The option that applies to 2cos(x)+sqrt2=0 less than x less than 2pi is options C and D:
c.5pi/4
d.7pi/4
What is the solution about?To solve this equation, we can start by isolating the cosine term on one side of the equation:
[tex]2cos(x) = -\sqrt{2[/tex]
[tex]cos(x) = \sqrt{\frac{2}{2} } }[/tex]
The cosine function has a range of [-1, 1], so the only possible value for cos(x) is -sqrt(2)/2. This means that the only solution to the equation is x = acos(-sqrt(2)/2).
The inverse cosine function, denoted as "arccos," gives us the angle whose cosine is a given value. In this case, we want to find the angle whose cosine is -sqrt(2)/2. The domain of the arccos function is [-1, 1], so the range of the function is [0, pi]. This means that the solution x must be an angle in the range [0, pi].
Since the problem specifies that the solution must be in the range [0, 2pi], we need to consider all possible angles in that range that satisfy the equation. This means that the possible solutions are:
[tex]x = acos(-\sqrt (2)/2) + 2\pi *k[/tex]
where k is an integer.
Substituting the values from the given choices into this equation, we find that the possible solutions are:
[tex]a. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 0 = \pi /4 + 0 = \pi /4\\b. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 1 = \pi /4 + 2\pi = 3\pi /4\\c. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 2 = \pi /4 + 4\pi = 5\pi /4\\d. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 3 = \pi /4 + 6\pi = 7\pi /4[/tex]
Therefore, the correct answer is c. and d.
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Answer:
b.3pi/4
c.5pi/4
Step-by-step explanation:
if x = -6 then -x 2 =
- (-6) 2 =
Answer:
12
Step-by-step explanation:
negative times a negative equals a positive.
so, 6 times 2 is 12.
Answer: 12
Step-by-step explanation:
Negative number multiplied by negative numbers get you to positive numbers so 6x2 is going to get you to 12. I think someone said this before me but here you go!
the length and the breadth of a rectangular Garden are 0.8 km and 0.6 km respectively find the length of a wire required to put a fivefold fans around the garden
Answer:
Length of wire required for 5 fold of garden = 14 km
Step-by-step explanation:
Given:
Length of rectangle garden = 0.8 km
Width of rectangle garden = 0.6 km
Find:
Length of wire required for 5 fold of garden
Computation:
Perimeter of rectangle = 2[l + b]
Perimeter of garden = 2[0.8 + 0.6]
Perimeter of garden = 2[1.4]
Perimeter of garden = 2.8 km
Length of wire required for 5 fold of garden = 5 x Perimeter of garden
Length of wire required for 5 fold of garden = 5 x 2.8
Length of wire required for 5 fold of garden = 14 km
What is the equation of the following line?
Answer:
E
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
slope = rise / run = 7 / 1 = 7
m = 7
y-intercept = 0
So:
y = 7x + 0
y = 7x
A sealed room in a hospital, measuring 5m wide, 10m long, and 3m high, is filled with pure oxygen.
One cubic meter volume of oxygen contains 1000L gas, and 22.4L of oxygen gas contains
6.02 x 1023 molecules (Avogadro's number).
A. 2.1976 x 100 molecules
B. 3.0051 x 1026 molecules
C. 4.0313 x 1027 molecules
D. 7.5014 x 1030 molecules
Answer:
Option C. 4.0313×10²⁷ molecules.
Step-by-step explanation:
We'll begin by calculating the volume of oxygen in the room. This can be obtained by calculating the volume of the room since the gas will eventually fill the room.
Width (W) = 5 m
Length (L) = 10 m
Height (H) = 3 m
Volume (V) =?
V = L × W × H
V = 10 × 5 × 3
V = 150 m³
Thus, the volume of oxygen is 150 m³
Next, we shall convert 150 m³ to L. This can be obtained as follow:
1 m³ = 1000 L
Therefore,
150 m³ = 150 m³ × 1000 L / 1 m³
150 m³ = 150000 L
Finally, we shall determine the number of molecules of oxygen in the room. This can be obtained as follow:
22.4 L = 6.02×10²³ molecules
Therefore,
150000 L = 150000 × 6.02×10²³ / 22.4
150000 L = 4.0313×10²⁷ molecules
Thus, the number of molecules of oxygen in the room is 4.0313×10²⁷ molecules
Answer it right and i'll try to give you brainliest.
Answer:
384 cm²
Step-by-step explanation:
Since it is a square pyramid, the total surface area of the pyramid is the area of its square base plus the area of its 4 triangular faces.
[tex]\boxed{area \: of \: triangle = \frac{1}{2} \times base \times height }[/tex]
Area of a triangular face
= ½ ×12 ×10
= 60 cm²
[tex]\boxed{area \: of \: square = side \times side}[/tex]
Base area of pyramid
= 12 ×12
= 144 cm²
∴ Surface area of pyramid
= 4(60) +144
= 240 +144
= 384 cm²
This jar has 1 red, 74 yellow, and 25 green gumballs. What are the chances of picking a green gumball? the red one?
Answer: green = 25/100, red = 1/100
Step-by-step explanation: add ALL of the gumballs, there's your denominator, now you have 0/100 (1+74+25), count the amount of marbles you want to get the probability of, lets say green, there's your numerator (25) = 25/100
what would the circumference be of a circle if the radius is 14
Josephine owns a dress shop and purchases a dress for $20. She decides to mark up the dress 35% in order to sell it to her customers. What is the amount of profit Josephine will make when she sells a dress to a customer? o Josephine will make a profit of $35 O Josephine will make a profit of $27 O Josephine will make a profit of $10 O Josephine will make a profit of $7
Answer:
Josephine will have $15 profit
pls help I'm actually confused I've been trying to solve for over an hour.
( there both there own question but the 1st one you also need to solve the second)
Answer:
This is the famous "Ice cream cone" problem. notice that if you turn the object 90° counter clock wise , it looks like an ice cream cone. anyway
Step-by-step explanation:
the two triangles on the pointy end make a box , if you put them together, so it's a box of 4 x 11 or 44 [tex]in^{2}[/tex].
then the actual box part in the middle it's 3 x 8 or 24 [tex]in^{2}[/tex].
and finaly the ice cream :P or the round part. well half round part.
it's half of a circle..(we don't really know if the arc is really a circle from the problem but I'm guessing that we are supposed to assume that it is ) and the area of a circle is [tex]\pi[/tex][tex]r^{2}[/tex]
then [tex]\pi[/tex]*[tex]4^{2}[/tex] = 50.2655 which is the entire circle but we only have half.. so divide by 2 = 25.1327 [tex]in^{2}[/tex].
add the 3 parts
93.1327 [tex]in^{2}[/tex].
that's the total area of the "ice cream cone"
now just multiply by 3.1 to find the cost of the flooring
$ 288.71
Hope that helps :)
Is this a function? please explain if possible.
Answer:
Yes, it is a function.
Step-by-step explanation:
A function is a relation where each x-value (input value) has exactly one y-value (output value) that is related to it or mapped to it. In order words, in a function, an input value can only have one output value.
Thus, the relation represented by the table of values above is a function because every x-value (input value) has exactly one y-value (output value).
Evaluate x2 + 6, when x=8
Help.
Its says in question 4 tue horizontal translation is A right.?
Answer:
Here we have:
g(x) = 3*f( 2*x - 2) - 1
We want to know the horizontal translation used here.
We need to discuss two types of transformations here.
horizontal translation.
If we have a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N is negative, the translation is to the right.
if N is positive, the translation is to the left.
Horizontal dilation.
For a function f(x) an horizontal dilation of scale factor k is written as:
g(x) = f( x/k)
You can see that in our function we have both of these transformations.
Because we compare the translation with f(x), we assume that the horizontal translation is the first thing we did, then we must have
translation:
g(x) = f(x + N)
and now a horizontal dilation of scale factor k
g(x) = f( (x + N)/k)
Then we must have that the argument of the above function is the same as the argument of the given function.
(x + N)/k = 2*x - 2
then:
k = 1/2
(x + N)/1/2 = 2*x + 2*N = 2*x - 2
2*N = -2
N = -2/2 = -1
This means that we have a translation of 1 unit to the right.
which graph represents the function f(x) = 4|x|?
the answer to your question is B / the second graph
Answer:
the 2nd one(the steep one thats in the middle of top row)
Step-by-step explanation:
it transformed the function with a vertical stretch of 4
how do you graph the inequality of x<-3
NO LINKS I WILL REPORT YOU
Answer:
The graph is all of the plane on and to the right of the vertical line whose equation is x=-3. Take two points whose x-coordinates are -3, say (-3,-3), and (-3,3), connect with a straight line.
Step-by-step explanation:
10 points is all i have. PLEASE HELP!!
Answer:
Step-by-step explanation:
Answer:
Look Below
Step-by-step explanation:
2. X - 5 = -2 / X = 3
3. 2X = 10 / X = 5
4. 5X + 10 = 10 / X = 0
If you find any fault in my answers please let me know! Thanks! Have a good day! Hope this helps!
2
15% of a number is 54. What is of that number?
Answer:36
Step-by-step explanation:
Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy?
Which equation BEST represents this situation?
Answer: Miranda can buy 18 dolls.
Step-by-step explanation: Equation: 45 divided by 2.50
What is the circumference of the circle with a radius of 3.22 Round to the nearest tenth.
I need help with this equation!!
Answer:
6,4
Step-by-step explanation:
Answer:
6 and 4
Step-by-step explanation:
So for the pattern, on the left side it's going up 2. And on the right side it's going down 2.
Hopefully this helps
Find the value of the variable:
Answer:
∠v = 76°
Step-by-step explanation:
since it is an isosceles triangle, both angles at the top of the picture are 52°.
∠v = 180° - 52° - 52° = 76°
the larger of two numbers is twice the smaller. if the larger is x what is the smalller. I NEED HELP PLSSS!!
Answer:
Easy. The smaller is x/2.
Step-by-step explanation:
2 times is larger, so larger divided by 2 is the smaller.
Find the area of the polygon to the nearest square inch.
Answer: 70
Step-by-step explanation:
Find the volume of the cylinder. Round your answer to the nearest tenth.
3ft.
10 ft.
Enter only the numerical value with the units of measure.
⚠️⚠️HELP PLEASE DUE BY MIDNIGHT⚠️⚠️
*explain if you can*
Write two different quadratic equations to represent the function with a vertex of (3,-5).
what is the value of log39?
Find the indicated side of the
right triangle
60°
7
30°
х
X=
= [?] )
The value of x is 14 units.
Trigonometry valuesWhen handling and dealing with difficulties involving the measurement of length and angles of a right-angled triangle, trigonometric values of ratios such as sine, cos, tan, cosec, cot, and secant come in handy. The trigonometric function is widely used to solve trigonometric issues at 0°, 30°, 45°, 60°, and 90°.
How to determine value of x?We know for angle of 30° the base is 7 and perpendicular is x
then
sin30° = 7/x
[tex]\frac{1}{2} =\frac{7}{x}[/tex]
x = 7
hence, the value of x = 14 units
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Solve the following inequality.
PLEASE HELP ASAP
Kelly had an apple. She cut it in half, and then she cut it in half again.
She ate three pieces of the apple. How many pieces did Kelly have left?
Answer:
1
Step-by-step explanation:
Answer:
kelly had only 1 piece left
Step-by-step explanation:
she cut it in half she got 2 pieces , when she cut it again in half she got 2 more . she then ate 3 pieces and 1 got left.
total piece= 4
eaten =3
left = 1
What is the product?
Answer:
it is B
Step-by-step explanation:
Brainliest or
5 stars and 1 heart or both if your realy kind
PS correct me if im wrong on the answer
Which function has a greater rate of change?
pls help me lol