Answers
Answer:
[tex]\int\limits {{(sin \ x})^{-1} } \, dx = \text{ln}\left |{tan\, \left (\dfrac{x}{2} \right)} \right |[/tex]
Step-by-step explanation:
[tex]\int\limits {(sin \ x)^{-1}} \, dx = \int\limits {\dfrac{1}{sin \ x} } \, dx[/tex]
We have the following relationships;
[tex]\dfrac{1}{sin \ x } = csc \, x[/tex]
We can write;
[tex]csc \, x = csc \, x \times \dfrac{csc \, x + cot \, x}{csc \, x + cot \, x} = \dfrac{csc^2 \, x + csc \, x \cdot cot \, x}{csc \, x + cot \, x}[/tex]
We note that the numerator of [tex]\dfrac{csc^2 \, x + csc \, x \cdot cot \, x}{csc \, x + cot \, x}[/tex] , which is [tex]{csc^2 \, x + csc \, x \cdot cot \, x}[/tex] is the derivative of the denominator, [tex]{csc \, x + cot \, x}[/tex], therefore, we can use integration by substitution method and write;
[tex]{csc \, x + cot \, x} = u[/tex], from which we get;
[tex]({csc^2 \, x + csc \, x \cdot cot \, x}) \cdot dx = (-1)du[/tex]
Therefore, we can write;
[tex]\int\limits {\dfrac{1}{sin \ x} } \, dx = \int\limits {\dfrac{{csc^2 \, x + csc \, x \cdot cot \, x}}{{csc \, x + cot \, x}} } \, dx \Rightarrow -\int\limits {\dfrac{1}{u} } \, du = -ln \left |u \right |[/tex]
[tex]\text{-ln} \left |u \right | = \text{-ln}\left |{csc \, x + cot \, x} \right |[/tex]
Therefore;
[tex]\int\limits {\dfrac{1}{sin \ x} } \, dx = \text{-ln}\left |{csc \, x + cot \, x} \right |[/tex]
csc x + cot x = (1/sin x) + ((cos x)/(sin x)) = (1 + cos x)/(sin x)
(1 + cos x)/(sin x) = (cos²(x/2) + sin²(x/2) + cos²(x/2) - sin²(x/2))/(2sin(x/2)·cos(x/2)) = (2·cos²(x/2))/((2sin(x/2)·cos(x/2)) = cos(x/2)/sin(x/2) = cot(x/2)
Therefore;
[tex]\text{-ln}\left |{csc \, x + cot \, x} \right | = \text{-ln}\left |{cot \, \left (\dfrac{x}{2} \right) } \right | = \text{ln}\left |{cot \, \left (\dfrac{x}{2} \right)} \right | ^{-1} = \text{ln}\left |{tan\, \left (\dfrac{x}{2} \right)} \right |[/tex]
Therefore;
[tex]\int\limits {{(sin \ x})^{-1} } \, dx = \int\limits {\dfrac{1}{sin \ x} } \, dx = \text{ln}\left |{tan\, \left (\dfrac{x}{2} \right)} \right |[/tex]
Related Questions
Nike is offering a 30% discount on shirts. A shirt at the store has an original cost of $25. What is the cost of the shirt, in dollars, after the discount
Answers
Answer:
$17.5
Step-by-step explanation:
original price of shirt=$25
discount on shirt=30%
discount on shirt in $=$25*30%
discount on shirt=$7.5
cost of shirt after discount=origanl price-discount
=$25-$7.5
=$17.5
What is the length of AC?
Answers
Because all the angles are congruent (the same), this is an equilateral triangle. All equilateral triangles have congruent angles and congruent sides, so all sides has to be 14.
A circle has a radius of 11m . Find the radian measure of the central angle that intercepts an arc of length 6 m .
Answers
Answer:
Step-by-step explanation:
θ=l/r
θ=6/11 radians
≈0.555... radians
In ΔRST, m∠R = 92° and m∠S = 71°. Which list has the sides of ΔRST in order from shortest to longest?
Answers
Answer:
RS, RT, ST
Step-by-step explanation:
We require the third angle in the triangle
∠ T = 180° - (92 + 71)° = 180° - 163° = 17°
The shortest side is opposite the smallest angle
∠ T = 17° → opposite side RS
The longest side is opposite the largest angle
∠ R = 92° → opposite side ST
Then sides from shortest to longest is
RS, RT, ST
can somene explain this to me please?
Answers
Answer:
10/3
Step-by-step explanation:
rate of change = gradient
(17-7)/(6-3) = 10/3
basically difference of y values / difference of x values
there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three times greater than the number of nickels, and the number of quarters is one greater than double the number of nickels. how many quarters, nickels, and dimes are there?
Answers
Answer:
4 nickels
12 dimes
9 quarters
Step-by-step explanation:
x = number of nickels
y = number of dimes
z = number if quarters
0.05×x + 0.1×y + 0.25×z = 3.65
y = 3x
z = 2x + 1
0.05x + 0.1×3x + 0.25×(2x + 1) = 3.65
5x + 30x + 25×(2x + 1) = 365
35x + 50x + 25 = 365
85x = 340
x = 340/85 = 4
y = 3×4 = 12
z = 2×4 + 1 = 9
The graph of h(x) = (x - 3)2 is a translation of the
graph of f(x) ….. blank
by
…. Blank units.
Answers
Answer:
right by 3 I think
Step-by-step explanation:
Answer: Right by 3 Units
Step-by-step explanation:
Right on edge 2021
Help anyone can help me do this question,I will mark brainlest.
Answers
side of cube=5
We know
[tex]\boxed{\sf Side=\dfrac{Diagonal}{\sqrt{2}}}[/tex]
[tex]\\ \sf \longmapsto Diagonal =sude\times \sqrt{2}[/tex]
[tex]\\ \sf \longmapsto Diagonal=5\sqrt{2}[/tex]
[tex]\\ \sf \longmapsto Diagonal=5\times 1.4[/tex]
[tex]\\ \sf \longmapsto Diagonal=7cm[/tex]
Answer:
Hello,
Step-by-step explanation:
[tex]Using\ the\ Pythagorian's\ theorem,\\\\EC^2=EA^2+AC^2\\\\=EA^2+AB^2+BC^2\\\\=3*5^2\\\\EC=5\sqrt{3} \approx{8,660...}[/tex]
Zero is_______greater than any negative integer.
always
never
sometimes
Answers
Answer:
always
Step-by-step explanation:
Zero is always greater than any negative integer.
All the negative integers lie to the left of 0 on the number line. This implies that zero is always greater than any negative integer.If the mean of a normal distribution is 210, what is the median of the
distribution?
210
B. 315
C. 105
D. 420
Answers
Answer:
210
Step-by-step explanation:
In a normal distribtuion mean=mode=median
so 210=median
If sin A= 0.8, find the positive value of cos A
Answers
Answer:
cosA = 0.6
Step-by-step explanation:
Using the Pythagorean identity
sin²A + cos²A = 1 ( subtract sin²A from both sides )
cos²A = 1 - sin²A ( take the square root of both sides )
cosA = ± [tex]\sqrt{1-sin^2A[/tex]
Since only the positive value is required , then
cosA = [tex]\sqrt{1-(0.8)^2}[/tex]
= [tex]\sqrt{1-0.64}[/tex]
= [tex]\sqrt{0.36}[/tex]
= 0.6
Answer:
Answer:
Answer:x = 25°
Answer:x = 25°Step-by-step explanation:
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2}
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 2
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2}
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 2
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )
Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is\frac{1}{2} 21 ( BD - FE ) = ∠ FGE, that is\frac{1}{2} 21 (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )x = 25°
5. There are 5,280 feet in a mile. What part of a mile, in decimal form, will you drive until you reach the exit?It is 1,000 feet away. I need it quick plz I will GIVE you 50pts!
Answers
Answer:
1 mile = 5280 feet, then
1 foot = 1 / 5280 milesFind 1000 feet in miles:
1000 feet = 1000 * 1/5280 miles = 1000/5280 miles = ~0.1894 miles[tex]\\ \sf\longmapsto 1feet= \dfrac{1}{5280}miles[/tex]
Now
[tex]\\ \sf\longmapsto 1000feet[/tex]
[tex]\\ \sf\longmapsto 1000\times \dfrac{1}{5280}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1000\times 1}{5280}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1000}{5280}[/tex]
[tex]\\ \sf\longmapsto 0.18miles[/tex]
8 cm 10 cm 15 cm surface area of a rectangle
Answers
Answer:
surface area of a square = 2 ( lb + bh + hl )
given that,
length = 8cm
breadth = 10cm
height = 15 cm
surface area = 2 ( 8* 10 + 10*15 + 15*8 )
= 2 ( 80 + 150 + 120 )
= 2 * 350
= 700 [tex]cm^{2}[/tex]
hope this answer helps you!!
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units
Answers
Answer: 4. A base area of 16y^2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Using the distributive property; you can see that 16y^2(y^2+y+3)=
16y^4+16y^3+48y^2
Answer:
D. a base area of 16y2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Ed22
-(2x +y) - 2 ( -x - y)
....................
Answers
Answer:
First, we apply the Distributive property and then we combine like terms,
To combine like terms, we add or subtract.
[tex]-(2x +y) - 2 ( -x - y)[/tex]
[tex]=-2x-y+2x+2y[/tex]
[tex]=(-2x+2x)+(-y+2y)[/tex]
[tex]=0+y[/tex]
[tex]=y[/tex]
OAmalOHopeO
Answer:
y is the simplest result here.
Step-by-step explanation:
Perform the indicated multiplication as a first step towards simplifying this expression:
-2x - y + 2x + 2y
-2x and 2x cancel each other out, leaving 2y - y, or just y
How long would it take a garden snail at his top speed of 0.01 m/s to travel 1 mile? Use 1 mile = 1609 meters. Round to the nearest whole hour.
Answers
Answer:
45 hours
Step-by-step explanation:
1 mile * 1609 meters * 1 s = 160900 sec
1 mile .01 meters
160900 sec / 60 /60 = 44.7 = 45 hours
Step-by-step explanation:
This is a cute question lol.
So this lil snail is trying to go 1609 meters, at a speed of 0.01 m/s (meters per second). Lets see how long that takes.
The way I like to do conversion problems is by starting with the value that doesn't have something on the bottom (1609 m) then multiplying to get rid of that variable.
I'll show you what I mean:
[tex]\frac{1609 m}{1} *\frac{1 s}{0.01 m} *\frac{1 min}{60s} *\frac{1 hr}{60 min}[/tex]
Then, we just multiply everything.
[tex]\frac{1609 *1*1}{1*0.01*60*60}hr[/tex]
Simplify.
[tex]\frac{1609}{36}hr[/tex]
Divide.
[tex]44.694444444...hr[/tex]
Round to the nearest whole hour.
[tex]45 hr[/tex]
Answer:
45 hours
which kind of triangle is shown.
1. obtuse isosceles
2. acute equilateral
3. obtuse scalene
4. right scalene
Answers
Answer: 2, acute equilateral
Step-by-step explanation:
the image shows a triangle with all 3 sides congruent and 3 acute angles
What is the domain of the function graphed below?
Answers
Answer:
(-2,4] and [7,α)
Step-by-step explanation:
the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..
The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = x²+1 if (-2,0]
This the sub-function define between the interval (-2,0].
f(x) = -1 if (0, 4]
This the sub-function define between the interval (0, 4].
f(x) = -(x-7)² if [7, ∞)
This the sub-function define between the interval [7, ∞).
Thus, the domain of the given function is (-2,4] U [7, ∞).
Learn more about the piecewise function here:
https://brainly.com/question/12700952
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A car travels 52/5 kilometers in 23/4 minutes. What is the unit rate in kilometers per minute?
Answers
The unit rate of the car that travels 5 2/5 km in 2 3/4 mins is: 1.96 km/min.
What is Unit Rate?Unit rate can be defined as the ratio of one quantity in comparison to another.
Distance travelled by a car = 5 2/5 km = 5.4 km
Time travelled = 2 3/4 mins = 2.75 mins
Unit rate in km/min = 5.4/2.75
Unit rate in km/min = 1.96 km/min.
Learn more about the unit rate on:
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if you get 76% on a 50 question test how many questions did you get wrong?
Answers
Answer:
100% - 76% = 24%
24% = 0.24
0.24*50 = 12
You got 12 questions wrong.
Step-by-step explanation:
Please mark brainliest!
Number of questions that got wrong are 12 .
Given,
76% on a 50 question test.
Here,
Let total percentage value be 100%.
Then,
100% - 76% = 24%
24% questions got wrong.
Number of questions that got wrong out of 50 will be ,
24% of 50
= 0.24*50
= 12
Therefore 12 questions got wrong.
Know more about percentages,
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Does anyone know the equation to this trigonometric function? Step by step?
Answers
A general cosine function (we could also use a sine function) is written as:
y = A*cos(k*x + p) + M
We will find that the function of the graph is:
f(x) = 2*cos(2*x + 2.09) - 2
Let's return to the general function:
y = A*cos(k*x + p) + M
A is the amplitude, it defines the distance between the value of a maximum and the value of the minimum, such that A is exactly half of that difference.
Here we can see that the maximum is 0, and the minimum is -4
The differene is: 0 - (-4) = 4
Then:
A = 4/2 = 2
f(x) = 2*cos(k*x + p) + M.
M is the midline, this is, the horizontal line that cuts the graph in two halves. Here we can see that the midline is x = -2, then:
M = -2
f(x) = 2*cos(k*x + p) - 2
p is the phase shift.
In the graph, we can see that f(0) = -3, so we have:
f(0) = 2*cos(0 + p) - 2 = -3
cos(p) = -1/2
p = Acos(-1/2) = 2.09
Then we have:
f(x) = 2*cos(k*x + 2.09) - 2
Finally, k is related to the frequency of the function.
We can see that the function does a complete cycle at x = pi
This means that:
f(x) = f(x + pi)
Knowing that the period of a cosine function is 2*pi, then:
k*(x + pi) = k*x + 2*pi
k = 2
Then the equation of the graph is:
f(x) = 2*cos(2*x + 2.09) - 2
If you want to learn more, you can read:
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Answer(s):
[tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\pi) - 2 \\ y = 2cos\:(2x - 1\frac{1}{4}\pi) - 2[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{5}{8}\pi} \hookrightarrow \frac{-1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{5}{8}\pi} \hookrightarrow \frac{1\frac{1}{4}\pi}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 2[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then by all means, go for it, but be careful and follow what is explained here. Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:(2x - 1\frac{1}{4}\pi) - 2,[/tex] in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex] which means the C-term will be negative. Now, BEFORE we go any further, we must remember that this particular cosine graph [thank goodness it is a cosine graph we are working with] ALREADY has a horisontal shift and does not have a single crest oscıllαtıng about any endpoint on the y-axis. So, in this case we need to figure out how far the FIRST oscıllαtıng crest is from the origin, and that obviously would be [tex]\displaystyle \frac{5}{8}\pi\:units.[/tex] Though, sinse we want the sine equation of this graph, it must be “negative”; so, by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{5}{8}\pi} = \frac{-1\frac{1}{4}\pi}{2},[/tex] in which the value of C is [tex]\displaystyle -1\frac{1}{4}\pi.[/tex] So, the sine equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(2x + 1\frac{1}{4}\pi) - 2.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [\frac{7}{8}\pi, -2],[/tex] from there to [tex]\displaystyle [-\frac{\pi}{8}, -2],[/tex] they are obviously [tex]\displaystyle \pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -2,[/tex] in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
**As you can see, this is one of those moments where you will really need to be careful because if you notised, both equations have OPPOCITE horisontal shifts and C-values. Now, the ONLY TIME this occurs is when all crests in a SINUSOIDAL graph cycle half-way in between endpoints. Your best bet is to jot this down for when you see graphs like these in the future.
I am delighted to assist you at any time.
change the following to grams only
a. 7kg 85g
b. 6kg 346g
c. 5kg 342g
Answers
Answer:
a) 7085g
b) 6346g
c) 5342g
Step-by-step explanation:
1kg = 1000g
write following ratio in simplest form :
125 g : 1 kg
Answers
Answer:
125g:1Kg
=> 125g : 1000g
=> 1:4Answer:
1:8
Step-by-step explanation:
125 g:1 kg
125g:1000 g
1 g:8 g
Keep smiling and hope u will be satisfied with my answer.Have a good day :)
mΖΗ - 67
pleas please please help!! i’m doing angles
Answers
Answer:
could u take a picture of the angles please
Step-by-step explanation:
Algebra pleaseeeeeee help
Answers
Answer:
Step-by-step explanation:
Remark
I have to assume that you know calculus. It is the only way the problem can be done that I know of. If you don't, I'm not sure how you will do this.
The curve is of y = e^(-2x) + x^2 - 3
The curve crosses the y axis when x = 0. The y value is
y = e^0 + x^2 - 3
yint = 1 + 0 - 3
yint = -2
The slope at point (0,-2) is
y' = -2e^(-2x) +2x
y' = -2 at point A
Therefore the normal will have a slope
m1 * m2 = - 1
The slope of the curve C at A = -2
The equation of the tangent line at A = -2x - 2
Call this m1
m2 = slope of the normal
-2 * m2 = -1
m2 = 1/2
Equation of the line (l) =
y = 1/2 x - 2
The graph is shown below. Notice the two lines actually look like they are at a 90 degree angle.
Need help asapppppppppp
Answers
can you help me? im so confused
Answers
Answer:
(AB) is longer than (AC)
Step-by-step explanation:
1. Approach
Use the distance formula to find the length of the segments (AC) and (AB); substitute their endpoints into the distance formula and simplifying to solve for the length. After finding the length of each segment, compare their lengths to find out which of the statements is true. The distance formula is as follows:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the endpoints of the segment.
2. Find the length of (AC)
Coordinates of point (A): [tex](-1,1)[/tex]
Coordinates of point (C): [tex](-4,4)[/tex]
Substitute these points into the distance formula,
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D=\sqrt{((-1)-(-4))^2+((1)-(4))^2}[/tex]
Simplify,
[tex]D=\sqrt{((-1)-(-4))^2+((1)-(4))^2}[/tex]
[tex]D=\sqrt{(-1+4)^2+(1-4)^2}[/tex]
[tex]D=\sqrt{(3)^2+(-3)^2}[/tex]
[tex]D=\sqrt{9+9}[/tex]
[tex]D=\sqrt{18}[/tex]
3. Find the length of (AB)
Coordinates of point (A): [tex](-1,1)[/tex]
Coordinates of point (B): [tex](0,-4)[/tex]
Substitute these points into the distance formula,
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D=\sqrt{((-1)-(0))^2+((1)-(-4))^2}[/tex]
Simplify,
[tex]D=\sqrt{((-1)-(0))^2+((1)-(-4))^2}[/tex]
[tex]D=\sqrt{(-1-0)^2+(1+4)^2}[/tex]
[tex]D=\sqrt{(-1)^2+(5)^2}[/tex]
[tex]D=\sqrt{1+25}[/tex]
[tex]D=\sqrt{26}[/tex]
4. Find the correct statement
(AB) is longer than (AC)
This statement is true for the following reason:
[tex]\sqrt{18}>\sqrt{26}[/tex]
A candybar box is in the shape of a triangular prism. the volume of the box is 1,200 cubic centimeters.
Part A; what is the height of the base. show your work.
Part B; What is the approximate amount of the cardboard used to make the candybox? Explain how you got your answer.
Answers
Classify each number as rational or irrational.
Answers
Answer:
π - irrational
0.04053.. - irrational
0.76 - rational
3.565565565 - irrational
-17 - rational
3.275 - rational
Step-by-step explanation:
rational = can express as fraction
irrational = cannot
ANSWER PLEASE
simplify 2n(n2+2n+3)-3(2n+7) and (-4n2-3n-8)+2(n+9)
Answers
Step-by-step explanation:
> 2n³+4²+6n-6n-21
2n³+4n²-21
> -4n²-3n-8+2n+18
-4n²-3n-8+2n+18
-4n²-n-8+18
-4n²-n+10
