Recall that
tan(x) = sin(x)/cos(x)
and
sin(x) = x - x ³/6 + x ⁵/120 - x ⁷/5040 + …
cos(x) = 1 - x ²/2 + x ⁴/24 - x ⁶/720 + …
Truncate the series to three terms. Then
[tex]\displaystyle \lim_{x\to0}\frac{\tan(x)-x}{x^3} = \lim_{x\to0}\frac{\frac{x-x^3/6+x^5/120}{1-x^2/2+x^4/24}-x}{x^3} \\\\ = \lim_{x\to0}\left(\frac{x-x^3/6+x^5/120}{x^3-x^5/2+x^7/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2-x^4/2+x^6/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac{1-x^2/2+x^4/24}{x^2\left(1-x^2/2+x^4/24\right)}\right) \\\\ = \lim_{x\to0}\frac{x^2/3-x^4/30}{x^2\left(1-x^2/2+x^4/24\right)} \\\\ = \lim_{x\to0}\frac{1/3-x^2/30}{1-x^2/2+x^4/24} = \boxed{\frac13}[/tex]
trigonometric identities
Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.
4 sin²(θ) - 1 = 0
==> sin²(θ) = 1/4
==> sin(θ) = ±1/√2
==> θ = π/4, 3π/4, 5π/4, 7π/4
The 7-digit numbers in a given area code have the form ABC-XXXX. Given ABC is 972, how many
possible phone numbers are there? (The form is 972-XXXX and the numbers 0-9 can be used)
Total number of possibilities is 10,000.
Step-by-step explanation:
Given:
Total number between (0-9) = 10 number
Frequency of unknown number = 4 times
Find:
Total number of possibilities
Computation:
Total number of possibilities when repetition is allowed;
Total number of possibilities when repetition is allowed = 10 × 10 × 10 × 10
Total number of possibilities when repetition is allowed = 10,000
Total number of possibilities when repetition is allowed = 10,000 times
Learn more:
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Given:
Overall number [tex]\bold{(0-9) = 10}[/tex]
Unknown source frequency [tex]= \bold{4\ times}[/tex]
Find:
The overall amount of opportunities=?
Calculation:
The total possible number for repeaters [tex]=\bold{ 10 \times 10 \times 10 \times 10}[/tex]
The total amount of repeat possibilities [tex]=\bold{ 10,000}[/tex]
Total amount of repeating options [tex]=\bold{ 10,000\ times}[/tex]
So, the "total number of possibilities is [tex]\bold{ 10,000}[/tex]"
Learn more:
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Question 12
A leaking pond loses 16 gallons of water in 5 hours. How many gallons of water will it lose in 41 hours?
Answer:
131.2 gallons
Step-by-step explanation:
1)16/5= 3.2 gallons - of water are lost in 1 hour;
2)3.2*41=131.2 gallons
if a bicycle is 2.5 feet in diameter and races for 345 feet how many time does the wheel turn
NEED HELP ASAP
David is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 10% sales tax plus a state-mandated $60 fee for disposing of his old tires. If David has determined that he will spend less than $578.10 total, then what is the price range he can spend on the tire set?
Select one:
a.
Less than $471
b.
At least 475
c.
$471 or more
d.
Less than 476
Answer:
a. Less than $471
Step-by-step explanation:
The total price must be less than $578.10.
Let the price of the 4 tires = x.
He pays 10% tax on x. That means he pays x + 10%x = 1.1x including tax.
Then he pays the $60 fee.
He pays a total of 1.1x + 60
That must be less than $578.10
1.1x + 60 < 578.10
Subtract 60 rom both sides.
1.1x < 518.1
Divide both sides by 1.1
x < 471
Answer: a. Less than $471
Use the vertex
(h, k)
and a point on the graph
(x, y)
to find the general form of the equation of the quadratic function.
(h, k) = (−4, −1), (x, y) = (−7, 8)
Answer:
Step-by-step explanation:
Let the quadratic function be
y=a(x+4)²-1
∵(-7,8) lies on it.
8=a(-7+4)²-1
8+1=a(-3)²
9a=9
a=9/9=1
so quadratic function is
f(x)=1(x+4)²-1
or
f(x)=x²+8x+16-1
so quadratic function is
f(x)=x²+8x+15
Find the second partial derivatives of the following functions
a) z = 3x^2 − 4xy + 15y^2
b) z = 4xe^y
c) z = 6xln(y)
(a) z = 3x ² - 4xy + 15y ²
has first-order partial derivatives
∂z/∂x = 6x - 4y
∂z/∂y = -4x + 30y
and thus second-order partial derivatives
∂²z/∂x ² = 6
∂²z/∂x∂y = -4
∂²z/∂y∂x = -4
∂²z/∂y ² = 30
where ∂²z/∂x∂y = ∂/∂x [∂z/∂y] and ∂²z/∂y∂x = ∂/∂y [∂z/∂x].
(b) z = 4x eʸ
∂z/∂x = 4eʸ
∂z/∂y = 4x eʸ
∂²z/∂x ² = 0
∂²z/∂x∂y = 4eʸ
∂²z/∂y∂x = 4eʸ
∂²z/∂y ² = 4x eʸ
(c) z = 6x ln(y)
∂z/∂x = 6 ln(y)
∂z/∂y = 6x/y
∂²z/∂x ² = 0
∂²z/∂x∂y = 6/y
∂²z/∂y∂x = 6/y
∂²z/∂y ² = -6x/y ²
What is the value of x that makes l1||l2?
A. 15
B. 25
C. 18
D. 29
Answer:
x = 29
Step-by-step explanation:
The angles are corresponding angles and corresponding angles are equal when the lines are parallel
3x+17 = 4x-12
Subtract 3x from each side
3x+17-3x = 4x-12-3x
17 = x-12
Add 12 to each side
17+12 = x-12+12
29 =x
Answer:
D. 29
Step-by-step explanation:
If you plug in 29 in the missing values for L1 and L2, you get
L1 = 3(29) + 17 = 104
L2 = 4(29) - 12 = 104
I know I am correct because since both L1 and L2 are parallel and T in cutting them, I know that they are both going to be the same degrees, 104.
So, your answer would be D. 29
Hope the helps! :)
THE DISTANCE OF A PARTICLE FROM
IT'S STARTING POINT AT TIME T
SECONDS IS GIVEN BY S= 80T - 1672.
WHAT IS THE VELOCITY OF THE
PARTICLE AFTER 2 SECONDS?
Answer:
the answer will be 3.........
The strength of a school Increased from 400 to 500 find the Increase percent.
Answer:
25
Step-by-step explanation:
I'm sorry but I rlly don't rember how I did it because I did this question on a quiz and the teacher said this was that answer but not how to get it.
look at the image for the answer below?
Answer:
Does the answer help you?
-3(y-5)+6y-2 simplify using distributive property and then combine like terms ANOTHER ONE PLEASE
Answer:
3y+13
Step-by-step explanation:
-3(y-5)+6y-2
Distribute
-3y +15 +6y-2
Combine like terms
-3y+6y +15-2
3y +13
[tex]\bf \large{\purple{ \implies}} \tt \: - 3(y - 5) \: + \: 6y \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 15 \: + \: 6y \: - 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: - 3y \: + \: 6y \: + \: 15 \: - \: 2[/tex]
[tex]\bf \large{\purple{ \implies}} \tt \: 3y \: + \: 13[/tex]
A hot air balloon descends 200 feet per
minute from an altitude of 1000 feet. Write a expression
Please help!
The quantities x and y are proportional.
x: 4 5 10
y: 10 12.5 25
Find the constant of proportionality (r) in the equation y=rx.
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Answer:
r = 2.5
Step-by-step explanation:
The constant of proportionality can be found by solving the equation for r:
r = y/x
Then any corresponding values of x and y can be used to find r:
r = 25/10 = 2.5
The constant of proportionality is 2.5.
Find the equation of the line: with a slope of -1/2 through (4,5)
Answer:
y=-1/2x+3
Step-by-step explanation:
y=mx+c
5=-1/2*4+c
5=-2+c
c=5-2
c=3
y=-1/2x+3
To make a stemplot of these rainfall amounts, round the data to the nearest 10, so that stems are hundreds of millimeters and leaves are tens of millimeters. Make two stemplots, with and without splitting the stems. Which plot do you prefer
The two stem plots (with and without splitting the leaves) are plotted below using the data given in the attached picture :
The stem and leaf plots are given below:
Rounding the data to the nearest 10;
The values obtained are :
630, 670, 740, 650, 710, 740, 720, 700, 650, 600, 780, 780, 790, 810, 830, 860, 860, 900, 810, 790, 790, 960, 870
Ordering the data allows for easier generation of the plot.
Ordered data : 600, 630, 650, 650, 670, 700, 710, 720, 740, 740, 780, 780, 790, 790, 790, 810, 810, 830, 860, 860, 870, 900, 960
The stem plot without splitting :
STEM __ LEAF
6 ___ 00, 30, 50, 50, 70
7 ___ 00, 10, 20, 40, 40, 80, 80, 90, 90, 90
8 ___ 10, 10, 30, 60, 60, 70
9 ___ 00, 60
KEY : 6 | 00 = 600
The stem plot WITH splitting :
STEM __ LEAF
6 ___ 00, 30
6 ___ 50, 50, 70
7 ___ 00, 10, 20, 40, 40
7 ___ 80, 80, 90, 90, 90
8 ___ 10, 10, 30
8 ___ 60, 60, 70
9 ___ 00
9 ___ 60
KEY : 6 | 00 = 600
The stem plot with splitting gives a cleaner and more arranged output of the data as the values aren't congested on a single line.
Learn more on stem and leaf plot : https://brainly.com/question/12857419?
A rotation or turn always moves clockwise and never counterclockwise.
True
False
Answer:
False
Step-by-step explanation:
It can go in any direction
Answer:
False
Step-by-step explanation:
Rotations can be either clockwise or counterclockwise
can someone help? i can’t figure this out; i’ll give brainliest:))
What we need to memorize when finding the slope is this formula:
[tex] \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
m here represents the slope. I hope this does not confuse you with line m.
The problem here is that we do not have any given points, but we have a way.
If we notice on the graph, the graph contains or passes through (2,-1) and (-2,1). We can use these points to find the slope. So let these be the following:
[tex] \displaystyle \large{(x_1,y_1) = (2 ,- 1)} \\ \displaystyle \large{(x_2,y_2) = ( - 2 ,1)} [/tex]
Then we substitute these points in the formula.
[tex] \displaystyle \large{m = \frac{ 1 - ( - 1)}{ - 2 - 2} }[/tex]
negative × negative = positive.
[tex] \displaystyle \large{m = \frac{ 1 + 1}{ - 2 - 2} } \\ \displaystyle \large{m = \frac{ 2}{ - 4} } \longrightarrow \boxed{m = - \frac{1}{2} }[/tex]
Since m represents the slope. Therefore, the slope of line m is -1/2
Plz help me solve need help
Answer:
t=1, u=-2, w=-2
Step-by-step explanation:
Let f(x) =
[tex] \sqrt[3]{11x - 3 \:} determine \: {f}^{ - 1} (x)[/tex]? here
Step-by-step explanation:
Set up f(x).
[tex] \sqrt[3]{11x - 3} = f(x)[/tex]
Replace f(x) with y
[tex] \sqrt[3]{11x - 3} = y[/tex]
Swap x and y
[tex] \sqrt[3]{11y - 3} = x[/tex]
Solve for y
Cube both sides
[tex]11y - 3 = {x}^{3} [/tex]
Add 3 to both sides
[tex]11y = {x}^{3} + 3[/tex]
Divide both sides by 11
[tex]y = \frac{x {}^{3} + 3 }{11} [/tex]
so
[tex]f {}^{ - 1} (x )= \frac{ {x}^{3} + 3}{11} [/tex]
find value of x and YZ if Y is between X and Z
XY=2x+1, YZ =6x, and XZ=81
Answer:
10
Step-by-step explanation:
Applying the segment addition theorem, the value of x = 10
YZ = 60
What is the Segment Addition Theorem?The segment addition theorem states that if a point, C, lies between two endpoints of a segment, A and B, then: AC + CB = AB.
Given:
XY = 2x+1
YZ = 6x
XZ = 81
Thus:
XY + YZ = XZ (segment addition theorem)
2x + 1 + 6x = 81
Find x
8x = 81 - 1
8x = 80
x = 10
Find YZ:
YZ = 6x
Plug in the value of x
YZ = 6(10)
YZ = 60
Therefore, applying the segment addition theorem, the value of x = 10
YZ = 60
Learn more about the segment addition theorem on:
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Use AABC shown below to answer the question that follows:
Which of the following is a step towards proving the similarity of triangle so AABC and ADBA? (5 points)
Segment BC is a hypotenuse.
Angle B is congruent to itself.
Segment BA is shorter than segment BC.
Segment BC is intersected by segment AD.
Answer:
Bc is intersected by segment AD
Answer:
Bc is intersected by segment AD
Step-by-step explanation:
There are 200 ounces in 6 liters. How many milliliter (ml) are in 6 liters? (How to do in dimensional analysis?)
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Answer:
6000 mL
Step-by-step explanation:
The prefix "milli-" is an SI standard prefix meaning 1/1000. So, 1 mL = (1/1000)L.
When doing dimension changes, you always want to use scale factors that have a value of 1, which is to say the numerator is equal to the denominator. For converting liters to milliliters, the scale factor you want will have mL in the numerator and L in the denominator:
(1 mL)/(1/1000 L) or (1000 mL)/(1 L)
To do your conversion, multiply your liter volume by this factor.
[tex](6\text{ L})\times\dfrac{1000\text{ mL}}{1\text{ L}}=\dfrac{6\times1000\text{ mL$\cdot$L}}{1\text{ L}}=6000\text{ mL}[/tex]
6 liters is 6000 milliliters.
__
You will notice that the dimensions "L" cancel, which is the point of the exercise.
_____
Additional comment
6 L is closer to 202.884 fluid ounces. The conversion factor is ...
[tex]\dfrac{128\text{ fl oz}}{231\text{ in}^3}\times\dfrac{1\text{ in}^3}{(0.254\text{ dm})^3}\times\dfrac{1\text{ dm}^3}{1\text{ L}}=\dfrac{128\text{ fl oz}}{3.785411784\text{ L}}\quad\text{exactly}[/tex]
there are 3 blouse and 2 pieces cloths for sale in the market. how many possible sets are there?
Answer:
Each item could be included in a set or not included. That gives 2^5 = 32 ways to choose sets, including 1 set with no items, 5 sets of 1 item, 10 sets of 2 items, 10 sets of 3 items, 5 sets of 4 items, and 1 set of 5 items.
[tex]log(x) * log(2)[/tex]
Why can't this problem be solved?
Answer:
Because it is not an equation.
Step-by-step explanation:
[tex] log(x) \times log(2) \\ = log(x + 2) [/tex]
Solve: 5 + n > 2
Just let me know because I am stuck and need to know the answer for this test please let me know thank you ❤️
[tex]\\ \sf\longmapsto 5+n>2[/tex]
We have to find n Take 5 to right side sign will be changed[tex]\\ \sf\longmapsto n>2-5[/tex]
Simplify[tex]\\ \sf\longmapsto n>-3[/tex]
what is 4 and 5???????
Answer:
586 cm^3 and 486 in^2
Step-by-step explanation:
4) The volume of the triangular prims is (1/2)*(a*c*h) = 0.5*(8*9*16)=586 cm^3
5) Wrapping paper needed is equal to the surface area of the cube, 6s^2=486 in^2
base:10 height:2.5 what is the slope of the ramp
Answer:
Slope is B. ¼
Step-by-step explanation:
Slope: is hypotenuse
[tex] = { \sf{ \frac{ \delta \: height}{ \delta \: base} }} \\ \\ { \sf{ = \frac{2.5}{10} }} \\ \\ = { \sf{ \frac{1}{4} }}[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE answer thoroughly. Chapter 9 part 2
4. How can you determine the maximum number of solutions for a polynomial? How are these counted on the graph?
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Answer:
a) the degree of the polynomial
b) count the x-intercepts, with attention to multiplicity
Step-by-step explanation:
The Fundamental Theorem of Algebra tells you the number of zeros of a polynomial is equal to the degree of the polynomial. That is, for some polynomial p(x), the number of solutions to p(x)=0 will be the degree of p.
__
On a graph, a real zero of the polynomial will be an x-intercept. The "multiplicity" of a zero is the degree of the factor giving rise to that zero. When the multiplicity is even, the graph does not cross the x-axis at the x-intercept. The greater the multiplicity, the "flatter" the graph is at the x-intercept.
If all solutions (zeros) are distinct, then the number of real solutions can be found by counting the number of x-intercepts of the graph.
_____
By way of illustration, the attached graph is of a 6th-degree polynomial with 6 real zeros. From left to right, they are -1 (multiplicity 1), 1 (multiplicity 2), 4 (multiplicity 3). The higher multiplicities are intended to show the flattening that occurs at the x-intercept, and the fact that the graph does not cross the x-axis where the multiplicity is even.
I really need help on this been trying for ages
Answer:
cos F = adjacent/hypotenuse
= 15/28
