Demuestra las funciones trigonométricas de 45o a partir de un cuadrado con longitud de lado igual a 1.
Answers
The most appropriate choice for trigonometric function will be given by -
sin 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = 1
cot 45° = 1
sec 45° = [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\sqrt{2}[/tex]
What are trigonometric functions?
Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.
There are six trigonometric functions-
[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin \theta[/tex] = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]cos\theta[/tex] = [tex]\frac{Base}{Hypotenuse}[/tex]
[tex]tan\theta[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]
[tex]cot\theta[/tex] = [tex]\frac{Base}{Perpendicular}[/tex]
[tex]sec\theta[/tex] = [tex]\frac{Hypotenuse}{Base}[/tex]
[tex]cosec\theta[/tex] = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
Here,
The diagram of the square has been attached with this answer
∠ABC = 90° [Side of a square is 90°}
∠BAC = [tex]\frac{90}{2}[/tex]
= [tex]45[/tex]°
Side of square = 1 unit
Length of diagonal of a square = [tex]\sqrt{2}[/tex] [tex]\times[/tex] side
= [tex]\sqrt{2}[/tex] [tex]\times[/tex] [tex]1[/tex]
= [tex]\sqrt{2}[/tex] units
From [tex]\Delta[/tex] ABC,
sin 45° = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
= [tex]\frac{BC}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{Base}{Hypotenuse}[/tex]
= [tex]\frac{AB}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = [tex]\frac{Perpendicular}{Base}[/tex]
= [tex]\frac{BC}{AB}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
cot 45° = [tex]\frac{Base}{Perpendicular}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
sec 45° = [tex]\frac{Hypotenuse}{Base}[/tex]
= [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
= [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
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Related Questions
the ratio of 26,000 bytes to 48,000 bytes can be written in fractional form as
Answers
Answer:
26000:48000
26000/48000
26/48(cancel the zeros)
13/24
fractional form=13/24
The equation y = 0.43x + 50 models the cost y of renting a car if the car is driven x
miles.
According to the model, what is the best estimate of the cost for renting a car if you
plan to drive 489 miles? Please round your answer to the nearest dollar.
Answers
By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.
What do we mean by equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.
Now, solve for y when the value of x is 489.
y = 0.43x + 5y = 0.43(489) + 5y = 210.27 + 5y = $215.27Rounding off: y = $215
Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.
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Karen is driving her moterhome. It uses 3 gallons of gas for every 24 milesComplete the table below showing the number of gallons used and the distance traveled.
( The table is 3,24 6, ? 7,? ? , 72 and 10, ?)
Answers
Answer: 6, 48 and 7, 56 and 9, 72 and 10,80
Step-by-step explanation:
Divide
-36
-8
Enter your answer as a mixed number, in simplified form, in the box.
Answers
the answer is this
4 4/8.
Bob makes some fruit punch that contains apple and mango juice in a 1:5 ratio. If he uses 15 pints of the mango juice how many pints of apple juice will he need
Answers
he needs 3 pints of mango
Answer:3
Step-by-step explanation:
If the ratio is 1:5 that means that the number of pints of apple juice is multiplied by 5 to get the nimber of pints of mango juice
n(x) = -1-x+4
n(-2) =
n(0)=
n(5)=
Answers
Step-by-step:
n(x) = -1 - x + 4
n(-2) = -1 - (-2) + 4
= -1 + 2 + 4
= 5
___________________________
n(0)= -1 - 0 + 4
= 3
___________________________
n(5)= -1 - 5 + 4
= -2
for a sequence of events in which the first event can occur n 1 ways, the second event can occur n 2 ways, the third event can occur n 3 ways, and so on, the events together can occur a total of n 1 times n 2 times n 3 times ... ways. this is called .
Answers
The most appropriate choice for Independent event and multiplicative counting rule will be given by
This is known as multiplicative counting rule.
What is Independent event and multiplicative counting rule?
Event that is not dependent on any other event is called independent event.
Let A and B be two independent events.
P(A∩B) = P(A) [tex]\times[/tex] P(B)
If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.
Here,
Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on
Also assuming that the events are independent
The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways
This is known as multiplicative counting rule.
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Mrs. argueta needed to fill up her gas tank. gas cost $3.66 per gallon and she needed 9 1 2 gallons. how much did it cost mrs. argueta to fill up her tank?
Answers
Answer:
$3337.92
Step-by-step explanation:
$3.66 x 912 = $3337.92
If f(x) = 4x6 + x² + 4, then what is the remainder when f(x) is divided by x -1?
Answers
Answer:
9
Step-by-step explanation:
[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]
You cut a 90-foot rope into 6 pieces of equal length. What is the length of
each piece?
Answers
Answer:
Length = 15
Step-by-step explanation:
The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation
90 feet / 6 pieces
Which equals
90 feet / 6 pieces = 15 feet/piece (15 feet per peice)
Hope this helps :)
round to the underlined digit:
Answers
Answer:
c because if the number next to the underlined is above 5 u round up under 4 u round down
Step-by-step explanation:
Answer: c. 76
Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Answers
We can conclude that the probability of the randomly selected person does not use any facility is 0.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.Statistics is the study of events that follow a probability distribution. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the selected person does not uses any facility:
According to the given data, we can easily say that all the people use some or the other facility.So, there are 0 people present who do not use the facility.Then, the probability that the selected person does not use any facility will be 0.Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.
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How is the graph of each equation related to
standard form Ax + By = C?
Answers
Answer:
When A = 0 and y = 1 and C = 2
0x + 1y = 2
y = 2 No matter what x is, y will always be 2 and this will create a horizontal line.
Step-by-step explanation:
help asap please and thank u
Answers
Answer:
y = 5, 3
x = 155, 171
(y = 5, x = 155)
(y = 3, x = 171)
Step-by-step explanation:
(8y - 15) = (y²)
-8y + 15 -8y + 15
--------------------------------
y² - 8y + 15 = 0
(y - 5) (y - 3) = 0
--------------
y = 5, 3
----------------------------------------------------------------------------------------------------------
y² + x = 180
(5)² + x = 180
25 + x = 180
-25 -25
--------------------
x = 155
(3)² + x = 180
9 + x = 180
-9 -9
------------------
x = 171
----------------------------------------------------------------------------------------------------------
I really hope this helps!
Find the area of the pool. Write as a polynomial.
Pool
6x
3x-5
Answers
Please answer the question in the photo
Answers
Answer:
u= 30
Step-by-step explanation:
the sum of all angles on a triangle is 180* so u add the others (120+30)
that brings it to 150 then 180-150=30*
find the number of sides of a regular polygonwhose exterior angle measure 18°
Answers
Answer:
20
Step-by-step explanation:
The sum of the exterior angles of a polygon add to 360. 360 divided by 18 is 20.
Which expression is equivalent to t
3(x+24)?
A-2/3x+24
B-2/3x+16
C -2/3x-16
D 2/3x-16
Answers
Because of -2 the answer is c
1. 5- (-8) =
2. -3 1/2 - 4 1/2 =
3. -7 - 4 =
4. -0.5 - 3.5 =
Answers
Answer:
1. 5- (-8) = 13
2. -3 1/2 - 4 1/2 = -7 1/2
3. -7 - 4 = -11
4. -0.5 - 3.5 = -4
Step-by-step explanation:
1. 5- (-8) =
5 + 8
13
2. -3 1/2 - 4 1/2 =
-7 1/2
3. -7 - 4 =
-11
4. -0.5 - 3.5 =
-4
8. Which best describes the relationship between the line that passes through (-1, -8) and (4,-4) and the line
that passes through (2, -9) and (7,-5)?
a. parallel
b. perpendicular
C.
same line
d. neither perpendicular nor parallel
Answers
Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Relationship between lines in this caseIn this case, you can calculated in this case:
Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:
m= (-4 - (-8))÷ (4 - (-1))
m= (-4 + 8)÷ (4 + 1)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-8= 4/5× (-1) + b
-8= -4/5 +b
-8 + 4/5= b
-36/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.
Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:
m= (-5 - (-9))÷ (7 - 2)
m= (-5 + 9)÷ (5)
m= 4÷ 5= 4/5
Considering point 1 and the slope m, you obtain:
-9= 4/5× (-2) + b
-9= -8/5 +b
-9 + 8/5= b
-37/5=b
The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.
You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.
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1) The compound interest of a sum of money is Rs 13310 and in 4 years is Rs 14641. Find the rate of interest and sum.
Answers
The rate of interest is 10% and the sum is Rs 10,1000.
What is compound interest?The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.
The compound interest formula is given by
Compound Interest = Amount – Principal
Here, the amount is
[tex]A=P(1+\frac{r}{100} )^{n}[/tex] where,
A = amount
P = principal
r = rate of interest
n = time (in years)
Given:
C.I. of a sum of money in 3 years = Rs 13310
C.I. of a sum of money in 4 years = Rs 14641
Let the principal be P and the rate of interest be r%
Then, according to the question,
For 3 years:
[tex]13310=P(1+\frac{r}{100} )^{3}[/tex] ..... (1)
For 4 years:
[tex]14641=P(1+\frac{r}{100} )^{4}[/tex] ..... (2)
Dividing equation (2) by (1), we obtain
[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]
⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]
⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]
⇒[tex]r=\frac{100}{10}[/tex]
⇒ r = 10%
Now, substituting r in equation (1),
[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]
⇒[tex]13310=P(\frac{1331}{1000} )[/tex]
⇒P = Rs 10,000
Therefore, the rate of interest is 10% and the sum is Rs 10,1000.
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What is the smallest possible degree that the polynomial can have and why?
Answers
Check the picture below.
i need help with this, thanks
Answers
Answer: 11
Step-by-step explanation:
8x + 7 = 9x - 4
7 = x - 4
11 = x
PLEASE HELP!: I'm so confused about what equations to write for the problem. All I need is the equations and I can solve it alone! I'll give brainly!
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal, and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
Answers
Using simple interest, the amounts invested into each account are given as follows:
Paper returns: $3,500.Metal returns: $1,500.Glass returns: $3,000.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = P(1 + rt)
In which:
P is the initial amount.r is the interest rate, as a decimal.The amount of interest after t years is given by:
I(t) = Prt
You invest $8,000 in 3 investment accounts, hence:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
From the rates of the account, we have that:
[tex]I_1 = 0.02P_1[/tex][tex]I_2 = 0.04P_2[/tex][tex]I_3 = 0.05P_3[/tex]The amount invested in the glass account was double the amount invested in the metal account, hence:
[tex]P_3 = 2P_2[/tex]
The yield was a total of $280 at the end of one year, hence:
[tex]I_1 + I_2 + I_3 = 280[/tex]
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
From the first and the third equations, we have that:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
[tex]P_1 + 3P_2 = 8000[/tex]
[tex]P_1 = 8000 - 3P_2[/tex]
Hence the amount of the metal investment can be found as follows:
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]
[tex]0.08P_2 = 120[/tex]
[tex]P_2 = \frac{120}{0.08}[/tex]
[tex]P_2 = 1500[/tex]
Hence the other investments are given as follows:
Paper: 8000 - 3 x 1500 = $3,500.Glass: 2 x 1500 = $3,000.More can be learned about simple interest at https://brainly.com/question/20690803
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You purchase a home for $200,000 which appreciates at 2.5%. How much is it worth in 7 years?
Answers
Answer: The answer I came up with is: $237,737
help i don’t get it
answers pls
Answers
Answer: 13
Step-by-step explanation:
As the sum of the angles of a triangle is 180, we have that 39 + 90 + 3x+12 = 180.
3x = 180 - 39 - 90 - 12
3x = 39
x = 13
Find the value of x if T is the midpoint of segment XY. Segment XT = 3x-14, Segment XY = 8x-56
Answers
The value of x if T is the midpoint segment XY is 14.
How to find the mid point of a segment?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints.
The midpoint is halfway between the two end points.
Therefore, the end point of the segment is XY.
The midpoint is T.
Hence,
XY = XT + YT
XT = 3x - 14 = YT
XY = 8x - 56
Let's find the value x.
Therefore,
8x - 56 = 3x - 14 + 3x - 14
8x - 56 = 6x - 28
8x - 6x = -28 + 56
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
Therefore, the value of x is 14
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7. If Antonio makes x dollars per regular hours, and his boss tells him that he is
going to get paid over time at double time, write an equation to find his hourly
rate if he makes $1578.5 working 55 hours this week.
Answers
The equation for the hourly rate is 55x = 1578.5
For double hourly rate for overtime, it is 55 x 2x= 1578.5
Given
Antonia makes X dollars for regular hours
And 2x dollars for over time
Since he works 55 hours this week he works 8 hours a day
Hence the equation is as follows
55x = 1578.5
x= $28.7
In case of double payment during overtime
He gets double amount as following equation
55 x 2x
55 x 2(28.7) = $3157
Hence the equation to find his hourly rate is 55x = 157.85
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Someone please help me!!! ( I'll mark brainliest )
Answers
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
F(4) if f(x) = 3 x -1
Answers
Answer:
f(4) = 11
Step-by-step explanation:
f(x) = 3 x -1
Let x = 4
f(4) = 3*4 -1
= 12-1
= 11
f (x) = 3x - 1
f (4) = 3 × 4 - 1
f (4) = 12 - 1
f (4) = 11
Hope Helpful :-;