Given that:
Cos θ = Sin 2θ
⇛ Cos θ = 2 Sin θ Cos θ
⇛ Cos θ / Cos θ = 2 Sin θ
⇛ 1 = 2 Sin θ
⇛ 1/2 = Sin θ
⇛ Sin θ = 1/2
⇛ Sin θ = Sin 30°
⇛ θ = 30°
Therefore, θ = 30°
Answer :-The value of θ for the given problem is 30°
Check:-
LHS = Cos θ
⇛ Cos 30°
⇛ √3/2
RHS = Sin 2θ
⇛ Sin (2×30°)
⇛ Sin 60°
⇛ √3/2
LHS = RHS is true for θ = 30°
»If you have any doubt, then you can ask me in the comments.
MATHEMATICS Proportion Х Y Z 145) If line XY is 24in, lines XY:YZ = 1:2. What is the length of line YZ? A) 12 in B) 24in C) 48in D) 72 in 147) If line YZ is 9ft, lines XY:YZ= 2:3. What is the length of line XY? A) 3ft B) 6ft C) 9ft D) 12ft 148) If line YZ is 1ft, line XY:YZ = 1:4. What is the length of line XY? A) 3in B) 27in C) 2ft D) 18in
Answer:
145. YZ = 48 in
147. XY = 6 ft
148: XY = 3 in
Step-by-step explanation:
In each case, multiply the given proportion by a value that makes it match the given information about the segments.
145)XY is 24in, lines XY:YZ = 1:2. What is the length of line YZ?
Multiply the proportion by 24 in:
XY : YZ = (24 in)(1) : (24 in)(2) = 24 in : 48 in
YZ = 48 in . . . (C)
__
147)YZ is 9ft, lines XY:YZ= 2:3. What is the length of line XY?
Multiply the proportion by 3 ft:
XY : YZ = (3 ft)(2) : (3 ft)(3) = 6 ft : 9 ft
XY = 6 ft . . . (B)
__
148)YZ is 1ft, line XY:YZ = 1:4. What is the length of line XY?
Multiply the proportion by 3 in:
XY : YZ = (3 in)(1) : (3 in)(4) = 3 in : 12 in = 3 in : 1 ft
XY = 3 in . . . (A)
Simplify -3(xy + 2y) + 5y - x.
Answer:
Step-by-step explanation:
-3 (xy+2y)+5y-x
-3xy-6y+5y-x
-3xy-y-x
i will be asking multiple questions (true or false ) you can just tell me which ones are true and which ones are false
4 is 10 times as much as 0.4 0.05 is 10 times as much as 50 0.3 is 10 times as much as
3 0.09 is 1/10 of 0.9 6 is 1/10 of 0.6 80 is 1/10 of 0.08
True, False, False, True, False, False
why is upendrakishore roy chouwdhury remembered
Answer:
Upendrakishore Roy Chowdhury; 12 May 1863 – 20 December 1915) was a Bengali writer and painter. He was the first person who introduced the colour printing in bangal. He started the first color children's magazine Sandesh in 1913.
Step-by-step explanation:
history ig
-2(2v + 11) + 1 =-5(9v – 4)
Answer:
v=1
Step-by-step explanation:
-2(2v + 11) + 1 =-5(9v – 4)
Distribute the -2 and -5.
-4v-22+1=-45v+20
Calculate the sum.
-4v-21=-45v+20
Move the variable to the left-hand side and change the sign.
-4v-21+45v=20
Move the constant to the right-hand side and change the sign.
-4v+45v=20+21
Collect like terms.
41v=20+21
Add the numbers.
41v=41
Divide both sides by 41
v=1
Hope this helps :)
Answer:
v = -1/49
Step-by-step explanation:
distribute
-4v - 22 + 1 = 5(9v-4)
add the numbers -21 + 1 = -21
distribute the other parenthesis
-4v - 21 = 45v -20
add 21 to both sides to get v by itself
-4v - 21 + 21 = 45v + 20 + 21
-4v = 45v + 1
substract 45 v on both side now
-4v - 45v = 45v + 1 - 45v
simplify
-49v = 1
divide -49 on both side
v = -1 / 49
Dita adds 2 oz of milk to an 18 oz cup of coffee that is 10% milk. What is the percentage of milk in the resulting mixture?
SHOW YOUR WORK!
Increasing the amount of milk in the coffee increases the percentage of milk in the cup of coffee.
The resulting mixture is 19% milkReasons:
The known quantities are;
The volume of milk Dita adds to an cup of coffee = 18 oz
The percentage of milk in the cup of coffee = 10%
Required:
The percentage milk in the resulting mixture.
Solution:
Initial amount of milk initially in the cup of coffee = 10% × 18 oz = 1.8 oz
The total amount of milk in the resulting mixture = 2 oz + 1.8 oz = 3.8 oz
Volume of the resulting mixture = 2 oz + 18 oz = 20 oz
The percentage of milk in the resulting mixture is therefore;
[tex]\displaystyle \mathrm{Percentage \ of \ milk = } \frac{3.8}{20} \times 100 = 19\%[/tex]
The resulting mixture is 19% milk.
Learn more here:
https://brainly.com/question/22599498
60 children went to the beach.. 4/5 of them could swim. How many 60 children went to the beach. children could not swim?
Answer:
75
Step-by-step explanation:
60 divided by 4/5 is 75
Beth drops a bouncy ball, which bounces back up again. The graph 'below shows the
beginning path of the ball.
Answer:
Step-by-step explanation: its a
simplify the ratio 12 1/4 : 8
Answer: 49 : 32
Step-by-step explanation:
12 1/4 = 49/4
12 1/4 : 8 = 49/4 : 8
12 1/4 : 8 = 49/4 : 8/1
12 1/4 : 8 = 49/4 : 32/4
12 1/4 : 8 = 49 : 32
12 1/4 : 8 = 49 : 32
Use the Chain Rule to express the second derivative of f∘g in terms of the first and second derivatives of f and g.
The second derivative of the composition between two functions is described by the following expression:
[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]
Mathematically speaking, a composition between two functions is defined by the following operation:
[tex]f\,\circ\,g\,(x) =f(g(x))[/tex] (1)
By Chain Rule we get the first and second derivatives of the composition:
First derivative
[tex]\frac{d}{dx} (f\,\circ\,g\,(x)) = \frac{df}{dg}\cdot \frac{dg}{dx}[/tex] (2)
Second derivative
[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex] (3)
The second derivative of the composition between two functions is described by the following expression:
[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]
We kindly invite to check this question on chain rule: https://brainly.com/question/23729337
The angle of depression from the top of a cliff to a
nearby town is 12 degrees. If the top of the cliff is
277 feet above the town, how far is the town from
the base of the cliff?
Round your answer to the nearest tenth of a foot
Answer:
Step-by-step explanation:
d = 277/tan12 = 1,303.1825... m = 1.3 km
The nearest tenth of a foot, the distance from the town to the base of the cliff is approximately 1337.3 feet.
The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
The angle of depression is 12 degrees, and the side opposite the angle is the height of the cliff (277 feet), while the side adjacent to the angle is the distance from the town to the base of the cliff (which we want to find).
Let's denote the distance from the town to the base of the cliff as "d."
The tangent of the angle of depression is given by:
tan(12°) = opposite / adjacent
tan(12°) = 277 / d
Now, solve for "d":
d = 277 / tan(12°)
Using a calculator:
d ≈ 1337.25 feet
To know more about distance here
https://brainly.com/question/34779919
#SPJ3
the bottom the range has the same numbers so I just need the domain and range help plz!!
Step-by-step explanation:
The domain is set of x-values:
0 ≤ x ≤ 7.5 as both points are inclusiveThe range is set of y-values:
0 ≤ y ≤ 14 as both points are inclusivewhich of the following is a number where the digit 2 represents 1/10 the value of the digit 2 in the number 1,947.5286
Answer:
0.002
Step-by-step explanation:
the digit "2" in this equation represents 0.02 or also 2/100
1/10 of 2/100 would be like multiplying 1/10 and 2/100 and that would get us 2/1000
2/1000 is also 0.002
0.002 is the value of the digit 2 in the number 1,947.5286.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here we have,
the number 1,947.5286.
the digit "2" in this equation represents 0.02 or also 2/100
1/10 of 2/100 would be like multiplying 1/10 and 2/100
and that would get us 2/1000
i.e.
2/1000 is also 0.002
Hence, 0.002 is the value of the digit 2 in the number 1,947.5286.
To learn more on number click:
brainly.com/question/17429689
#SPJ2
Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 34-5=-2N+ 10? Select two options Ox= 5 0 -15 = -5x 0 5x = 15 0 -15 = 5x Ox = -5
Answer:
-15 = -5x
5x = 15
Step-by-step explanation:
A 44-foot long wire will be attached to the top of a
pole for support, and will be pulled tight and
anchored to the ground. If the wire makes a 13
degree angle with the ground, how tall is the pole?
Round your answer to the nearest hundredth of a
foot
Answer:
Step-by-step explanation:
h = 44sin13 = 9.89784... = 9.90 ft
what’s the correct answer i will give brainlist
The scenario could be modeled as a linear equation to produce the mathematical model written as : y = 10x + 7
Number of cards from previous card = 7
Number of cards per cardstock purchased = 10
Let :
Number of cardstocks purchased = x
Total Number cards made = y
The total number of cards made, y can be expressed thus :
(Number of cards per cardstock purchased × number of cardstocks purchased) + number of previous cards
This means :
y = 10x + 7
Therefore, the required equation is y = 10x + 7
What is sin 60°?
WA :)
an
2
90
30
5
A. I
оо
B.
-IS
o
C. 1
D.
O
E. 5
o
OF
PREVIOUS
Answer:
F
Step-by-step explanation:
If you look at that triangle and do trigonometry with sin, you would have to do opposite/hypotenuse. This would be (square root of 3)/2
When thirteen is reduced by two-thirds of a number, the result is 7. Find the number.
The number is
Answer:
30Step-by-step explanation:
Let,
The req. number be = x
So,
Two - thirds of the number
[tex] = \frac{2}{3} x[/tex]
Then, it is reduced by 13
[tex] = \frac{2}{3} x - 13[/tex]
After that,
The req. result we get is = 7
Therefore,
By the problem,
[tex] = > \frac{2}{3} x - 13 = 7[/tex]
(On putting like terms on one side)[tex] = > \frac{2}{3} x = 7 + 13[/tex]
(On Simplification)[tex] = > \frac{2}{3}x = 20[/tex]
(On multiplying both sides with 3/2)[tex] = > \frac{2}{3} x \times \frac{3}{2} = 20 \times \frac{3}{2} [/tex]
(On Simplification)=> x = 30
Hence,
The req. number is 30.
Given that :
Thirteen is reduced by two-thirds of a number. And their result is 7.To Find :
The number.Solution :
Let's assume the number as x
According to the question :
[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 = 7 }[/tex]
Adding 13 to both sides we get :
[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 + 13 = 7 + 13 }[/tex]
[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x = 20 }[/tex]
Now, Multiplying both sides by [tex] \dfrac{3}{2} [/tex] we get :
[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x \times \dfrac{3}{2} = 20 \times \dfrac{3}{2} }[/tex]
[tex]\qquad \sf \: { \dashrightarrow \dfrac{ \cancel2}{ \cancel3}x \times \dfrac{{ \cancel3}}{ \cancel{2}} = \cancel{20} \times \dfrac{3}{ \cancel{2}} }[/tex]
[tex]\qquad \sf \: { \dashrightarrow x = 10 \times {3} }[/tex]
[tex]\qquad \bf \: { \dashrightarrow x = 30 }[/tex]
Therefore, The number is 30.
Find two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum.
The two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16
Let the two variables be x and y
If the product of the numbers is 300, hence
xy = 300
x = 300/y ........ 1
If the sum of the first and four times the second is a minimum, then;
P(x, y) = x + 4y .................. 2
Substitute equation 1 into equation 2:
P(x, y) = x + 4y
P(y) = 300/y + 4y
If this function is at mimimum, hence dP/dy = 0
dP/dy = -300/y² + 4 = 0
-300/y² + 4 = 0
-300 + 4y² = 0
4y² = 300
y² = 300/4
y²= 75
y = 7.66
Since xy = 300
x = 300/7.66
x = 39.16
Hence the two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16
Learn more here: https://brainly.com/question/19531412
Like always, I need help :(
Answer:
The equation of the line is: x = 0
Is the Ordered Pair (6, 8) a solution to the equation y=12x+4?
True, the Ordered Pair is a solution to the equation.
False, the Ordered Pair is NOT a solution to the equation.
Answer:
The answer would be B. You solve it by substituting the x and y values in the expression, and seeing if it makes a true statement.
Step-by-step explanation:
What amount did Kayla withdraw from her account if she wrote four checks of $54.28, $675.45,
$95.22, and $76.25?
Answer:
I believe that it is $901.20
Step-by-step explanation:
I make this assumption Because when we withdraw, we take away. If Kayla wrote these for checks, you just simply add them up and you get a total of $901.20.
We aren’t sure how much she had before withdrawing this money
Which equation represents a line passing through the point (8, 33) with a slope of 3?
A. y = 3x – 15
C. y = 3x – 8
B. y = 3x + 33
D. y = 3x + 9
Answer:
Is ka answers D ha.........
Answer:
The answer is D.
Step-by-step explanation:
(8 ,33) = ([tex]x_{1} , y_{1} )[/tex]
m = 3
To find the equation, use the formula:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
Put the values in the equation
y - 33 = 3(x - 8)
y - 33 = 3x - 24
Now to get only the y, put the [tex]y_{1}[/tex]
y - 33 = 3x - 24
33 33
------------------------
y = 3x + 9
how much water should be added to 5 gallons of 50% acid solution to get a 20% solution?
ASAP!!! PLS
Answer:
22.5
Step-by-step explanation:
50%of5+20%=22.5
50/100×5=2.5
2.5+20=22.5%
Answer:
3 gallons
Step-by-step explanation:
10=100 percent
10/5 =2
5-2=3
3 gallons
Which point on the number line could represent
-2
7?
ABC D
十十一十十一十
-5 -4 -3 -2 -1 0 1 2
+
4 5
3
A
O
B
ОО
Answer:
B
Step-by-step explanation:
since the value is -2 1/4, the point must be less than -2, so it cant be C or D. Since A is less than -3, it cant be A so the point is B
Apply the distributive property to create an equivalent expression
Answer:
3e-3/2f-3/8
Step-by-step explanation:
You multiply everything in the parenthesis with 1/2. 1/2*6e=3e, 3f*1/2=3/2f, 3/4*1/2=3/8. This would be the answer.
Choose the missing step in the given solution to the
inequality -X - 10 > 14 + 2x.
_X
- 10 > 14 + 2x
-3X - 10 > 14
x<-8
0 -3x > 24
0 -3x > 4
0-3x>.
- 4
0 -3x < 24
Answer:
Step-by-step explanation:
PLS HELP! Worth 15 Points and Will give brainlest
Answer:
D
Step-by-step explanation:
What is 15.56 rounded to the nearest tenth?
Answer: 15.6
Step-by-step explanation:
In 15.56, the digit in the tenths place is the second 5. 15.56. So look at the hundredths place (6). If the digit in the hundredths place is smaller than 5, round down. If it's 5 or more, round up. 6 > 5, so we round the tenths place up by one number to get 15.6.
49-6(4x-7) pls help me.