Answer:
Below
Step-by-step explanation:
sin(2x) = 2 ×cos(x)× sin(x)
● sin(x) = 2 × cos(x) × sin(x)
● 2 × cos(x) = 1
● cos (x) = 1/2
So we can deduce that:
● x = Pi/3 + 2*k*Pi
● or x = -Pi/3 + 2*k*Pi
K is an integer
The Solution of x:
x = π/3 + 2πn, where n is an integer.
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
x = 120° + 360°n, where n is an integer.
To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.
First, let's simplify the equation using the double angle identity for sine:
sin(2x) = 2sin(x)cos(x).
Now we can rewrite the equation as:
2sin(x)cos(x) = sin(x).
2cos(x) = 1.
Dividing both sides of the equation by cos(x), we get:
2 = 1/cos(x).
Now, we can find the value of cos(x) by taking the reciprocal of both sides:
cos(x) = 1/2.
From the unit circle or trigonometric values,
we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .
So, the solutions for x are:
x = π/3 + 2πn, where n is an integer.
or
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
or
x = 120° + 360°n, where n is an integer.
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What is the surface area of the sphere below?
Hey there! I'm happy to help!
To find the surface area of a sphere, here is what you do.
You square the radius.
4²=16
You multiply by 4.
16×4=64
And you multiply by pi!
64×π=64π
Therefore, the surface area of the sphere is A. 64π units². It's that easy!
Now you can find the surface area of a sphere! Have a wonderful day! :D
Question :-
What is the surface area of the sphere that has a radius of 4 units?Answer :-
The surface area of the sphere is 64π units².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.
To calculate the surface area of the sphere, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}[/tex]
Therefore :-
The surface area of the sphere is 64π units².[tex]\\[/tex]
Learn more about the surface area of the sphere at https://brainly.com/question/28988747
Have a great day! <33
i need help. Can u help me solve for x?
Answer:
[tex] x = \sqrt {40}[/tex]
Step-by-step explanation:
Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:
[tex] {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ [/tex]
Answer:
D. x = sqrt(52).
Step-by-step explanation:
Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.
a^2 + b^2 = x^2
4^2 + 6^2 = x^2
16 + 36 = x^2
52 = x^2
x = sqrt(52)
x = sqrt(2 * 2 * 13)
x = 2sqrt(13)
x = 7.211102551.
Hope this helps!
A coin is tossed. What is the theoretical probability of the coin NOT showing tails?
P(Not tails) =
Answer:
50%
Step-by-step explanation:
its 50% it will land on head and 50% it will land on tails since there is only two sides on a coin
Answer:
1/2 or .5
p(1/2)
Step-by-step explanation:
its simple, there are 2 sides to a coin, so there are 2 possible outcomes. and the question asks what is the probability of the coin landing on one or in other wrds, its asking what is te probilitity of one of the two heads to be up. SO the probility is 1/2
f(x) = x^2. What is g(x)?
The point shown on g(x) is (1,3)
If x = 1 and y = 3, this means x is multiplied by 3 ( 1 x 3 = 3)
This makes g(x) 3x^2
The answer is A.
If a+8√5b = (8+√5)÷(8-√5) + (8-√5)÷(8+√5)
Answer:
3 or at least i think
Step-by-step explanation:
Answer:
a= 138/59 - 8√5b B=69√5/1180 - a√5/40
Step-by-step explanation:
yuh
Mia’s house and her aunt’s house are 15.4 inches apart on the map. If every 4 inches on the map represents 10 miles, what is the actual distance from Mia’s house to her aunt’s house, to the nearest tenth of a mile? 2.6 6.2 38.5 61.6
Answer:
38.5 miles
Step-by-step explanation:
Proportions:
4 inches ⇔ 10 miles
15.4 inches ⇔ M miles
M = 15.4*10/4
M = 38.5 miles
Answer: 38.5
Step-by-step explanation: cuz im smart
What is the the product of (-1 - 3i) and it’s conjugate?
Answer:
10
Step-by-step explanation:
(-1 - 3i)(-1 + 3i) = 1 - 3i + 3i -9i²
1 - 9i²; i² = -1, therefore 1 - 9(-1) = 1 + 9 = 10
a plank is 2m long and30cm wide has volume of 0.018m. what is its thickness
FORM A CUBIC POLYNOMIAL WHOSE ZEROS ARE -3,-1 AND 2
[tex](x+3)(x+1)(x-2)=\\(x^2+x+3x+3)(x-2)=\\(x^2+4x+3)(x-2)=\\x^3-2x^2+4x^2-8x+3x-6=\\x^3+2x^2-5x-6[/tex]
Erica can run 1 / 6 fraction of a kilometer in a minute. Her school is 3 / 4 of a kilometer away from her home. At this speed, how long would it take Erica to run home from school? answer quick plz
Answer:
the result is 4.5 minutes.
- Erica runs 1/6 km in a minute.
- The school is 3/1 km away from her home.
Step-by-step explanation:
th
A sum of Rs. 700 grows by 1/20 of itself every year. At what time would it amout to Rs.1050?
a) 8 years
b) 10 years
c) 12 years d) 15 years
Answer:
b) 10 yearsStep-by-step explanation:
1/20 of 700: 1/20•700 = 35
700 + n•35 = 1050
n•35 = 350
n = 10
-18 = -3x + 6 can anybody help me solve this problem
Answer:
[tex]\huge\boxed{x = 8}[/tex]
Step-by-step explanation:
[tex]\sf -18 = -3x+6\\Subtracting \ 6 \ to \ both \ sides\\-18-6 = -3x\\-24 = -3x\\Dividing \ both \ sides \ by \ -3\\8 = x\\OR\\x = 8[/tex]
Answer:
x = 8
Step-by-step explanation:
Here, -3x = -24
x = 8
hope that helps you
PLEASE HELP ME!!! I will mark brainliest!!!
The image above shows two dilated figures with lines IJ and JK drawn. If the smaller figure was dilated by a scale factor of 2, what relationship do lines IJ and KL have?
Answer:
parallel lines
Step-by-step explanation:
Lines IJ and KL are parallel. Since in a dilation there is no rotation, a line becomes either the same line or a parallel line.
SOMEBODY PLS HALP ;( According to the number line, which statement MUST be true? A) A > 1 B) B > 4 C) C < 4 D) D < 0
Answer:
B
Step-by-step explanation:
B sqrtb is right in front of 2, so 2 squared is 4, so a little bit more than 2 squared will be a little more than four.
Answer:
C) C < 4
Step-by-step explanation:
because c is on the right side of four on the number line
If the amount of VAT paid for an item at 13% was Rs 390, at what price was the item sold?
Answer:
Step-by-step explanation:
Let the price of the item = Rs x
13% of x = 390
[tex]\frac{13}{100}*x=390\\\\\\x = 390*\frac{100}{13}\\\\\\[/tex]
x = Rs. 3000
PLZ ANSWER THIS QUESTION..Plzz
Answer:
x = 2 units
Step-by-step explanation:
Diagonals of rectangle are congruent and bisect each other
Therefore, OB = OA
5x + 4 = 3x + 8
5x = 3x + 8 -4
5x = 3x + 4
5x - 3x = 4
2x = 4
x = 4/2
x =2
betty's bakery calculates the total price d in dollars for c cupcakes using the equation d=2c. What does 2 mean in this situation?
Answer:
2 means dollars per cupcake
Step-by-step explanation:
it makes sense because it says d=2c which is
money = $2 per cupcake
so if their are 2 cupcakes then
d=2*2 = $4
Cada par de numeros esta a razon de 2:3
(0,8)+(7,-52) eso es la problema
A shopkeeper allowed 10% discount on his goals
to make 20% profit If he sold a watch for
Rs.10,170 with 13 %. VAT, by what percent
is the discourt to be increased to make only
12% profit
Answer:
To make only 12% profit, the discount should be increased to 16%
Step-by-step explanation:
The given information are;
The percentage discount on goods = 10%
The profit made from the sale of the watch = 20%
The amount the watch was sold = Rs.10,710
The percentage VAT included = 13%
Let the recommended selling price of the watch = X
Therefore, we have;
The price after 10% discount = 0.9×X
Which gives;
The amount the watch was sold = Price after 10% discount + Price after 10% discount ×VAT
The amount the watch was sold = 0.9×X + 0.9×X×13% = 0.9×X + 0.9×X×0.13
Rs.10,710 = 0.9×X + 0.9×X×0.13 = 1.017×X
X = Rs.10,170/1.017 = Rs. 10,000
The recommended selling price of the watch = Rs. 10,000
The profit was 20% of selling price which gives;
Profit = Selling price - Cost price = Rs. 9,000 - Rs. X = 0.2 × Rs. X
9000 - X = 0.2×X
9000 = X + 0.2×X = 1.2×X
X = 9000/1.2 = Rs. 7,500
To make only 12% profit, we have;
12% of Rs. 7,500 = 0.12 × Rs.7,500 = Rs. 900
Selling price = Cost price + Profit = Rs. 7,500 + Rs. 900 = Rs. 8,400
Percentage discount from Rs.10,000 to get Rs. 8,400 is given as follows;
Percentage discount = Y%
Therefore;
Y = (10,000 - 8,400)/10000 × 100 = 0.16 × 100 = 16%
Y = 16%
Therefore, to make only 12% profit, the discount should be increased to 16%.
1. A cone is 8cm high and has a base diameter of 12cm.its slant height is a.6cm b.8cm c.10cm d.12cm
Answer:
10
Step-by-step explanation:
it is Pythagoras theorem
6*6=36
8*8=64
64+36=100
square root of 100 is 10
What is the quotient ? -4 /5 divide 2 A . - 1 3/5 B . -2 /5 c. 1/2 D . 1 3/ 5
Answer:
[tex] \boxed{ - \frac{2}{5} }[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}[/tex]
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}[/tex]
[tex] \mathrm{ - \frac{4}{5} \times \frac{1}{2} }[/tex]
[tex] \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}[/tex]
[tex] \mathrm{ - \frac{2}{5} }[/tex]
Hope I helped!
Best regards!
The quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
We have been given that -4 /5 divide 2
Thus, we have to divide the terms as;
-4 /5 ÷ 2
Therefore, -4 /5 x 1/ 2
-2/5
Hence, the quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
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6) By which least number should each of the following numbers be divided to make them perfect squares? b) 45125
45125|5
9025|5
1805|5
361|19
19|19
1
[tex]45125=5^3\cdot 19^2=5^2\cdot 5\cdot19^2[/tex]
It's 5
Find a linear inequality with the following solution set. Each grid line represents one unit.
Pllzzzzzzz help!!!!!!!!!!
The equation of the line is y = 3x - 4, so the inequality is y <= 3x - 4.
Answer:
y <= 3x - 4
Standard form: [tex]3x-y-4\geq 0[/tex]
Copy-paste: 3x-y-4>=0
I need help with this please.
Answer:
the slope is 60
Step-by-step explanation:
the slope is the number multiplying the x value, or t in this case.
Answer:
The slope is 60, and create the graph by dragging one point to (0,0) and one point to (1,60).
Step-by-step explanation:
If we have the proportional relationship [tex]d=60t[/tex], then the slope will be what we multiply t by to get d, therefore the slope is 60.
Since there is no y-intercept, the line WILL pass through the origin (0,0), so a point goes there.
If we make t 1, then d will be at point (1,60) because [tex]60\cdot1=60[/tex].
Hope this helped!
Maria is buying new carpet for her bedroom .Her bedroom is in the shape of a square and the length of each side is 12 feet write and simplify an exponential express to find how much carpet she needs.
Answer:
well just do area, and since it's the same in each side 12×4= 144
A plumber’s apprentice needs to cut a 54-inch length of pipe so that one piece is twice the length of the other piece. How far from the endpoint should the apprentice cut the pipe?
Answer:
18 inches
Step-by-step explanation:
To to this you would just divide 54 by 3 and you would get how far away from the endpoint which is 18 inches
Find the decimal number exactly halfway between 1.01 and 1.02.
please help
Answer:
1.015
Step-by-step explanation:
just find their average, which is adding them up and dividing by 2
(1.01 + 1.02)/2 = 1.015
The decimal number exactly halfway between 1.01 and 1.02 is 1.015.
What are decimals?A decimal numeral system is the standard system for denoting integer and non-integer numbers. The way of denoting numbers in the decimal system is often referred to as decimal notation.
The given numbers are,
1.01 and 1.02
Now to find the halfway between the number we need to find their sum first and then the half of the sum.
So, the sum of number,
1.01 + 1.02 = 1.03
Now for half way divide the sum by 2
1.03/2 = 1.015
Hence, The decimal number exactly halfway between 1.01 and 1.02 is 1.015.
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find the Perimeter Of a circle whose radius is 14cm
Answer:
Step-by-step explanation:
Firstly, we will use the formula π × d
Which will be 22\7 × 28 (this is the radius multiplied by 2)
After multiplying you will get 88 cm as your perimeter
=88 cm
In ΔABC,if a=6cm,b=5cm and c=4cm.find the value of ∠A.PLZ solve it fast plz help me out of it it's urgent
Answer:
the value of angle A is 82.819°
Jacob’s age is two years more than the sum of the ages of his siblings Becky and Micah. Which equation represents Jacob’s age? A. z = x + y − 2; x represents Micah's age, y represents Becky's age, and z represents Jacob's age B. x = y + z + 2; x represents Jacob's age, y represents Micah's age, and z represents Becky's age C. x = 2 + y + z; x represents Becky's age, y represents Jacob's age, and z represents Micah's age D. y = x + z − 2; x represents Jacob's age, y represents Becky's age, and z represents Micah's age
The equation that represents Jacob's age is x = y + z + 2
From the question, the following information was provided :
Jacob's age is two years more than the sum of the ages of his siblings Becky and Micah.
This above information can be represented with the equation below
Jacob = 2 + ( Becky + Micah) (equation 1)
If :
x represents Jacob's age
y represents Micah's age
z represents Becky's age
Equation 1, can be rewritten as x = y + z + 2
Micah's age can be determined by making Micah the subject of the formula in the above equation
Micah = Jacob - Becky - 2 (equation 2)
If :
x represents Micah's age
y represents Becky's age
z represents Jacob's age
Micah's age can be rewritten as :
x = z - y - 2
Becky's age age can be determined by making Becky the subject of the formula in the first equation.
Becky = Jacob - Micah - 2 (equation 3)
If:
x represents Becky's age
y represents Jacob's age
z represents Micah's age
Equation 3 can be rewritten as :
x = y - z - 2
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Using a system of equations, it is found that the correct equation is given by:
[tex]x = y + z + 2[/tex], which is option B.
---------------
Jacob's age is given by x.Becky's age is given by y.Micah's age is given by z.Considering that Jacob's is 2 years older than Becky's and Micah's combined, which is of y + z, his age is represented by the following equation:[tex]x = y + z + 2[/tex]
Which is given by option B.
A similar problem is given at https://brainly.com/question/24233433
