Find csc 0, sin 0, and cot 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
PLZ HELP I BEEN STUCK FOR AN HOUR I WILL MARK BRAINLIEST!!!
Answers
Answers:
[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
=============================================
Explanation:
Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]
The vertical side is [tex]\sqrt{33}[/tex] units long.
------------------------------------
The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)
The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.
Divide the hypotenuse over opposite to get the cosecant.
[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]
Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.
------------------------------------
Recall that sine is the reciprocal of cosecant, and vice versa.
So we'll use the same idea as before, but flip the original fraction.
[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]
The denominator is already a rational number, so there's not much else to do here.
--------------------------------------
Cotangent is the ratio of adjacent over opposite
[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).
Related Questions
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
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Answer:
y-y1=m(x-x1)
y-2=1/3(x-3)
y=1/3x+1
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Answer:
gotta be answer A
Step-by-step explanation:
you can search up f(x) = square root of x
Please help me on this question
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Answer:
A = 6π
Step-by-step explanation:
Expression for the area of a sector is given by,
A = [tex]\frac{\theta}{360}(\pi r^{2} )[/tex]
For θ = 240° and r = 3,
By substituting these values in the given expression,
A = [tex]\frac{240}{360}(\pi) (3)^{2}[/tex]
= [tex]\frac{240\times 9}{360}\pi[/tex]
= 6π
Therefore, A = 6π is the answer.
Find the volume.
I need this in now like ASAP 10 points
Answers
Answer:
0.48 m^3
Step-by-step explanation:
volume = length * breadth * height
=6m * 4m * 0.02m
=0.48 m^3
Determine the value for x in the picture below.
Please help me
Answers
Given:
The figure of a right angle triangle.
A line segment intersect the two sides and parallel to third side of the triangle
To find:
The value of x.
Solution:
According to basic proportionality theorem, if a line segment intersect the two sides and parallel to third side of the triangle, then it divides the two sides proportionally.
Using basic proportionality theorem, we get
[tex]\dfrac{8}{20-8}=\dfrac{6}{x}[/tex]
[tex]\dfrac{8}{12}=\dfrac{6}{x}[/tex]
[tex]\dfrac{2}{3}=\dfrac{6}{x}[/tex]
On cross multiplication, we get
[tex]2\times x=6\times 3[/tex]
[tex]2x=18[/tex]
[tex]x=\dfrac{18}{2}[/tex]
[tex]x=9[/tex]
Therefore, the value of x is 9.
What is the solution to the equation 3(x - 1) – 2(2x + 1) = 8(x - 1)?
Answers
3x - 3 - 4x - 2 = 8x - 8
2. simplify the first side of the equation
- x - 5 = 8x - 8
3.move all the x’s to one side
-5 = 9x - 8
4. completely isolate the 9x
3 = 9x
5. solve
x = 1/3
let me know if this is correct :)!
Keelie has a triangular-shaped card. The lengths of its sides are 3 cm, 4 cm, and 5 cm. Is the card a right triangle?
Answers
Answer:
Yes, the card is a right triangle.
Step-by-step explanation:
The card is a right triangle, specifically a 3-4-5 right triangle.
A 3-4-5 right triangle is any right triangle that has side lengths in the ratio of 3:4:5.
The 3-4-5 rule says that any triangle with a side length ratio of 3:4:5 is a right triangle.
So, the card is a right triangle.
Worth 20 points Il will mark brainiest! :)
The picture is included too oh and the question is already in the picutre but just incase you cant see what it says it says this
In the diagram below lines, AB and CD are . sorry if the picture is a bit dark
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A. Perpendicular!
Because they cross with a 90 degree angle :]
Answer: Perpendicular
Step-by-step explanation: Hope this helps
Find the percent of markup on a T-shirt that has a store cost of $4.87 and a selling price of $15.95
Answers
Answer:
69.47%
Step-by-step explanation:
Calculation to determine Find the percent of markup
Using this formula
Percent of markup=New price-Old price/Old price
Let plug in the formula
Percent of markup=$15.95-$4.87/$15.95
Percent of markup=$11.08/$15.95
Percent of markup=0.6947*100
Percent of markup=69.47%
Therefore the percent of markup is 69.47%
Which correctly uses bar notation to represent the repeating decimal for
fi
O 0.54
O 05454
O 054
O 0.545
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Work out the perimeter of this semicircle.
Take a to be 3.142
10 cm
Answers
Answer:
perimeter=1/2*2πr
Step-by-step explanation:
1/2*2*3.142*10
=31.42
Find a round to the nearest tenth 12 22 75 x x=?
Answers
Answer:
By law of Sines[tex]\frac{Sin75^o}{22} =\frac{Sinx}{12}[/tex][tex]\frac{Sin75}{22}(12)=\frac{Sinx}{12} (12)[/tex][tex]0.5268=Sinx[/tex][tex]Sin^(0.5268)=x[/tex][tex]x=31.789[/tex][tex]x=31.79^o[/tex]-----------------------hope it helps..have a great day!!Calcula el ancho de un terreno rectangular si el largo mide 20 metros y la superficie es de 280 metros cuadrados
Answers
Answer:14 m
Step-by-step explanation:
Dada
larga [tex]l=20\ m[/tex]
superficie [tex]A=280\ m^2[/tex]
Suponga que el ancho es w
La superficie está dada por el producto de la longitud y la anchura.
[tex]\therefore A=lw\\\Rightarrow 280=20\times w\\\Rightarrow w=14\ m[/tex]
Por lo tanto, el ancho es de 14 m.
Which is longer - the radius or the circumference of a circle?
Answers
Answer:
Circumference of a circle
Step-by-step explanation:
The circumference of a circle is longer than its radius of the circle.
Confused on this work
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We know that :
⊕ Sum of the interior angles in a Pentagon should be equal to 540°
⇒ x° + (2x)° + (2x)° + 90° + 90° = 540°
⇒ (5x)° = 540° - 180°
⇒ (5x)° = 360°
[tex]\sf{\implies x^{\circ} = \dfrac{360^{\circ}}{5}}[/tex]
⇒ x° = 72°
la figure ci-dessus représente une pyramide du sommet S.
Sa base le rectangle EFGH et sa hauteur SO, tel que O est le centre
du rectangle EFGH.
PETIT PLUS: SE=6.5 cm , EF= 4 cm , FG=3cm.
1)- calculer la distance EG.
2)-Montrer que: SO=6 cm
3)-Calculer le volume de la pyramide SEFGH
SVP JE DOIS LE RENDRE DEMAIN .
ET MERCI
Answers
Answer:
Step-by-step explanation:
Voir le diagramme ci-attaché.
1) Distance EG
À l'aide du théoreme Pythagore, EG^2 = EF²+FG² = 4²+3² = 25
=> EG = sqrt(25) = 5
2) Distance SO
Par la symétrie, EO=OG=(EG/2)=5/2 = 2.5
Encore, à l'aide du même théoreme,SE^2 = SO²+EO²
SO^2 = SE² - EO² = 6.5²-2.5² = 42.25 - 6.25 = 36
SO = sqrt(36) = 6 QED
3) Volume de la pyramide
V = (Aire de la base * hauteur ) /3
= (EF * FG) * SO /3
= (4*3) * 6 /3
= 24 cm³
Lee ran a mile in 7 1/3 minutes. His friend Sam ran the same mile in 8 5/9 minutes. How many minutes faster did Lee run? (First answer will be the brainliest)
Answers
Answer:
1 2/9 minutes faster
Step-by-step explanation:
Take the larger number and subtract the smaller number
8 5/9 minutes - 7 1/3 minutes
Get a common denominator
8 5/9 - 7 1/3 *3/3
8 5/9 - 7 3/9
1 2/9 minutes faster
according to a survey, the population of a city doubled in 12 years.
The annual rate of increase of the population of this city is approximately _____. The population will grow to three times its current size in approximately ______.
First box of answers: 2.50, 5.78, 12.0, 50.0
Second box of answers: 18, 19, 23, 24.
Answers
Answer:
5.78
19
Step-by-step explanation:
Let original population be, P = x
Growth in 12 years, A = 2x
Rate be = r
Time = 12years
Find the rate :
[tex]A = P(1 + \frac{r}{100})^t[/tex]
[tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]
The annual rate of increase of the population of this city is approximately 5.78.
Find time in which the population becomes 3 times.
That is A = 3x
P = x
R= 5.78%
[tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]
The population will grow to three times its current size in approximately 19years .
5.78% ,19 years are the answers.
2=(1+r)^12
r=(2)^(1÷12)−1
R=0.0578*100=5.78%
3=(1+0.0595)^t
t=log(3)÷log(1.0595)
t=19 years
What is an exponential growth model?
Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky
exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.
The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.
Learn more about exponential function here:https://brainly.com/question/2456547
#SPJ2
If a square table can fit 8 people and a round table can fit 6 people, the equation 150= 8x + 6y , if Y =9 what is the value of x ? The committee needs how many square tables?
Answers
Answer:
The committee needs 12 square tables!
Step-by-step explanation:
[tex]8x+6y=150[/tex]
[tex]y=9[/tex]
[tex]8x+6(9)=150[/tex]
[tex]8x+54=150[/tex]
[tex]-54[/tex] [tex]-54[/tex]
[tex]8x=96[/tex]
[tex]/8[/tex] [tex]/8[/tex]
[tex]x=12[/tex]
Hope this helps!
The circumference of a circle is 8.34cm. Find the length of the diameter. Give your answer rounded to 2 DP.
Answers
Answer:
Diameter, D = 2.65 cm
Step-by-step explanation:
Given the following data;
Circumference of circle = 8.34 cm
To find the length of its diameter;
Mathematically, circumference of a circle is equal to;
C = πD
Where;
C is the circumference of a circle.D is the diameter of a circle.Pie, π = 3.142Substituting into the formula, we have;
8.34 = 3.142 * D
[tex] D = \frac {8.34}{3.142} [/tex]
Diameter, D = 2.65 cm
Cho tam giác ABC có AB =4cm ,AC=5cm,BC=6cm.Trên tia đối của tia AB lấy điểm D sao cho AD=5cm a) chứng minh : tam giác ABC đồng dạng với tam giác CBD b) tính CD
Answers
Answer:
meta beta
Step-by-step explanation:
diem ryugudnhkng.
please help me :(
I am in Great trouble:(
Answers
Answer: (I am not a maths moderator)
x=4
Step-by-step explanation:
Multiply the exponents
(2x-4)^12=(4^2)^6 (exponents multiply so)
(2x-4)^12=4^12
4^12 = 16777216
(2x-4)^12= 16777216
Take the 1/12 exponent for both sides
that will remove the ^12 exponent from the left side and will take the 12th root for the right.
2x-4=4
add 4 to both sides
2x=8
divide both sides by 2
x=4
This is correct? I need help please :(
Answers
Answer:
well, we only no that
2l + 2w is 80
(lengths and widths on all 4 sides
and that w * l is A
so the function should be w times what's left for l, but also expressed by something with w
2l + 2w = 80 | -2w
2l = 80 -2w | devide by 2
l = 80 - w
now we can substitute l in
A = w * l
so that we only need w's
A(w) = w * (80-w)
for any w it will give us the area, makes only sense for 0<w<80
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Which expressions are equivalent to One-half + 3 c + StartFraction 4 Over 5 EndFractionCheck all that apply.
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Answer:
(13+30c)/10
Step-by-step explanation:
Given the expression;
1/2 + 3c + 4/5
Find the LCM
= 5(1)+10(3c)+2(4)/10
= (5+30c+8)/10
= (13+30c)/10
Hence the required sum is (13+30c)/10
helpppppppppppppppppppppppppppppppppp!!!!!!!!!
Answers
Which of the following is an equivalent trig ratio for tan 28
Cos 62
1/ tan 62
1/ tan152
Cos 28
Answers
Answer:
B
Step-by-step explanation:
tan28=tan (90-62)=cot 62=1/tan 62
Adam is refinishing his basement. 30 ft by 50 ft are the dimensions of Adam's rectangular basement. How much tile would he need to cover the floor? If the height of the basement is 6 ft, how much wall area is there to paint?
Answers
Answer:
Area of four walls is 3960 square feet.
Step-by-step explanation:
length, L = 30 ft
Width, W = 50 ft
height, H = 6 ft
The area of walls is
= 2 (L W + W H + H L)
= 2 (30 x 50 + 50 x 6 + 6 x 30)
= 2 (1500 + 300 + 180)
= 3960 square feet
Answer/Step-by-step explanation:
How much tile would he need to cover the floor?
Answer: 1500 Ft^2
If the height of the basement is 6 ft, how much wall area is there to paint?
Answer: 960 Ft^2
Lily weighs 57.7 kg while her sister weighs 59.02 kg, how much more does Lily's sister weigh then her? Please provide the calculation!
Answers
The answer is 1.32
For this calculation, assuming that no conversions are required, the calcitonin goes as follows:
All that is needed is to subtract 57.7 from 59.02.
59.02 - 57.7 = ?
59.02 - 57.7 = 1.32
Hope this helps! Have a great day.
Find the mean, median, mode, range.
Answers
Answer:
1. mean: 5
2. median: 6
3. mode: 80% or 8
4. range: 7
Step-by-step explanation:
Answer:
mean = 5
median = 6
mode = 80%(aka 8)
range = 7
Step-by-step explanation:
Pls help me with this
Answers
Answer:
5.85
Step-by-step explanation:
100%-> 6.50
100%-10% = 90 %
90%-> 6.50/100 x 90
=5.85
