In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?
Answers
In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?
Answer:
[tex] BD = c*sin(A) [/tex]
[tex] BD = c*cos(B) [/tex]
[tex] BD = b*tan(A) [/tex]
Step-by-step explanation:
∆ABD is a right triangle.
Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.
SOH => sin(θ) = opposite/hypotenuse
CAH => Cos(θ) = adjacent/hypotenuse
TOA = tan(θ) = opposite/adjacent
Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:
Let BD = x
AB = c
AD = b
=>The sine ratio for the length of line segment BD = x, using SOH.
θ = A
Opposite = DB = x
hypotenuse = AB = c
[tex] sin(A) = \frac{x}{c} [/tex]
Make x the subject of formula.
[tex] c*sin(A) = x [/tex]
[tex] BD = x = c*sin(A) [/tex]
=>The Cosine ratio for the length of line segment BD = x, using CAH
θ = B
Adjacent = DB = x
hypotenuse = AB = c
[tex] cos(B) = \frac{x}{c} [/tex]
Make x the subject of formula.
[tex] c*cos(B) = x [/tex]
[tex] BD = x = c*cos(B) [/tex]
=>The Tangent ratio for the length of line segment BD = x, using TOA
θ = A
Adjacent = DB = x
hypotenuse = AD = b
[tex] tan(A) = \frac{x}{b} [/tex]
Make x the subject of formula.
[tex] b*tan(A) = x [/tex]
[tex] BD = x = b*tan(A) [/tex]
Related Questions
The surface area of a cylinder?
Answers
Answer:
18. 84 ft² or 18.85 ft² when rounded to the nearest tenth
Step-by-step explanation:
2πrh+2πr²
2× 3.14 × 1 × 2= 12.56
2 × 3.14 × 1² = 6.28
12.56 + 6.28 = 18.84
Have a great day :)
Answer:
18.85 [tex]ft^2\\[/tex]
*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*
Step-by-step explanation:
Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]
Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.
I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.
Radius: 1 Height: 2
Plug numbers into equation:
[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]
I hope that helps!
How much can 1/2 go into 25
Answers
Answer:
50
Step-by-step explanation:
please mark me as brainliest
Answer:
50
Step-by-step explanation:
Hi there!
Determining how much 1/2 can go into 25 is the same as solving for 25÷1/2:
[tex]25\div\frac{1}{2}[/tex]
Dividing by a fraction is the same as multiplying its reciprocal:
[tex]=25\times\frac{2}{1}\\=25\times2\\=50[/tex]
I hope this helps!
One more than three times a number is the same as four less than double a number
Answers
Answer:
3x + 1 = 2x - 4. x = -5
Step-by-step explanation:
Which is the solution to the inequality?
2 3/5 <b-8/15
Answers
Answer:
3 2/15 <b
Step-by-step explanation:
2 3/5 <b-8/15
Add 8/ 15 to each side
2 3/5 + 8/ 15 <b-8/15 + 8/15
2 3/5 + 8 /15 <b
Get a common denominator
2 3/5 *3/3 + 8/15
2 9/15 + 8/15 < b
2 17/15 < b
2 + 15/15 + 2 /15 < b
3 2/15 <b
Answer:
B > 3 2/15
Step-by-step explanation:
Theresa bought 2 pineapples for $6. She be wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part A
Using the diagram, find the constant of proportionality in terms of dollars per pineapple.
Answers
Answer:
$3 per pineapple
Step-by-step explanation:
Hey there!
If 2 pineapples are $6,
6 / 2 = 3
So 1 pineapple is $3.
Hope this helps :)
Answer:
3 dollars for 1 pineapple
Step-by-step explanation:
well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.
Find the value of x.
Answers
the tic marks show that all sides are congruent, same with the angles. 60+60+60=180 also.
I need help with this math problem please (3x+2)(5x-7)
Answers
Answer:
Hey there!
Using the foil method: (3x+2)(5x-7)
15x^2+10x-21x-14
15x^2-11x-14
Let me know if this helps :)
Here’s your answer (3x+2)x(5x-7)
What percent of the area underneath
this normal curve is shaded?
Answers
Answer:
The area shaded is 95%
Step-by-step explanation:
The total area under the curve is 100 percent
1 standard deviation away from the mean is 68 percent
2 standard deviations away is 95 percent
The area shaded is 95%
The percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.
What is the 68-95-99.7 rule?The 68-95-99.7 rule is also referred to as the empirical rule or the three-sigma rule and it can be defined as a shorthand which is used in statistics to determine the percentage of a population parameter that lie within an interval estimate in a normal distribution curve.
Basically, the 68-95-99.7 rule states that 68%, 95%, and 99.7% of the population parameter lie within one (1), two (2), and three (3) standard deviations of the mean respectively.
This ultimately implies that, the percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.
Read more on 68-95-99.7 rule here: https://brainly.com/question/24768583
#SPJ2
Sebastian studies from 3:15 - 4:45 p.m his sister,Sara studies from 4:30 -6:15 p.m who studies longer and by how,much?
Answers
Answer:
Sara studies longer by 15 minutes.
Step-by-step explanation:
Let's calculate how long Sebastian studies for. From 3:15 - 4:15, there is 1 hour and from 4:15 to 4:45, there are 30 minutes so Sebastian studies for 1 hour and 30 minutes. Now, let's calculate how long Sara studies for. From 4:30 - 5:30, there is 1 hour, from 5:30 - 6:00, there are 30 minutes and from 6:00 - 6:15, there are 15 minutes so Sara studies for 1 hour 45 minutes. This means that Sara studies longer by 45 - 30 = 15 minutes.
Consider the following two questions designed to assess quantitative literacy: a. What is 15% of 1000? b. A store is offering a 1596 off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale? Suppose the first question is asked of 200 randomly selected college students, with 165 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 142 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.) Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context.
Answers
Answer:
The calculated value of z= 2.7225 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
Step-by-step explanation:
a: 15 % of 1000= 150
b. 15.96 % of $ 1000= $ 159.6
The customer would pay = $ 1000- $ 159.6= $ 840.4 and save $ 159.6
Formulate the hypotheses as
H0: p1= p2 true proportion of correct responses to the question without context is equal that for the one with context.
Ha : p1≠ p2
We choose the significance level ∝= 0.05
The critical value for two tailed test at alpha=0.05 is ± 1.96
The test statistic is
Z = p1-p2/ √pq (1/n1+ 1/n2)
p1= true proportion students who answered the question without context correctly = 165/200=0.825
p2= true proportion of students who answered the question with context correctly = 142/200= 0.71
p = an estimate of the common rate on the assumption that the two proportions are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.825) + 200 (0.71) / 400
p= 165+ 142/400= 307 /400 =0.7675
now q = 1-p= 1- 0.7675= 0.2325
Thus
z= 0.825- 0.71/ √0.7675*0.2325( 1/200 + 1/200)
z= 0.115/√ 0.17844( 2/200)
z= 0.115/0.04224
z= 2.7225
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
In the figure above, point O is the center of the circle,
line segment BC is tangent to the circle at point B,
point A lies on the circle, and point O lies on line
segment AC. If the circumference of the circle is 50,
what is the length of minor arc AB ?
Answers
Answer:
16.67 or 16 2/3
Step-by-step explanation:
so, as BC is a tangent, it means the angle OBC is 90 degrees.
therefore, the angle BOC is 180 - 90 - 30 = 60 degrees.
that means the angle AOB is 180 - 60 = 120 degrees.
the triangle ABO must be an isosceles triangle, as the sides are both the radius of the circle. so, both remaining angles are the same : half of 180 - 120 = 60 = 30 degrees.
and so, we know that ABC is an isosceles triangle, because both "side angles" are equal = 30 degrees.
so, AB = BC.
and we know the circumference of the circle (50) and can calculate the radius
50 = 2×pi×r
25 = pi×r
r = 25/pi ≈ 7.96
now we have multiple ways to calculate AB.
AB = BC = tan(60) × r
or
AB = sqrt(r² + r² - 2×r×r×cos(120))
or ...
the first one might be easiest.
AB = tan(60) × 7.96 ≈ 13.78
oh, I just recognized, we need the arc AB (not the straight line).
even easier.
50 is the full "arc" of the circle for all 360 degrees.
but we only need the part of the angle AOB = 120 degrees.
so, this is then only the 120/360 part of the full circle circumference.
ABarc = 50 × 120/360 = 50 / 3 ≈ 16.67 or 16 2/3
For the function G defined by G(x) = 5x + 3, find G(2)
Answers
G(x)=5x+3
[tex]\\ \sf\longmapsto G(2)[/tex]
[tex]\\ \sf\longmapsto 5(2)+3[/tex]
[tex]\\ \sf\longmapsto 10+3[/tex]
[tex]\\ \sf\longmapsto 13[/tex]
Option c is correct
What are the factors of 60 ???
Answers
Answer:
Factors are 1,2,3,4,5,6,10,12,15,20,30,60
Step-by-step explanation:
Hope this helps
Factors refers to those numbers which muntiplied that no.here, numbers that muntiply 60 are 1,2,3,4,5,6,10,12,15,20,30,60.
thus these numbers are factors of 60.
PLEASE it's easy - "collecting like terms" It's algebra
Answers
Answer: The equation is correct.
Step-by-step explanation:
from the expression,
5x + 3( y + 4x² + 3x ) + 2( y - x² ) = 14x + 10x² + 5y
Open brackets with 3 and 2
5x + 3y + 12x² + 9x + 2y - 2x²
Now collect like terms
5x + 9x + 12x² - 2x² + 3y + 2y
14x + 10x² + 5y = 14x + 10x² + 5y (Q.E.D)
TH equation is correct
Please help! I’ll mark you as brainliest if correct.
Answers
Answer:
160 liters of 25%, 20 liters of 40%, 60 liters of 60%
Step-by-step explanation:
x + y + z = 240
0.25x + 0.4y + 0.6z = 0.35*240 = 84
z = 3y
x = 160
y = 20
z = 60
Eliminate the parameter for the following set of parametric equations: x= t + 6 y= 3t – 1
Answers
Answer:
Solution : Option A
Step-by-step explanation:
What we want to do here is eliminate the parameter t. In order to do that, we can isolate t in our first equation x = t + 6 ----- ( 1 ) and then plug that value for t in the second equation y = 3t - 1. Our solution will be an equation that is not present with t.
( 1 ) x = t + 6, t = x - 6
( 2 ) y = 3( x - 6 ) - 1 ( Distribute the " 3 " in 3( x - 6 ) )
y = 3x - 18 - 1 ( Combine like terms )
y = 3x - 19
As you can see our result will be option a, y = 3x - 19.
Is 1.45 times 10 to the -7 power a scientific notation
Answers
Answer:
Yes.
It is 1.45 x 10^-7 or 0.000000145
Hope it helps!
Answer:
It is 1.45 x 10^-7 or 0.000000145
Step-by-step explanation:
solve 2root3+7root3
Answers
Answer:
(2+7) root 3 equals 9 root 3
A household survey of 10 families was conducted by students of 4th year MBBS. In the collected data, the ages of heads of families were: 32, 34, 35, 36, 36, 42, 44, 46, 48, and 52. The mean age of heads of families is
a. 36
b. 38.5
c. 40
d. 40.5
e. 42
Answers
Answer:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14
Step-by-step explanation:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT
Area of a triangle
A/12 = 12/12bh
solve for b
Answers
Step-by-step explanation:
I hope this works for ya.
the mass of 2bags of beans and
3 bags of salt is 410kgs
if the mass of 3bags of beans and
2bags of salt is 390kg find the
mass of each item.
Answers
Answer:
70kg- weight of the bag of beans, 90 kg- weight of the bag of salt
Step-by-step explanation:
Suppose the mass of a bag of beans - x kg, the mass of a bag of salt - y kg
The mass 2 bags of beans 2x, The mass 3 bags of salt 3y
2x+3y= 410
The mass of 3 bags of beans 3x, for 2 bags of salt it is 2y
3x+2y=390
We have system of equations (the equations are simultaneous)
2x+3y=410
3x+2y=390
2x= 410-3y
x=205-1.5y
3* (205-1.5y)+2y=390
615-4.5y+2y=390
2.5y= 225
y=90- the mass of the bag of salt
x= 205 - 1.5*90= 205-135= 70- the mass of the bags of beans
a team's stadium has a capacity of 86,047. The fan base is notorious for selling out of tickets every game. If every game sells out this year, how many tickets are sold in their 12 game regular season play?
Answers
Answer:
1,032,564 tickets
Step-by-step explanation:
Find how many tickets they sell in total by multiplying the capacity of the stadium by the number of games in the season:
86,047(12)
= 1,032,564
So, if every game sells out, 1,032,564 tickets will be sold.
solve the following equations for x (3x-6)=18
Answers
Answer:
x = 8
Step-by-step explanation:
Hello!
What we do to one side of the equation we have to do to the other side.
3x - 6 = 18
Add 6 to both sides
3x = 24
Divide both sides by 3
x = 8
The answer is 8
Hope this helps!
Answer:
x=8
Step-by-step explanation:
(3x-6)=18
Add 6 to each side
(3x-6+6)=18+6
3x= 24
Divide by 3
3x/3 = 24/3
x = 8
The value of y varies directly with x . Find the value of k when y 33.6 and x = 4.2
Answers
Answer:
k=8
Step-by-step explanation:
Since y and x are in direct proportions, the equation is
y= kx, where k is a constant.
when y= 33.6, x=4.2,
33.6= k(4.2)
k= 33.6 ÷4.2
k=8
Answer:
k=8
Step-by-step explanation:
Please help me
(3 more coming soon so if you want points you can do those too when they come out
Answers
Answer:
The choose D. 15/16
Step-by-step explanation:
[tex] 1\frac{1}{4} \times \frac{3}{4} = \frac{15}{16} [/tex]
I hope I helped you^_^
Which equation is represented by the graph?
Answers
Answer:
I don't knowledge bro sorry
Given the function h(t) = 2t to the power of 2 + 9 evaluate h(5)
Answers
9514 1404 393
Answer:
59
Step-by-step explanation:
Put 5 where t is and do the arithmetic.
[tex]h(t)=2t^2+9\\\\h(5)=2\cdot5^2+9=2\cdot25+9\\\\\boxed{h(5)=59}[/tex]
Urgent!!! Please simplify
Answers
Answer:
The answer is
3x² - 2x³Step-by-step explanation:
First factor (x+1)² out of the expression
That's
[tex] \frac{ ({x + 1})^{2} (6 \cos( \frac{\pi}{3} )) {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) }{ ({x + 1})^{2} } [/tex]
Reduce the expression by (x + 1)²
We have
[tex]6 \cos( \frac{\pi}{3} ) \times {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) [/tex]
Using trigonometric values table
[tex] \cos( \frac{\pi}{3} ) = \frac{1}{2} [/tex]
[tex] \sin( \frac{\pi}{2} ) = 1[/tex]
So we have
[tex]6 \times \frac{1}{2} \times {x}^{2} - {x}^{3} \times 2 \times 1[/tex]
Simplify
We have the final answer as
[tex] {3x}^{2} - 2 {x}^{3} [/tex]
Hope this helps you
6th grade math. :) help me please
Answers
Answer:
8 3/4
Step-by-step explanation:
The decimal 3.5 as an improper fraction is 35/10.
Answer:
[tex]8\frac{3}{4}[/tex]
Step-by-step explanation:
To write as a mixed number means that you will have a whole number and a fraction together. To find the mixed fraction version, see how many times the denominator (bottom) fits into the numerator (top) evenly.
4, 8, 12, 16, 20, 24, 28, 32, 36
1 2 3 4 5 6 7 8 9
4 can go into 35 '8' times without being greater than the numerator. 8 is the whole number. Now subtract the original numerator by the product of 4 and 8, which is 32:
[tex]35-32=3[/tex]
3 is the new numerator. Keep the same denominator. Insert all values:
[tex]\frac{35}{4}=8\frac{3}{4}[/tex]
:Done
Complete the equation describing how x
and y are related.
х у
y = [ ? ]x
-2
-1
0
1
2
3
-6
-3
0
3
6
9
Enter the answer that
belongs in [?]
Answers
Answer:
y=3x
Step-by-step explanation:
-6/-2=3, -3/-1=3, 3/1=3. 6/2=3