Answers
Answer:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Step-by-step explanation:
The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.
__
top triangleThe law of sines applied to the top triangle is ...
BC/sin(A) = AC/sin(θ)
Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...
∠A = 180° -θ -θ = 180° -2θ
A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...
sin(A) = sin(180° -2θ) = sin(2θ)
and our above Law of Sines equation tells us ...
BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)
__
bottom triangleThe law of sines applied to the bottom triangle is ...
DC/sin(B) = BC/sin(D)
d/sin(α) = BC/sin(β)
Multiplying by sin(α) we have ...
d = BC·sin(α)/sin(β)
__
Using our expression for BC gives the desired relation:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Related Questions
Evaluate:
2/3 + 4/5 x 7/5 - 8/3
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
-0.88
Explanation:
2/3 + 4/5 x 7/5 - 8/3
2/3 + 28/25 - 8/3
2/3 - 8/3 + 28/25
-6/3 + 28/25
-2 + 28/25
-50/25 + 28/25
-22/25
-0.88
what is the solution to this equation? 8(e)^2x+1=4
Answers
Answer:
Exact Form:
x=3/8e^2
Decimal Form:
x=0.05075073…
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after t seconds is given by the following.
Answers
A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The complete question is:
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth.
The time at which the height of the ball is 16 feet can be found by,
h = 2 + 31t - 16t²
16 = 2 + 31t - 16t²
16 - 2 - 31t + 16t² = 0
16t² - 31t + 14 = 0
[tex]t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\[/tex]
t = 0.717 , 1.221
Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
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8x3+70÷7-7
tell accordingly the correct answer will be marked as brainliest
Answers
U have to solve it by order of operation ( u start solving from right to left)
Order of operation in this case:
- ➗or✖️
- ➕or➖
So we can see that 70 divided by 7 is first so we solve it and it will give us 10.
Then we solve 8x3 which is 24, so now we have 24 +70+10-7, so the FINAL ANSWER IS 27
Answer:
27
Step-by-step explanation:
When solving complicated equations like this, we need to remember the order of operations (PEMDAS), which is the order that we solve an equation
P arentheses
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
now, here's the thing: we actually to multiplication/division at the same time, and the same thing with addition/subtraction
(as in, adding -4 is the same thing as subtracting 4, so we can't truly make a distinction between the two)
so, when we have multiple instances of multiplication/division , we solve left to right
(and then the same thing for addition/subtraction)
8 × 3 + 70 ÷ 7 - 7
so, we first need to multiply 8 by 3
8 × 3 = 24
next, we move to the right:
and we divide 70 by 7
70 ÷ 7 = 10
let's rewrite our equation:
(24) + (10) - 7
24 + 10 - 7 = 27
so, the answer to this expression is 27
hope this helps!! have a lovely day :)
pls help asap!!!!
Which number best represents the slope of the graphed line?
Answers
Answer:
C: 1/2
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: C. \cfrac{1}{2}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Slope of line - } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{rise}{run} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 4)}{8 - 0} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 4}{8 } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 1}{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Select the correct answer.
Which function is the inverse of ?
Answers
Answer:
B. [tex]f^{-1}(x) = \frac{x + 3}{9}[/tex]
Step-by-step explanation:
[tex]let \space\ y = f(x)\\\\y = 9x -3\\[/tex]
• Now make x the subject of the equation:
[tex]9x = y + 3\\\\x = \frac{y + 3}{9} \\[/tex]
• Replace x with f⁻¹(x) and y with x:
[tex]f^{-1}(x) = \frac{x + 3}{9}[/tex]
A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
•4/1001
• 15/1001
•10/143
•133/143
Answers
Answer:
The answer is 10/143
Step-by-step explanation:
need help asap!!! ill give brainliest for right answer!
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
Answers
Answer:
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct
Got it right one the test! <3
Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
Answers
In the case above, Jaime claim is true.
The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.What is the claim about?1. Note that radian measure:
= [tex]\frac{60° }{360°}[/tex] x 2π x 3
= 1/6 x 6π
= π
2. Note that radian measure:
= [tex]\frac{60° }{360°}[/tex] x 2π x 6
= 1/6 x 2π x 6
=2π
So we can write it as:
π/3 x 180°/π = 60°
Therefore, via the solution above, Jaime claim is true.
3. Note that: Radian measures: the percentage of arc measures x 2π x radius and so one can say that The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.
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Consider a quadrilateral with vertices A(2,2) , B(2,5) , C(7,2), and D(7,5). What is the shape and area of quadrilateral ABCD
Answers
Answer:
Shape is rectangle
Area of rectangle = length * width
= 5 * 3
= 15 units²
There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
How many people didn't use any facilities?
Answers
Answer:
200wuwusjjdhsuauuaiajjduwiqisidiwiwia
Answer:
n(U) = n(G)+n(S)+n(T)-n(GnS)-n(GnT)-n(TnS)+n(GnTnS) + n(GnTnS)^c
135= 73+59+31-19-9-16+4+ n(GnTnS)^c
no. of people not using any facility =12
This is math proportion :
I change $60 into 45 euros
How many euros would i get for 50$?
Answers
22.5 euros
Explanation:
$60 = 45 euros
$10 = 4.5 euros
$50 = 22.5 euros
Answer:
33.75 Euros
Step-by-step explanation:
Trust me bro, I did the working.
is 4+-x equivalent to 4-x
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
4 + -x ==> 4 - x
Example
x = 3; 4 + (-3) = 4-3 =1
Now evaluate f(x)=2x^4-4x^3-11x^2+3x-6 for x=-2.
F(-2)=
Answers
Answer:
8
Step-by-step explanation:
f(x)=2x^4-4x^3-11x^2+3x-6
f(-2)=2(-2)^4-4(-2)^3-11(-2)^2+3(-2)-6
f(-2)=2(16)-4(-8)-11(4)-6-6
f(-2)=32+32-44-12
f(-2)=64-44-12
f(-2)=20-12
f(-2)=8
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I. Answer each question. Write the letter of the correct answer in your paper.
Read and analyze the following problems carefully. Then, write your answer on a separate sheet of paper.
_____1. In a given circle, the radius is 9 cm. What is its diameter?
A. 18 m
B.18 cm
C. 4.5 m
D. 4.5 cm
_____2. Which of the following is the formula in solving for the area of a circle?
A. A= 2πr
B. A= πr2
C. A= πd
D. A=2 πr2
_____3. The diameter of a circle is8 cm, what is its area?
A.50.24 cm2
B.200.96 cm2
C.25.12 cm2
D.100.48 cm2
_____4. What is the radius of a circle if the area is 36m2?
A. 0.339 m
B. 3.39 m
C. 33.9 m
D. 339m
_____5. What is the area of a circle if the radius is 5m?
A. 15. 7 m2
B. 31.4 m2
C. 78.5 m2
D. 157 m2
Answers
1) B) 18 cm
Radius (r) = 9 cm
Diameter (d) = 2r = 9 * 2 = 18 cm
2) B) A = πr^2
3) A) 50.24 cm^2
Diameter (d) = 8 cm
Radius (r) = d/2 = 8/2 = 4 cm
Area (A) = πr^2
Therefore,
= πr^2
= 3.14 * 4 * 4
= 3.14 * 16
=> 50.24
Area (A) = 50.24 cm^2
4) B) 3.39 m
Area (A) = πr^2 = 36 m^2
Therefore,
πr^2 = 36
3.14 * (r^2) = 36
r^2 = 36/3.14
r^2 = 3600/314
r^2 = 11.46
r = √11.46
=> r = 3.39
Radius (r) = 3.39 m
5) C) 78.5 m^2
Radius (r) = 5 m
Area (A) = πr^2
Therefore,
= πr^2
= 3.14 * 5 * 5
= 3.14 * 25
=> 78.5
Area (A) = 78.5 m^2
A triangle has the dimensions shown. The perimeter of the triangle would be represented by which type of expression?
linear expression
quadratic expression
exponential expression
rational expression
Answers
The third side is a linear expression , Option A is the right answer.
The missing diagram is attached with the figure.
What is a Triangle ?A triangle is a polygon with three sides , three vertices , three angles .
It is given that the side of the triangle as 3x+1 , 5x-2 , y
Perimeter is given as 10x-1
Perimeter = 3x+1 +5x-2 + y = 10x-1
8x -1 +y = 10x -1
y = 2x
which is a linear expression.
Therefore the third side is a linear expression , Option A is the right answer.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answers
An expression is defined as a set of numbers, variables, and mathematical operations.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are given below,
If the given expression 2.3p – 10.1 = 6.5p – 4 – 0.01 is simplified, then the expression can be written as,
2.3p – 10.1 = 6.5p – 4 – 0.01
2.3p – 10.1 = 6.49p – 4
Thus, Option A is one of the option.
Using the multiplication property of Equality, if we multiply both the sides of the equation by 100, then we will get,
230p – 1010 = 650p – 400 – p
Thus, c is one of the option.
Hence, the correct options are A and C.
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Which choice is equivalent to the expression below?
450
OA. 45²
OB. 0
OC. 45
O D. 1
Answers
Answer:
D is the answer because according to the law any number which has 0 at their power is equal to 1.
The correct value of this expression is 1. Letter D
We know that a power is the multiplication of equal factors - according to the exponent. That is, we just multiply the sentence by itself with the value given by the exponent.
Therefore, any number raised to the power of zero will be 1.
The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete two rotations every minute.
Write a sine model, y = asin(bt) + k, for the hight (in feet) of the end of one blade as a function of time t (in seconds). assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
Options are displayed in the picture
Answers
Answer:
D: y= 10sin([tex]\frac{\pi }{15}t[/tex]) + 30
Step-by-step explanation:
30 feet above the ground is the k value.
10 feet long is how long the blades reach up and down which is also known as the amplitude.
The rest is given in all answers.
Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?
Angle 2 = °
Angle 3 = °
Angle 4 = °
Answers
The values of the angles based on the information will be:
Angle 2 = 110°Angle 3 = 70°Angle 4 = 70°How to calculate the angles?From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.
In this case, it should be noted that opposite angles are equal. Hence, angle 2 is also 110°.
Angle 3 will be:
= 180° - 110° = 70° (angle on a straight line).
Angle 4 will also be 70° as opposite angle to angle 3.
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I need help solving this
Answers
Answer: y = -x + 5
Step-by-step explanation:
A slope-intercept equation is in the form y = mx + b where m is the slope and b is the y-intercept. Since we are given the slope, we will plug it in with the point they gave us, and solve for b.
y = mx + b
(1) = (-1)(4) + b
1 = -4 + b
5 = b
Lastly, we will write our equation by substituting m with -1 and b with 5.
y = mx + b
y = -1x + 5 or y = -x + 5
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What two numbers differ by 46. (29,17,38,71,35,63,24)
Answers
Answer: 63 and 17 differ by 46.
Step-by-step explanation:
63-17=46
Subtraction is what you do when trying to find the difference of something.
Select all that apply. Which of the following corresponds to absolute zero?
Answers
In thermodynamic system, Absolute Zero is that temperature implies Lowest energy level i.e. option a) 0 K or -273° C.
What is Absolute Zero?
Absolute Zero can describe as, in a thermodynamic system, there are certain energy levels depending upon the potentials of temperature. At Absolute zero the potentials of temperature are 0 K in Kelvin scale and -273° C in Celsius scale.
The question seem's to be incomplete. The option could be.
a) 0 K and -273° C
b) 273 K and 0° C
c) -273 K and 0° C
d) 0 K and 273° C
Hence, As per theory Value of The absolute zero is 0 K and -273° C
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This year, a small business had a total revenue of $44,100. If this is 26% more than their total revenue the previous year, what was their total revenue the previous year?
Answers
Answer:
look at the picture .
Step-by-step explanation:
look at the picture .
Using a left endpoint riemann sum approximation with four equal subintervals, the approximate value of integral from 0 to 8 g(x) dx is:
Answers
Subdividing [0, 8] into 4 equally-spaced subintervals, each one will have length ∆x = (8 - 0)/4 = 2, and the partition is
[0, 2] U [2, 4] U [4, 6] U [6, 8]
We approximate the integral with a left endpoint sum. The left endpoint of the i-th subinterval is
[tex]\ell_i = 2(i-1)[/tex]
where 1 ≤ i ≤ 4.
Then the integral is approximated by
[tex]\displaystyle \int_0^8 g(x) \, dx \approx \sum_{i=1}^4 g(\ell_i) \Delta x \\\\ = 2 (g(0) + g(2) + g(4) + g(6)) \\\\ = 2 (-1 - 3 - 1.25 - 1.5) = \boxed{-13.5}[/tex]
Can someone help me out with this problem
Answers
From the given options the options B and C are correct for the given equation.
we have given the equation,
70=10+12r
We have to determine the correct option
What is the equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Therefore from the given options the options B and C are correct for the given equation.
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According to the property
below?
√30
OA. 25
OB. -√5
O C. 5
OD. -5
OE. √5
Vo = √ which choice is equivalent to the quotient
4
Answers
Answer:
√30/6 = √5
The correct answer would be E
The value of the expression √30/√6 is √5, option E is correct.
What is Number system?A number system is defined as a system of writing to express numbers.
The given property is √a/√b = √(a/b)
Now we have to find the equivalent to the quotient √30/√6
By the given property let us plug in a as 30 and b as 6
√30/√6
= √(30/6)
When we simplify the fraction inside the root we get 5
= √5
Hence, the value of the expression √30/√6 is √5, option E is correct.
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Construct a truth table for the following symbolic statement.
Use the type of truth table where each variable or operator in the given expression has its own column. Fill in the rows of the truth table one at a time.
Answers
The truth table is completed for each column as T T F F T T T
What is a truth table?A truth table is a mathematical table which shows all the truth values of a given combination of logic statements.
Analysis:
The truth table is shown in the attached file
in the attached file, the first two columns were given,
The third column is the negation of p, and P is true(T) which means its negation is false(F).
The fourth column is the negation of Q, which means Q is true(T) so its negation is false(F).
In the fifth column, negation P is implies negation Q. The truth table for implication, is only false if Q is false, else it is True.
Same as in the sixth column.
The last column is bi-implication, the truth table for this only true, if both statements are false or both are true else, it is false.
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Help yalllll question is in the pic
Answers
Step-by-Step Solution:
=> f(x) = 5x - 1
=> g(x) = 2x^2 + 1
=> Find value of (f * g)(-3)
First Substitute x as -3 in f(x) and g(x) :-
f(x) = 5x - 1
f(-3) = 5(-3) - 1
f(-3) = -15 - 1
=> f(-3) = -16
g(x) = 2x^2 + 1
g(-3) = 2(-3^2) + 1
g(-3) = 2(9) + 1
g(-3) = 18 + 1
=> g(-3) = 19
Now Multiply f(-3) with g(-3) :-
= f(-3) * g(-3)
= -16 * 19
=> -304
Therefore, (f * g)(-3) = -304
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
-m-2=2+
m
O 2
O 3
04
O 5
