given the first limit is 0. This is what we are left with looking at:
[tex]f’(x)=\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)-h\sin(3x)}{x(x+h)h}[/tex]
I’m going to write this as a sum of limits:
[tex]\lim_{h \rightarrow 0}\frac{x\cos(3x)\sin(3h)}{x(x+h)h}+\lim_{h \rightarrow 0}\frac{-h\sin(3x)}{x(x+h)h}[/tex]
I can cancel out a factor of x in the first limit.
I can cancel out a factor of h in the second limit.
[tex]\lim_{h \rightarrow 0}\frac{\cos(3x)\sin(3h)}{(x+h)h}+\lim_{h \rightarrow 0}\frac{-\sin(3x)}{x(x+h)}[/tex]
Now I can almost use sin(u)/u goes to 1 as u goes to 0 for that first limit after writing it as a product of limits.
The second limit I can go ahead and replace h with 0 since it won’t be over 0.
So this is what we are going to have after writing the first limit as a product of limits and applying h=0 to the second limit:
[tex]\lim_{h \rightarrow 0}\frac{\sin(3h)}{h} \cdot \lim_{h \rightarrow 0}\frac{\cos(3x)}{(x+h)}+\frac{-\sin(3x)}{x(x+0)}[/tex]
Now the first limit in the product I’m going to multiply it by 3/3 so I can apply my limit as sin(u)/u->1 then u goes to 0:
[tex]\lim_{h \rightarrow 0}3\frac{\sin(3h)}{3h} \cdot \lim_{h \rightarrow 0}\frac{\cos(3x)}{(x+h)}+\frac{-\sin(3x)}{x(x)}[/tex]
[tex]3(1) \cdot \lim_{h \rightarrow 0}\frac{\cos(3x)}{(x+h)}+\frac{-\sin(3x)}{x(x)}[/tex]
So we can plug in 0 for that last limit; the result will exist because we do not have over 0 when replacing h with 0.
[tex]3(1)\frac{\cos(3x)}{x}+\frac{-\sin(3x)}{x^2}[/tex]
[tex]\frac{3\cos(3x)}{x}-\frac{\sin(3x)}{x^2}[/tex]
Related Questions
Solve the system of equations y=x^2-2 y=-2x+1
Answers
Answer:
D
Step-by-step explanation:
Given the 2 equations
y = x² - 2 → (1)
y = - 2x + 1 → (2)
Substitute y = x² - 2 into (2)
x² - 2 = - 2x + 1 ( subtract - 2x + 1 from both sides )
x² + 2x - 3 = 0 ← in standard form
(x + 3)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 1 = 0 ⇒ x = 1
Substitute these values into (2) for corresponding values of y
x = - 3 : y = -2(- 3) + 1 = 6 + 1 = 7 ⇒ (- 3, 7 )
x = 1 : y = - 2(1) + 1 = - 2 + 1 = - 1 ⇒ (1, - 1 )
Answer:
D. (-3, 7) and (1, -1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=x^2-2&(1)\\y=-2x+1&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\x^2-2=-2x+1\qquad\text{add 2x to both sides}\\x^2+2x-2=1\qquad\text{subtract 1 from both sides}\\x^2+2x-3=0\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x+3)(x-1)=0\iff x+3=0\ \vee\ x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1\\\\\text{put the value of x to (1):}\\\\for\ x=-3\\y=(-3)^2-2=9-2=7\\\\for\ x=1\\y=1^2-2=1-2=-1[/tex]
Factor by grouping. 6p2 – 17p – 45
Answers
Answer:
(2p - 9)(3p + 5)
Step-by-step explanation:
We have the polynomial: 6p2 – 17p – 45
Rewrite the middle term as a sum of two terms:
6p2 + 27p - 10p - 45
Factor:
3p(2p - 9) + 5(2p - 9)
→ (2p - 9)(3p + 5)
For this case we must factor the following expression:
[tex]6p ^ 2-17p-45[/tex]
We must rewrite the term of the medium as two numbers whose product is [tex]6 * (- 45) = - 270[/tex]
And whose sum is -17
These numbers are: -27 and +10:
[tex]6p ^ 2 + (- 27 + 10) p-45\\6p ^ 2-27p + 10p-45[/tex]
We group:
[tex](6p ^ 2-27p) + 10p-45[/tex]
We factor the maximum common denominator of each group:
[tex]3p (2p-9) +5 (2p-9)[/tex]
We factor[tex](2p-9)[/tex] and finally we have:
[tex](2p-9) (3p + 5)[/tex]
Answer:
[tex](2p-9) (3p + 5)[/tex]
a) 3(2x + 3) = -3 (-30 +4)
Answers
Answer:
3(2x+3)=-3(-30+4)
6x+9=90+12
6x+9=102
6x=93
x=15.5
-please mark as brainliest-
Answer:
11½ = x
Step-by-step explanation:
6x + 9 = 78
- 9 - 9
-------------
6x = 69 [Divide by 6]
x = 11½ [3⁄6 = ½]
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?
Answers
Answer:
20 feet wide, 24 feet long
Step-by-step explanation:
Let x - width, y - length.
The perimeter is given by the formula:
P = 2*(width + length) or using x, y
P = 2*(x + y) = 88
x + y = 44
And we know that the ratio between the sides is 5/6:
x/y = 5/6. x is on top because the length is bigger than the width
x = 5y/6
Plug this in the first expression:
y + 5y/6 = 44. Muliply by 6
6y + 5y = 264
11y = 264
y = 264/11 = 24.
So x = 5(24)/6 = 20
plz help meh wit dis question but I need to show work.....
Answers
Answer:
5
Step-by-step explanation:
16+24
--------------
30-22
Complete the items on the top of the fraction bar
40
----------
30-22
Then the items under the fraction bar
40
------------
8
Then divide
5
Step-by-step explanation:
First of all, solve the numerator.
16+24=40
Secondly, solve the denominator:
30-22 = 8
So now the fraction appear like this :
[tex] \frac{40}{8} [/tex]
40/8 = 5
The equations 3x-4y=-2, 4x-y=4, 3x+4y=2, and 4x+y=-4 are shown on a graph.
Which is the approximate solution for the system of equations 3x+4y=2 and 4x+y=-4?
A. (–1.4, 1.5)
B. (1.4, 1.5)
C. (0.9, –0.2)
D. (–0.9, –0.2)
i cant download the graph picture but please help.
Answers
Answer:
A (-1,4,1.5)
Step-by-step explanation:
Solve by graphing, the lines intersect near this point.
merical expression 6+2^3•3
Answers
For this case we must resolve the following expression:
[tex]6 + 2 ^ 3 * 3 =[/tex]
For the PEMDAS evaluation rule, the second thing that must be resolved are the exponents, then:
[tex]6 + 8 * 3 =[/tex]
Then the multiplication is solved:
[tex]6 + 24 =[/tex]
Finally the addition and subtraction:
30
Answer:
30
James wants to tile his floor using tiles in the shape of a trapezoid. To make
the pattern a little more interesting he has decided to cut the tiles in half
along the median. The top base of each tile is 15 inches in length and the
bottom base is 21 inches. How long of a cut will John need to make so that
he cuts the tiles along the median?
THE
A. 18 inches
B. 6 inches
HT
C. 3 inches
O
D. 36 inches
Answers
Answer:
A. 18
Step-by-step explanation:
Median of a trapezoid: Its length equals half the sum of the base lengths.
So the sum of the lengths is 15 + 21 is 36 and half is 18.
18 inches long of a cut will John need to make so that he cuts the tiles along the median.
Given that, the top base of each tile is 15 inches in length and the bottom base is 21 inches.
What is the median of a trapezoid?The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.
The length of the median is the average of the length of the bases.
Now, add the top base and bottom base,
That is 15+21=36.
Now, divide that by 2
That is, 36/2= 18 inches.
Hence, the answer would be 18 inches.
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Please answer ASAP!
Answers
Answer:
C 1 hours 12 minutes
Step-by-step explanation:
We know distance is equal to rate times time
d= r*t
We know the distance is 30 miles and the rate is 25 miles per hour
30 = 25 *t
Divide each side by 25
30/25 = 25t/25
30/25 =t
6/5 =t
1 1/5 =t
Changing 1/5 hour to minutes. We know there is 60 minutes in 1 hours so 1/5 of an hour is 60*1/5
1/5 *60minutes = 12 minutes
1 hours 12 minutes
1. Factor each of the following completely. Look carefully at the structure of each quadratic function and consider the best way to factor. Is there a GCF? Is it an example of a special case? SHOW YOUR WORK
Answers
Answer: 1) (x - 7)(x - 8)
2) 2x(2x-7)(x + 2)
3) (4x + 7)²
4) (9ab² - c³)(9ab² + c³)
Step-by-step explanation:
1) x² - 15x + 56 → use standard form for factoring
∧
-7 + -8 = -15
(x - 7) (x - 8)
************************************
2) 4x³ - 6x² - 28x → factor out the GCF (2x)
2x(2x² - 3x - 14) → factor using grouping
2x[2x² + 4x - 7x - 14]
2x[ 2x(x + 2) -7(x + 2)]
2x(2x - 7)(x + 2)
*************************************
3) 16x² + 56x + 49 → this is the sum of squares
√(16x²) = 4x √(49) = 7
(4x + 7)²
******************************************************
4) 81a²b⁴ - c⁶ → this is the difference of squares
√(81a²b⁴) = 9ab² √(c⁶) = c³
(9ab² - c³)(9ab² + c³)
Some trapezoids are rectangles.
O
A. True
O
B. False
Answers
It's false, trapezoids are not rectangles.
Myrtle took out a 3-year loan for 2050$ at a computer retailer to be paid back with monthly payments at 12% apr compounded monthly. If the loan offers no payments for the first 5 months about how much in total will myrtle pay in interest for the loan?
Answers
Answer:
466.27$ APEX
Step-by-step explanation:
Answer:
We have ; p = 2050
r = [tex]12/12/100=0.01[/tex]
n = [tex]3\times12=36[/tex]
But we will take [tex]36-5=31[/tex]
EMI formula is :
[tex]\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}[/tex]
Substituting values in the formula we get;
[tex]\frac{2050\times0.01\times(1+0.01)^{31}}{(1+0.01)^{31}-1}[/tex]
= [tex]\frac{2050\times0.01\times(1.01)^{31}}{(1.01)^{31}-1}[/tex]
= $77.24
Now for further working you can see the sheet attached.
Total interest paid for the loan = $446.76
what is the area of the sector shown
Answers
Answer:
[tex] D.~ 34.2~cm^2 [/tex]
Step-by-step explanation:
An arc measure of 20 degrees corresponds to a central angle of 20 degrees.
Area of sector of circle
[tex] area = \dfrac{n}{360^\circ}\pi r^2 [/tex]
where n = central angle of circle, and r = radius
[tex] area = \dfrac{20^\circ}{360^\circ}\pi (14~cm)^2 [/tex]
[tex] area = \dfrac{1}{18}(3.14159)(196~cm^2) [/tex]
[tex] area = 34.2~cm^2 [/tex]
i cant do this i you can help me
Answers
Answer:
C (-1,6).
Step-by-step explanation:
This is a horizontal line segment since A and B have the same y-coordinate. Point P will also have the same y-coordinate since P is suppose to be on line segment AB.
So the only choice that has the y-coordinate as 6 is C. So we already know the answer is C. There is no way it can be any of the others.
So we are looking for the x-coordinate of point P using the x-coordinates of A and B.
A is at x=-3
B is at x=0
The length of AB is 0-(-3)=3.
AP+PB=3
AP/PB=2/1
This means AP=2 and PB=1 since 2+1=3 and AP/PB=2/1.
So if we look at A and we know P is 2 units away (after A) then -3+2=-1 is the x-coordinate of P.
OR!
IF we look at B and we know P is 1 unit away (before B), then 0-1=-1 is the x-coordinate of P.
what is the value of x?
Answers
Answer:
x=35
Step-by-step explanation:
We have the two angles (6x -82) and (3x + 23) that are equal. To find 'x' we need to solve the system of equations:
6x -82 = 3x + 23
Solving for 'x':
3x = 105
x = 35
[tex]6x-82=3x+23\\3x=105\\x=35[/tex]
What is the equation of the graph below
Answers
Answer:
y=-(x-3)^2+2
Step-by-step explanation:
since the curve is convex up so the coefficient of x^2 is negative
and by substituting by the point 3 so y = 2
Answer:
B
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (3, 2), hence
y = a(x - 3)² + 2
If a > 0 then vertex is a minimum
If a < 0 then vertex os a maximum
From the graph the vertex is a maximum hence a < 0
let a = - 1, then
y = - (x - 3)² + 2 → B
children play a form of hopscotch called jumby. the pattern for the game is as given below.
Find the area of the pattern in simplest form.
Answers
Answer:
7t^2 + 21t
Step-by-step explanation:
You have 7 tiles of each t by t+3.
One tile has an area of
t * (t+3) = t^2 + 3t
So in total the area is
7* (t^2 + 3t)
7t^2 + 21t
Isabel is on a ride in an amusement park that Slidez the right or to the right and then it will rotate counterclockwise about its own center 60° every two seconds how many seconds pass before Isabel returns to her starting position
Answers
Final answer:
Isabel's ride rotates 60° every two seconds. It takes 6 intervals (360° divided by 60°) to make a full rotation. Multiplying 6 intervals by 2 seconds gives us 12 seconds for Isabel to return to the starting position.
Explanation:
To determine how many seconds will pass before Isabel returns to her starting position on the ride, we need to establish the total degrees of rotation that equate to a full circle, which is 360°. Since the ride rotates 60° every two seconds, we can calculate the number of two-second intervals required to complete a full 360° rotation.
Firstly, divide 360° by 60° to find the number of intervals:
360° / 60° = 6 intervals
Since each interval takes 2 seconds, multiply the number of intervals by 2 to find the total time:
6 intervals × 2 seconds/interval = 12 seconds.
Therefore, it will take Isabel 12 seconds to return to her starting position on the amusement park ride.
Which of the following is a geometric sequence? Help pleaseee!
Answers
Answer: B
Step-by-step explanation:
Division of components are consistent - the same
Answer:
B. -3, 3, -3, 3...
Step-by-step explanation:
There's two types of sequences, arithmetic and geometric.
Arithmetic equations are sequences that increase or decrease by adding or subtracting the previous number.
For example, take a look at the following sequence:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20...
Here, the numbers are increasing by +2. [adding]
So, this the sequence is arithmetic, since its adding.
Geometric sequences are sequences that increase or decrease by multiplying or dividing the previous number.
For example, take a look at the following sequence:
2, 4, 16, 32, 64, 128, 256, 512...
Here, the numbers are icnreasing by x2. [multiplying]
So, the sequence is geometric since its multiplying.
Based on this information, the correct answer is "B. -3, 3, -3, 3..." since its being multiplyed by -1.
A parallelogram has coordinates A(1,1), B(5,4), C(7,1), and D(3,-2) what are the coordinates of parallelogram A’BCD after 180 degree rotation about the origin and a translation 5 units to the right and 1 unit down ?
Answers
Answer:
The coordinates are (4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is (x , y - k)
* Now lets solve the problem
∵ ABCD is a parallelogram
∵ Its vertices are A (1 , 1) , B (5 , 4) , C (7 , 1) , D (3 , -2)
∵ The parallelogram rotates about the origin by 180°
∵ The image of the point (x , y) after rotation 180° about the origin
is (-x , -y)
∴ The images of the vertices of the parallelograms are
(-1 , -1) , (-5 , -4) , (-7 , -1) , (-3 , 2)
∵ The parallelogram translate after the rotation 5 units to the right
and 1 unit down
∴ We will add each x-coordinates by 5 and subtract each
y-coordinates by 1
∴ A' = (-1 + 5 , -1 - 1) = (4 , -2)
∴ B' = (-5 + 5 , -4 - 1) = (0 , -5)
∴ C' = (-7 + 5 , -1 - 1) = (-2 , -2)
∴ D' = (-3 + 5 , 2 - 1) = (2 , 1)
* The coordinates of the parallelograms A'B'C'D' are:
(4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)
Question 7 (5 points)
Find the first five terms of the sequence in which a1 =-10 and an = 4an - 1 + 7. if n
2.
Answers
Answer:
-10, -33, -125, -493, -1965
Step-by-step explanation:
a_1 = -10
a_n = 4a_(n - 1) + 7
The first five terms of the sequence are
a_1 = -10
a_2 = 4(-10) + 7 = -40 + 7 = -33
a_3 = 4(-33) + 7 = -132 + 7 = -125
a_4 = 4(-125) + 7 = -500 + 7 = -493
a_5 = 4(-473) + 7 = -1972 + 7 = -1965
Use the Quadratic Formula to solve the equation x2 - 4x = -7
Answers
The given quadratic equation x² - 4x = -7 is rearranged into standard form and then solved using the quadratic formula -b ± √(b² - 4ac) / (2a). The roots of the equation are realized from solving this formula.
Explanation:The subject of this problem is a quadratic equation in the form of ax²+bx+c = 0. The given equation is x² - 4x = -7, which can be rearranged into standard form as x² - 4x + 7 = 0. Thus, in this case, a=1, b=-4, and c=7.
The solutions or roots for this quadratic equation can be calculated using the quadratic formula, which is -b ± √(b² - 4ac) / (2a). Substituting the values of a, b, and c into the formula will give the roots of the given equation.
Doing that, we get: x = [4 ± √((-4)² - 4*1*7)] / (2*1)
The values that solve the equation are the roots of the quadratic equation.
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To solve the equation x^2 - 4x = -7 using the Quadratic Formula, we follow the steps of plugging the values of a, b, and c into the formula, evaluating the square root and simplifying to find the solutions.
Explanation:To solve the equation x2 - 4x = -7 using the Quadratic Formula, we first need to make sure the equation is in standard form, which is ax2 + bx + c = 0. In this case, a = 1, b = -4, and c = 7. Plugging these values into the Quadratic Formula, we get:
x = (-(-4) ± √((-4)2 - 4(1)(-7))) / (2(1))
x = (4 ± √(16 + 28))/2
x = (4 ± √44)/2
x = (4 ± 2√11)/2
x = 2 ± √11
So the solutions to the equation x2 - 4x = -7 are x = 2 + √11 and x = 2 - √11.
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What is the volume of a sphere that has a radius of 9?
Answers
Answer:
V = 3053.63
Step-by-step explanation:
The volume of a sphere that has a radius of 9 is 3053.63.
V=4
3πr3=4
3·π·93≈3053.62806
Answer is provided in the image attached.
Which of the following numbers are less than 9/4?
Choose all that apply:
A= 11/4
B= 15/8
C= 2.201
Answers
Answer:
OPTION B.
OPTION C.
Step-by-step explanation:
In order to know which numbers are less than [tex]\frac{9}{4}[/tex], you can convert this fraction into a decimal number. To do this, you need to divide the numerator 9 by the denominator 4. Then:
[tex]\frac{9}{4}=2.25[/tex]
Now you need convert the fractions provided in the Options A and B into decimal numbers by applying the same procedure. This are:
Option A→ [tex]\frac{11}{4}=2.75[/tex] (It is not less than 2.25)
Option B→ [tex]\frac{15}{8}=1.875[/tex] (It is less than 2.25)
The number shown in Option C is already expressed in decimal form:
Option C→ [tex]2.201[/tex] (It is less than 2.25)
Prove that the diagonals of a parallelogram bisect each other.
Plan: Since midpoints will be involved, use multiples of __ to name the coordinates for B, C, and D.
Answers
Answer:
2
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. Since midpoints will be involved, use multiples of 2 to name the coordinates for B, C, and D.
Answer:
2
Step-by-step explanation:
Well by definition a Rhombus is an equilateral paralelogram, AB =BC=CD=DA with all congruent sides, and Diagonals with different sizes.
Also a midpoint is the mean of coordinates, like E is the mean coordinate of A,C, and B, D
[tex]\frac{B+D}{2}=E\\ \\ B+D=2E\\ and\\\\ \frac{A+C}{2} =E\\ A+C=2E[/tex]
So the sum of the Coordinates B and D over two returns the midpoint.
And subsequently the sum of the Coordinates B +D equals twice the E coordinates. The same for the sum: A +C
Given to the fact that both halves of those diagonals coincide on E despite those diagonals have different sizes make us conclude, both bisect each other.
Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written using
function notation?
o AV=-=x+
o 0) = -3x+4
o Px) =-x+
o F) = - 3y+ 4
Answers
Answer:
f(x)=-3x+4
(can't see some of your choices)
Step-by-step explanation:
We want x to be independent means we want to write it so when we plug in numbers we can just choose what we want to plug in for x but y's value will depend on our choosing of x.
So we need to solve for y.
9x+3y=12
Subtract 9x on both sides
3y=-9x+12
Divide both sides by 3:
y=-3x+4
Replace y with f(x).
f(x)=-3x+4
Write a function rule based on the table below.
x f(x)
1 5
2 10
3 15
f(x) = x + 4
f(x) = 5x + 2
f(x) = 5x
f(x) = 5
Answers
Answer:
[tex]\large\boxed{f(x)=5x}[/tex]
Step-by-step explanation:
[tex]\begin{array}{c|c}x&f(x)\\1&5\\2&10\\3&15\end{array}\\\\\\f(1)=5(1)=5\\f(2)=5(2)=10\\f(3)=5(3)=15\\\Downarrow\\f(x)=5x[/tex]
A high school track is shaped as a rectangle with a half circle on either side . Jake plans on running four laps . How many meters will jake run ?
Answers
Answer:
[tex]1,207.6\ m[/tex]
Step-by-step explanation:
step 1
Find the perimeter of one lap
we know that
The perimeter of one lap is equal to the circumference of a complete circle (two half circles is equal to one circle) plus two times the length of 96 meters
so
[tex]P=\pi D+2(96)[/tex]
we have
[tex]D=35\ m[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]P=(3.14)(35)+2(96)[/tex]
[tex]P=301.9\ m[/tex]
step 2
Find the total meters of four laps
Multiply the perimeter of one lap by four
[tex]P=301.9(4)=1,207.6\ m[/tex]
Answer:
1207.6
Step-by-step explanation:
step 1
i got it right on the test
step 2
you get it right on the test
write a point slope equation for the line that has slope 3 and passes through the point (5,21). do not use parenthesis on the y side
Answers
Answer:
y - 21 = 3(x - 5)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 3 and (a, b) = (5, 21), hence
y - 21 = 3(x - 5) ← in point- slope form
The point slope form of an equation is y - y1 = m(x - x1). Substituting the given point (5,21) and slope 3 into the equation, we get y - 21 = 3(x - 5). To remove the parenthesis on the y side, we simplify the equation to be y = 3x + 6.
Explanation:The question asks for the writing of a point-slope equation of a line with a given slope of 3 that passes through a point (5,21). The point-slope form of an equation is generally denoted as:
y - y1 = m(x - x1)
Here, (x1, y1) = (5,21) and m (slope) = 3. Hence, substituting these values yields the equation:
y - 21 = 3(x - 5)
The asked equation without parenthesis on the y side would be:
y = 3x - 15 + 21
So, the final equation is:
y = 3x + 6
Learn more about Point-Slope Equationhttps://brainly.com/question/35491058
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What expression can be used to find 75% of 60%?
Answers
To find 75% of 60%, just multiply them together. 75% is 0.75 and 60% is 0.60 or 0.6. 0.75*0.6=0.45
Answer:
The expression used to find of 75 and 60 is 45.
Step-by-step explanation:
To find expression of 75 and 60, multiply decimals from left to right.
0.75*0.60=0.45 =45%
.75*.60=.45=45
45=45
True
45, which is our answer.