Answer:
The answer is below.
Step-by-step explanation:
PROVE √(1-〖cos〗^2 θ)/cosθ = tanθ
Now 1 - cos^2 θ = sin^2θ
So √(1 - cos^2 θ) = sin θ
and √(1 - cos^2 θ) / cos θ
= sin θ / cos θ
= tan θ
Step-by-step explanation:
[tex]\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\tan\theta\\\\\text{We know:}\\(1)\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\(2)\tan x=\dfrac{\sin x}{\cos x}\\\\\text{For}\ \sqrt{1-\cos^2\theta}\ \text{use}\ (1):\\\\L_S=\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\dfrac{\sqrt{\sin^2\theta}}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta\ \ \ _{used (2)}\\\\R_S=\tan\theta\\\\L_S=R_S[/tex]
[tex]\text{Of course, this equality is not true for everyone values of}\ \theta.\\\\1^o.\ \cos\theta\neq0\to\theta\neq\dfrac{\pi}{2}+k\pi,\ k\in\mathbb{Z}\\\\2^o.\ \sqrt{\sin^2\theta}=|\sin\theta|,\ \text{therefore}\\\\\text{for}\ \theta\in[2k\pi;\ (2k+1)\pi],\ \sin\theta\geq0\to|\sin\theta|=\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta[/tex]
[tex]\text{for}\ \theta\in\bigg((2k-1)\pi;\ 2k\pi\bigg),\ \sin\theta<0\to|\sin\theta|=-\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{-\sin\theta}{\cos\theta}=-\tan\theta\neq\tan\theta[/tex]
[tex]\text{Conclusion:}\\\\\text{This equality is true for}\ \theta\in\left[2k\pi;\ \dfrac{\pi}{2}+2k\pi\right)\cup\left(\dfrac{\pi}{2}+2k\pi;\ \pi+2k\pi\right],\ k\in\mathbb{Z}[/tex]
Simplify [tex]$\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$[/tex] $\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$
Answer:
[tex]3 -\sqrt[2]3[/tex]
Step-by-step explanation:
Given
[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex]
Required
Simplify
Rewrite the given expression in index form
[tex]\frac{2 * 9 ^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 9^{\frac{1}{3}}}[/tex]
Express 9 as 3²
[tex]\frac{2 * 3^2^*^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 3^2^*^{\frac{1}{3}}}[/tex]
[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}}[/tex]
Multiply the numerator and denominator by [tex]1 - 3^{\frac{1}{3}}[/tex]
[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}} * \frac{1 - 3^{\frac{1}{3}}}{1 - 3^{\frac{1}{3}}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) (1 - 3^{\frac{1}{3}})}{(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})(1 - 3^{\frac{1}{3}})}[/tex]
Open the bracket
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2}{3})(3^{\frac{1}{3}})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
Simplify the Numerator using Laws of Indices
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2+1}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
Further Simplify
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{3}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^1)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
Simplify the denominator
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1}{3}})(3^{\frac{1}{3}}) - (3^{\frac{1}{3}})(3^{\frac{2}{3}})}[/tex]
Further Simplify Using Laws of Indices
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1+1}{3}}) - (3^{\frac{1+2}{3}})}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^{\frac{3}{3}}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^1}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3}}[/tex]
Collect Like Terms
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 - 3+ 3^{\frac{1}{3}} - 3^{\frac{1}{3}}+ 3^{\frac{2}{3}} - 3^{\frac{2}{3}} }}[/tex]
Group Like Terms for Clarity
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{(1 - 3) + (3^{\frac{1}{3}} - 3^{\frac{1}{3}}) + (3^{\frac{2}{3}} - 3^{\frac{2}{3}} )}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{(- 2)+ (0) + (0)}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{-2}}[/tex]
Divide the fraction
[tex]-(3^\frac{2}{3}) + (3)[/tex]
Reorder the above expression
[tex]3 -3^\frac{2}{3}[/tex]
The expression can be represented as
[tex]3 -\sqrt[2]3[/tex]
Hence;
[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex] when simplified is equivalent to [tex]3 -\sqrt[2]3[/tex]
Which store has the lowest delivery charge?
Answer:
Igloo Ice has the lowest delivery charge.
Step-by-step explanation:
Igloo Ice when you plug in 120 for the y you get 25.714 as the x.
Freds freeze at 120 is 20.
And lastly Tasty treats at 120 is 24, so Igloo Ice has the lowest delivery charge per person (you pay $120 for 25.714 people.)
Answer:
Igloo Ice
Step-by-step explanation:
Igloo Ice C(n) = 1.75n + 75
Fred's Freeze C(n) = 2n + 80
Tasty Treats C(n) = 1.25n + 90
75 is the lowest delivery charge
C(n) is total charge including what they are delivering
Find the perimeter of a square with a diagonal of 15√2.
Answer:
15
Step-by-step explanation:
Answer:
21.213
Step-by-step explanation:
The baseball team has a double-header on Saturday. The probability that they will win both games is 50%. The probability that they will win just the first game is 65%, What is the probability that the team will win the 2nd game given that they have already won the first game? (PLEASE SHOW YOU'RE WORK)
Answer:
77%
Step-by-step explanation:
Given the following :
Probability of winning both games = 50%
Probability of winning just the first game = 65%
Let the probability of winning the ;
First game = p(A) = 65%
Second game = p(B)
Both games = p(A and B) = 50%
What is the probability that the team will win the 2nd game given that they have already won the first game
The above question is a conditional probability question :
Probability of winning the second Given that they've already won the first = p(B | A)
p(B | A) = (A and B) / p(A)
p(B | A) = 50% / 65%
p(B | A) = 0.5 / 0.65
p(B | A) = 0.7692307
= 76.9% = 77%
An integer minus 5 times its reciprocal is
76
9
What is the integer?
griffin ordered a pair of sneakers online. he had 16 credit that he applied toward the purchase, and then he used a credit card to pay for the rest of the cost. if the the shoes cost 80, then how much did griffin charge to his credit card when he bought the sneakers? PLEASE ANSWER I BEG Y'ALL
Answer: Griffin charge $79.854 to his credit card when he bought the sneakers.
Step-by-step explanation:
Griffin ordered a pair of sneakers online.
Value of each credit point = 1 cent
Then , value of 16 credit points = 16 cents = $0.16 [1$ = 100 cents]
Cost of shoes = Rs $80
Charge to credit card = (Cost of shoes) - (Value of 16 credit points)
= $(80-0.16)
= $79.84
Hence, Griffin charge $79.854 to his credit card when he bought the sneakers.
Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$
Answer:
2√2
Step-by-step explanation:
By simplifying we get the value is [tex]2\sqrt{2}[/tex]
What is expression ?The combination in which numbers, variables, functions are present, is called expression.
Example : 6y-3x+2, 2y-3 etc.
What is the simplified form of the expression ?
The given expression is [tex]\frac{1}{\sqrt{2}+1 } +\frac{1}{\sqrt{2}-1 }[/tex]
Simplifying,
First we take the LCM of [tex]\sqrt{2}+1[/tex] & [tex]\sqrt{2}-1[/tex]
Then expression becomes, [tex]\frac{(\sqrt{2}-1)-(\sqrt{2}+1) }{(\sqrt{2}+1)(\sqrt{2}-1)}[/tex]
Now, using [tex](a+b)(a-b)=a^{2}- b^{2}[/tex] we get, [tex]\frac{\sqrt{2}-1+\sqrt{2}+1 }{(\sqrt{2}) ^{2} - 1^{2} }[/tex]
Now, simplifying, we get, [tex]\frac{2\sqrt{2} }{2-1}[/tex] = [tex]2\sqrt{2}[/tex]
Learn more about expression here :
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The graph for the equation y = x minus 4 is shown below. On a coordinate plane, a line goes through (0, negative 4) and (4, 0). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y minus x = negative 4 y minus x = negative 2 y minus 4 = x y + 4 x = 1 Brainliest reward
Answer:
The correct option is;
y minus x = negative 4
(y - x = -4)
Step-by-step explanation:
Given that the line y = x - 4 of the graph passes through the points (0, -4) and (4, 0)
Comparing with the general equation of a straight line, y = m·x + c, where m is the slope and c is the y-intercept gives;
The slope of the equation y = x - 4 = 1
The y-intercept of the equation y = x - 4 = -4
Two equations will have an infinite number of solutions when they are on the same line, that is having the same slope and intercept, we check for the slope and the intercept of the given options as follows;
For y - x = -4, we have;
y = x - 4 which is the same as the given equation and both equations will have an infinite number of solutions
For y - x = -2 we have;
y = x - 2
The slope is the same as the given equation but the intercept is different giving no solution
For y - 4 = x, we have;
y = x + 4
The slope is the same as the given equation but the intercept is different giving no solution
For y + 4x = 1, we have;
y = 1 - 4x
The slope and intercept are different giving one solution.
Answer:
y - x = -4
Step-by-step explanation:
CAN SOMEONE PLEASE HELP IT'S URGENT!
Answer:
D. y = f(x/-1)
Step-by-step explanation:
The function f(x) is reflected across the y-axis to make the red graph. Such a reflection is accomplished by a horizontal scale factor of -1.
For some horizontal scale factor k, the transformed function is ...
y = f(x/k)
Here, we have k = -1, so the transformed function is ...
y = f(x/-1)
Please answer this question now
Answer:
44 degrees
Step-by-step explanation:
Since MN is a tangent, it forms a right angle wheng it intersects line MP since MP is the diameter. So, 90+46 is 136 and since there are 180 degrees in a traingle, 180-136 is 44.
Hope this is helpful! :)
The answer is 44 degrees.
:D
A particle moves along a straight line. The distance of the particle from the origin at time t is modeled by the equation below. s(t)equals2 sine t plus 3 cosine t Find a value of t between 0 and StartFraction pi Over 2 EndFraction that satisfies the equation s(t)equalsStartFraction 2 plus 3 StartRoot 3 EndRoot Over 2 EndFraction .
Answer:
The value of t that will satisfy the equation is π/6 (which is 30 degrees)
Step-by-step explanation:
The function that models the movement of the particle is given as;
S(t) = 2 sin(t) + 3 cos (t)
Now we want to the value of t between 0 and pi/2 that satisfies the equation;
s(t) = (2+ 3√3)/2 = 1 + 3√3/2
What we do here is simply find that value of t that would ensure that;
2sin(t) + 3cos(t) = 1 + 3√3/2
Without any need for rigorous calculations, this value of t can be gotten by inspection.
From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2
We can make a substitution for it in this equation.
We obtain the following;
2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2
Do not forget however that we have a range. And the range in question is between 0 and π/2
Kindly that π/2 in degrees is 90 degrees
So our range of values here is between 0 and 90 degrees.
So to follow the notation in the question, the value within the range that will satisfy the equation is π/6
The formula for the volume of a pyramid is =13ℎ
V
=
1
3
B
h
, where B is the area of the base and h is the height. Rearrange the formula to solve for the height (h).
Select one:
a. ℎ=3
h
=
3
V
B
b. ℎ=3
h
=
B
3
V
c. ℎ=3
h
=
V
3
B
d. ℎ=3
Answer:
h = V3B
Step-by-step explanation:
V = 1/3B · h
Divide volume by 1/3 B to get h by itself
V/1/3B = V3B
Which equation represents a line that is perpendicular to line FG? A. y=-1/2x+5 B. y=1/2x+2 C. y=-2x-3 D. y=2x-6
The equation of line which is perpendicular to the line FG is
y = -2x -3.
What is equation of line?
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
Formula for finding the equation of line from two points [tex](x_{1} ,y_{1} ) and (x_{2}, y_{2} )[/tex][tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]
What is the slope of two perpendicular lines?If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].
What is the slope intercept form of a line ?The slope intercept form of the line is given by y = mx + b
Where, m is the slope of a line.
According to the given question
We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.
Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]
⇒ The slope of the line which is parallel to line FG is -2
Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .
Hence, the equation of line which is perpendicular to the line FG is
y = -2x -3.
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wht is the solution of the system defined be y =-x+5 and 5x+2y=14
Answer:
1.33,3.667
Step-by-step explanation:
Use y=mx+b for second system
which is y=5/2x+7
Now use substitution,graph, or elimination method.
help me solve this Algebra problem please
Answer:
39858075
Step-by-step explanation:
Hello,
One basic way to see it is to compute the values.
75 = 25 * 3
225 = 75 * 3
675 = 225 * 3
etc ...
We can notice that this is multiplied by 3 every 10 years so we can compute as below.
year population
1970 25
1980 75
1990 225
2000 675
2010 2025
2020 6075
2030 18225
2040 54675
2050 164025
2060 492075
2070 1476225
2080 4428675
2090 13286025
2100 39858075
So the correct answer is 39858075
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the gradient and y intercept of the following lines 1) y= 2X + 3 2) y = 5X + 1 3) y= 3X + 2
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope( gradient ) and y the y- intercept )
The 3 equations are in this form
(1)
y = 2x + 3
with gradient = 2 and y- intercept = 3
(2)
y = 5x + 1
with gradient = 5 and y- intercept = 1
(3)
y = 3x + 2
with gradient = 3 and y- intercept = 2
Which circle has a center angle that measures 40 degrees
Answer: B
Step-by-step explanation:
A center angle is an angle that has rays that originate from the center.
A game has an expected value to you of $1200. It costs $1200 to play, but if you win, you receive $100,000 (including your $1200 bet) for a net gain of $98 comma 800. What is the probability of winning? Would you play this game? Discuss the factors that would influence your decision.
Answer:
A) the probability of winning is 0.24%.
B) Yes i will play the game
C) Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.
Step-by-step explanation:
Expected value of X is denoted by;
E(X) = x1•p1 + x2•p2 +..... xn•pn
Where;
xi is the observation and pi is the probability of xi
Now, let's make p the probability of the winning bet and 1 - p be the probability of losing the game
If the bet is win, the net gain is $98,800 and if the bet is lose, the loss is -$1200.
Hence the probability distribution will be;
For xi = $98,800, pi = p
For xi = -$1,200, pi = 1 - p
So;
E(X) = Σxi.pi
Thus;
1200 = 98800p - 1200(1 - p)
1200 = 98800p - 1200 + 1200p
1200 + 1200 = 100000p
2400 = 100000p
p = 2400/100000
p = 0.024
Thus, the probability of winning is 0.24%.
Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.
Jaden learns to perform 2 vocal pieces during each week of lessons . How many weeks of lessons will Jaden need before he will be able to sing a total of 24 pieces?
Answer:
12 weeks
Step-by-step explanation:
To solve this, all you need to do is divided 24 pieces by the two he learns per week. You'll then find it will take him 12 weeks
What is the maximum value of the function f(x)=-x^2+6x+1 (enter an exact number) rotate image to see the problem
Answer:
10
Step-by-step explanation:
f(x)=-x^2+6x+1
This is a parabola that opens downward( the - coefficient of x^2)
The maximumx is at the vertex
The x coordinate is at
-b/2a where ax^2 + bx +c a =-1 b=6 c=1
-6/(2*-1)
-6/-2 = 3
The x coordinate of the vertex is 3
f(3) = - (3)^2 +6(3)=1
= -9+18+1
= 10
The vertex is ( 3,10)
The maximum value is 10
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]f(x)=-x^2+6x+1[/tex]
x coordinate:
[tex]\frac{-b}{2a}[/tex]
[tex]a=-1\\b=6[/tex]
[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]
y-coordinate:
[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]
Hi May I know how to solve this step by step please
Answer:
2, 3 , 5, 7
Step-by-step explanation:
2(x - 2)/3 < (x + 1)/2 < 3(5x + 6)/4
Considering:
2(x - 2)/3 < (x + 1)/2
<=>(2x - 4)/3 < (x + 1)/2
<=> (2x - 4)*2 < (x + 1)*3
<=> 4x - 8 < 3x + 3
<=> 4x - 3x < 8 + 3
<=> x < 11
Considering:
(x + 1)/2 < 3(5x + 6)/4
<=>(x + 1)/2 < (15x + 18)/4
<=>(x + 1)*4 < (15x + 18)*2
<=> 4x + 4 < 30x + 36
<=> 4x - 30x < 36 - 4
<=> -26x < 32
<=> 26x > -32
<=> x > -32/26
=> -32/26 < x < 11
The prime numbers satisfy the above inequalities: 2, 3 , 5, 7
PLEASE HELP!
What is the length of the shortest altitude in a triangle, if the lengths of the sides are 15 cm, 17 cm, 8 cm. NO DECIMALS
Answer:
The shortest altitude = 8 cm
Step-by-step explanation:
Where we have the sides given by
15 cm, 17 cm, 8 cm
From cosine rule, we have;
a² = b² + c² - 2×b×c×cos(A)
We have
For the side 15 cm,
15² = 17² + 8² - 2×17×8 cos A
-388 = -612×cos×A
A = 61.93°
17² = 15² + 8² - 2×15×8 ×cos B
0 = -240·cos B
B = 90°
Therefore, 17 is the hypotenuse side and 15 and 8 are the legs, either of which can be the height which gives the shortest altitude as 8 cm
simplify
[tex] {a}^{ - 2} {b}^{3} [/tex]
Answer:
Below
Step-by-step explanation:
● a^(-2) *b^3
●(1/a^2) *b^3
● b^3 / a^2
Please help me as fast as you can. thanks
Answer:
<DEF = 40<EBF = <EDF = 56<DCF = <DEF =40<CAB = 84Step-by-step explanation:
In triangle DEF, we have:
Given:
<EDF=56
<EFD=84
So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)
____________
DE is a midsegment of triangle ACB
( since CD=DA(given)=>D is midpoint of [CD]
and BE = EA => E midpoint of [BA] )
According to midsegment Theorem,
(DE) // (CB) "//"means parallel
and DE = CB/2 = FB =CF
___________
DEBF is a parm /parallelogram.
Proof: (DE) // (FB) ( (DE) // (CB))
AND DE = FB
Then, <EBF = <EDF = 56
___________
DEFC is parm.
Proof: (DE) // (CF) ((DE) // (CB))
And DE = CF
Therefore, <DCF = <DEF =40
___________
In triangle ACB, we have:
<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)
[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK! [/tex]
(05.05)
Based on the graph, what is the initial value of the linear relationship?
-4
-3
5/3
5
Answer:
5
Step-by-step explanation:
The initial value is when x=0
When x=0, y =5
The initial value is 5
Jonathan was laying on the ground and enjoying the shade but now the sun is shining
on him. He knows he is 10 yards away from the building that was shading the sun and
that the building is 8 yards high. At what angle does the sunlight hit the ground? Write
only the number rounded to the nearest degree.
Answer:
38.5°
Step-by-step explanation:
Given that the height of the building is 8 yard and the distance between Jonathan and the building is 10 yards.
The sun is at the top of the building, let the distance between Jonathan laying on the ground and the top of the building be x. Using Pythagoras:
x² = 10² + 8²
x² = 100 + 64
x² = 164
x = √164 = 12.86 yards
For a triangle with sides a, b, c and their respective opposite angles A, B, and C. The sine rule is given as:
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
Let the angle that the sunlight hit the ground be y°. The andle between the building and the ground is 90°. Therefore using sine rule:
[tex]\frac{8}{sin(y)}=\frac{12.86}{sin(90)}\\\\sin(y)=\frac{8*sin(90)}{12.86}\\\\sin(y)=0.622\\\\y=sin^{-1}0.622\\\\y = 38.5^0[/tex]
PLEASE ASAP There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen. How many possibilities are there?
Answer: 380
Step-by-step explanation:
Total number of players = 20
To select a captain and a vice captain :
One captain from a total of 20 players :
20 combination 1 = 20C1 = 20 ways
Total number of players left after selecting a captain = 20 - 1 = 19
Number of players left from which to select a vice captain = 19
Therefore, one vice captain from a group of 19 players :
19 combination 1 = 19C1 = 19 ways
Therefore no of different possible ways to select a captain and a vice captain :
20C1 × 19C1 = 20 × 19 = 380 Ways
A steel wire, when bent in the form of a square, encloses an area of 121 sq cm. The same wire
is bent, in the form of a circle. Find the area of the circle.
Answer:
A = 49[tex]\pi[/tex]
Step-by-step explanation:
First, we need to find the length of the wire. We can calculate this because we are given the area of the square, so we can work backwards.
Use the area formula and plug in the numbers:
A = s²
121 = s²
11 = s
We can calculate the length of the wire by multiplying 11 by 4, which is 44.
Now, we know the circumference of the circle is 44 units because that is how long the wire is.
We can work backwards again to find the radius, using the circumference formula:
C = 2[tex]\pi[/tex]r
44 = 2[tex]\pi[/tex]r
22 = [tex]\pi[/tex]r
7 = r
Now, we can find the area of the circle:
A = [tex]\pi[/tex]r²
A = [tex]\pi[/tex](7)²
A = 49[tex]\pi[/tex]
convert this number to scientific notation 1260000
Answer:
1.26 * 10 ^6
Step-by-step explanation:
1260000
Scientific notation is of the form a* 10 ^b
where a is a number between 1 and less than 10
Move the decimal 6 places to the left
1.26 ( dropping the extra zeros)
b = +6 since we moved the decimal 6 places)
1.26 * 10 ^6
The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].
We have,
1260000
Write the zeroes in powers of 10.
Write a number between 1 to 10 along with the power of 10.
Now,
126 x 10000
This can be written as,
126 x [tex]10^4[/tex]
Now,
126 can be written as 126/100 x 100.
i.e
1.26 x 100 or 1.26 x 10²
Now,
1.26 x 10² x [tex]10^4[/tex]
1.26 x [tex]10^{2 + 4}[/tex]
1.26 x [tex]10^6[/tex]
Thus,
The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].
Learn more about scientific notation here:
https://brainly.com/question/18073768P
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Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
? = 23
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp/ adj
tan ? = 3/7
take the inverse tan of each side
tan ^-1 tan ? = tan ^-1 ( 3/7)
? = 23.19859051
To the nearest degree
? = 23