Answer:
Step-by-step explanation:
its 1
The given function f(x) = (1/4)ˣ, the initial value of the function when x is substituted in the function is , 1
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
Graph of function f(x) = (1/4)ˣ
when value of x is substituted in given function,
f(0) = (1/4)⁰
f(0) = 1
So, the initial value of the function is 1
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Which statements are true about surface area and volume? Check all that apply.
******************************************************************************************************
Volume is labeled with cubic units.
Surface area is labeled with cubic units.
Volume of a prism is the product of the area of the base and height.
Surface area is the sum of the areas of each side.
The volume of a prism is One-third the volume of a pyramid.
Answer:
1. True
2. False
3. True
4. True
5. False
Step-by-step explanation:
1. Volume is labeled in cubic units, as it is the multiplication of 3 dimensions
2. Surface area is only labeled in square units, not cubic units, it is area after all, and that is the multiplication of 2 dimensions
3. The volume of many figures in general is through multiplication of base and height. Though there are exeptions, the Volume of a Prism is computed through base and height multiplication
4. Yes, surface area is the sum of the areas of the sides of a 3-dimensional figure
5. Actually it is the volume of a pyramid that is One-third the volume of a prism, not the other way around
The statements 1,3 and 4 are true.
What is surface area?
Surface area is explained as the sum of the areas of all the closed surfaces of a solid. The surface of any area is the region occupied by the surface of an object.
What is volume?Volume is the amount of space available in an object. It is the space enclosed by a boundary or occupied by an object or the capacity to hold something.
For the given situation,
There are several statements, we need to check which statements are true.
Statement 1: Volume is labeled with cubic units.
Volume is the measure of three dimensional space. So volume should be labeled in cubic units.
Thus, statement 1 is true.
Statement 2: Surface area is labeled with cubic units.
Surface area is the total area of the faces of a three-dimensional shape. Surface area is labelled in square units.
Thus, statement 2 if false.
Statement 3: Volume of a prism is the product of the area of the base and height.
The volume of the prism is defined as the product of the area of the base and the length (height).
Thus, statement 3 is true.
Statement 4: Surface area is the sum of the areas of each side.
The surface area of a three-dimensional object is the total area of all its faces.
Thus, statement 4 is true.
Statement 5: The volume of a prism is One-third the volume of a pyramid.
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The volume of a pyramid is found using the formula V = (1/3) Bh, where B is the base area and 'h' is the height of the pyramid.
Thus, statement is false.
Hence we can conclude that the statements 1,3 and 4 are true.
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Which fractions are equivalent to 4/9?
Answer:
[tex] \frac{8}{18} [/tex]
Step-by-step explanation:
[tex] \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} \\ [/tex]
Answer:
8/18, 12/27, 16/36, 20/45
The angles of a quadrilateral, taken in order, are x, 5x, 4x and
2x Find these angles. Draw a rough sketch of the
quadrilateral What kind of quadrilateral is it?
Answer:
Convex or trapezium quadrilateral?
Step-by-step explanation:
All the angles are,
⇒ x = 30
⇒ 5x = 150
⇒ 4x = 120
⇒ 2x = 60
Therefore, The quadrilateral is a Trapezoid.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
The angles of a quadrilateral, taken in order, are x, 5x, 4x and 2x.
Since, We know that;
Sum of all angles of the quadrilateral are 360 degree.
Hence, We get;
⇒ x + 5x + 4x + 2x = 360
⇒ 12x = 360
⇒ x = 30
Thus, All the angles are,
⇒ x = 30
⇒ 5x = 5 × 30 = 150
⇒ 4x = 4 × 30 = 120
⇒ 2x = 2 × 30 = 60
Therefore, The quadrilateral is a Trapezoid.
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A circle has a sector with area 1/2pi and central angle of 1/9pi radians what is the area of the circle?
Answer:
Step-by-step explanation:
It’s daddy
Is flipping 2 coins dependent?
Answer:
No
Step-by-step explanation:
Flipping two coins is independent because the outcome of the first coin doesn't affect the outcome of the second coin. There is still a 1/2 chance of of getting heads or tails.
If this answer is correct, please make me Brainliest!
The area of each triangular base is: A = 1/2(b)(h) A = 1/2(4)(3) A = in.2 There are two bases, so total base area is in.2. The lateral area is: A = 8(4) + 8(3) + 8(5) A = in.2 The total surface area is in.2.
Answer:
6 in^2
12 in^2
96 in^2
AT = 108 in^2
Step-by-step explanation:
The area of one triangular face is
A1 = 1/2(4)(3) = 6 in^2
The area of the two triangular faces is:
A = 2A1 = 12 in^2
the area of the lateral faces is:
Al = 8(4) + 8(3) + 8(5) = 96 in^2
Hence, the total surface area is
AT = At + Al = 12 in^2 + 96 in^2 = 108 in^2
6
12
96
108
hope this helped <3
A skateboard’s wheel has a radius of 55 millimeters. What is the area of the wheel ?
Answer:
Step-by-step explanation:
[tex]A=\pi r^2=\pi *55^2[/tex] ≈ [tex]9503.31778mm^2[/tex]
Answer:
3025π
Step-by-step explanation:
A skateboard’s wheel is a circle and we need to work out the area of the skateboard’s wheel so we have utilise the formula π × r² where 'r' is the radius. So lets substitute in the values into the formula of finding out the area of the skateboard's wheel.
Area of skateboard's wheel = π × r²
→ Substitute in the values
Area of skateboard's wheel = π × 55²
→ Simplify
Area of skateboard's wheel = 3025π
Seven cups of yogurt cost $3.50. How much does one cup of yogurt cost?
Answer:
50 cents each
Step-by-step explanation:
3.50/7 = .50
Answer:
Each cup costs $0.50
Step-by-step explanation:
Take the total cost and divide by the number of cups
3.50/7 = .50
Each cup costs $0.50
How do I rewrite expressions as a power of 2!!!!
Final answer:
To rewrite expressions as a power of 2, one needs to understand exponent rules and binary representation. Squaring exponentials involves squaring the base and multiplying the exponent by 2. Simplification often involves adjusting prefactors and exponents while keeping the expression equivalent.
Explanation:
To rewrite expressions as a power of 2, it's important to understand how to manipulate exponents and to be familiar with the binary representation of numbers. For instance, squaring exponentials involves squaring the base number and multiplying the exponent by 2. As an example, if you have (23)4, it is the same as 23×4 or 212.
When dealing with decimal equivalents of powers of two, such as 1837, which can be written as (1 × 1024) + (1 × 512) + (1 × 256) + (0 × 128) + (0 × 64) + (1 × 32) + (0 × 16) + (1 × 8) + (1 × 4) + (0 × 2) + (1×1), the expression is already in powers of two. Similarly, recognizing patterns can help simplify expressions, for example, 24 × 1012 can be simplified by adjusting the prefactor and exponent to maintain equivalence.
Finally, powers are applied to everything inside parentheses. For instance, (27×3) and (4×22) becomes 2.1 × 10-33 when raised to the proper power.
Cuál es el área de superficie de una esfera con un diámetro de 10 mm ? Redondea al número entero más próximo
Step-by-step explanation:
¡Hola a todos!
Usa la fórmula para una esfera:
[tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} \pi (125)\\V=523.59877 mm^3[/tex]
No soy un hablante nativo de español, así que esto puede ser un poco confuso, ¡pero espero que ayude!
:)
What is the permutation of the word cheese
Answer:
120 Ways
Step-by-step explanation:
The permutation of the word 'cheese' considers the unique arrangements of its letters. Since 'e' repeats thrice, the permutations are calculated using the formula for a multiset, resulting in 120 unique permutations.
Explanation:The term 'permutation' typically refers to the possible arrangements of a set of items when the order of these items is important. In the context of English and the word 'cheese,' permutation would normally mean all the distinct arrangements of the letters in the word. However, since the letters 'e' and 'c' repeat in the word 'cheese,' the number of unique permutations is less than it would be if all the letters were different.
To calculate the permutations of 'cheese' specifically, we would have to account for these repeated letters. With six letters total and the letter 'e' appearing three times, we would use the formula for permutations of a multiset: 6! / (3! 1! 1! 1!), where the factorials represent the number of times each distinct letter occurs.
Steps to Calculate Permutations of 'Cheese'Count the total number of letters in 'cheese,' which is 6.Count the occurrence of each unique letter: 'c' = 1, 'h' = 1, 'e' = 3, 's' = 1.Apply the permutation formula for a multiset: 6! / 3!.Calculate: 6! is 720, and 3! is 6. So, the number of permutations is 720 / 6.The result is that there are 120 unique permutations for the word 'cheese.'Which shows all the exact solutions of sin^2x+3cosx-1=2? Give your answer in radians.
•0
•2pi
•2kpi
•pi+2kpi
Answer:
On edg it's 2kpi
Step-by-step explanation:
i took the test
The exact solution of the equation will be;
⇒ x = 2kπ
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ sin²x + 3cos x - 1 = 2
Now,
Since, The equation is,
⇒ sin²x + 3cos x - 1 = 2
We know that;
⇒ sin²x = 1 - cos²x
Substitute above value in equation (i), we get;
⇒ 1 - cos²x + 3cos x - 1 = 2
⇒ cos²x - 3 cos x + 2 = 0
⇒ cos²x - (2 + 1)cos x + 2 = 0
⇒ cos²x - 2cos x - cos x + 2 = 0
⇒ cos x (cos x - 2) - 1 (cos x - 2) = 0
⇒ (cos x - 2) (cos x - 1) = 0
This gives two solution,
⇒ cos x = 2
But it is not possible because the value of cos x is in between - 1 and 1.
⇒ cos x = 1
⇒ x = 2kπ + 0°
⇒ x = 2kπ
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The graph given above shows the following function.
What is the period of the function?
The amplitude of the cosine function "y = cos(x)" is 1. Therefore, the correct answer is "d. 1", as it represents the maximum absolute value of the function.
The function "y = cos(x)" represents a cosine function, and its amplitude is the maximum absolute value of the function. The amplitude of the cosine function "cos(x)" is 1. This is because the cosine function oscillates between -1 and 1, and the amplitude is the absolute value of this maximum value.
In mathematical terms, the amplitude (A) of a cosine function "A cos(x)" is equal to the absolute value of the coefficient of the cosine term. In this case, "A = |1| = 1".
Therefore, among the given options:
a. 2
b. π
c. 2π
d. 1
The correct answer is "d. 1" as it accurately reflects the amplitude of the cosine function "y = cos(x)".
The question probable may be:
The graph given above shows the following function y= cos(x)
What is the amplitude of the function?
a. 2
b. pi
c. 2pi
d. 1
PLEASE ANSWER IF YOU CAN!!
A holiday decoration is a construction from two square pyramids that are joined together at their bases. The edge of each square is 4.5 inches. The slant height of the triangular faces is 7 inches. What is the surface area of the decoration?
The surface area of the decoration is 126 inches².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
We have that, the holiday decoration is a construction from two square pyramids that are joined together at their bases.
Total surface area of a square pyramid = Area of the square + Area of 4 triangular faces
But total surface area of the decoration does not contain the area of the square base as it is joined together.
So surface area of the decoration = Area of 8 triangular faces
= 8 × ([tex]\frac{1}{2}[/tex] a l)
Here a is the length of the edge of the square and l is the slant height of the triangle.
Surface area = 4 a l
= 4 × 4.5 × 7
= 126 inches²
Hence the surface area of the decoration is 126 inches².
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To find the surface area of the holiday decoration, calculate the sum of the areas of the two square pyramids. Use the formula Surface Area = Base Area + 2 * (0.5 * Base Perimeter * Slant Height) and substitute the given values to find the surface area. The surface area of the decoration is 146.25 square inches.
To find the surface area of the holiday decoration, you need to find the sum of the areas of the two square pyramids. The formula for the surface area of a square pyramid is given by:
Surface Area = Base Area + 2 * (0.5 * Base Perimeter * Slant Height)
Since the base is a square, the base area is equal to the side length squared. Therefore, the base area is 4.5 inches * 4.5 inches = 20.25 square inches.
The base perimeter is equal to 4 times the length of one side. Therefore, the base perimeter is 4 * 4.5 inches = 18 inches.
Plugging these values into the formula, we have Surface Area = 20.25 square inches + 2 * (0.5 * 18 inches * 7 inches).
Simplifying the expression, we get Surface Area = 20.25 square inches + 2 * 63 square inches = 146.25 square inches.
i don’t understand how to solve this (geometry)
Answer:
29.9
Step-by-step explanation:
Last week, Kip went to the fair. It costs $3.50 to enter the fair and $0.75 per ticket. In the equation below, x represents the number of tickets Kip bought, and y represents the total amount Kip spent.
y = $0.75x + $3.50
If Kip spent $15.50 at the fair, how many tickets did he buy?
Answer:
16 tickets
Step-by-step explanation:
15.50-3.50=12
12/0.75=16
Rewrite the equation by completing the square.
x² + 8x + 12 =10
Answer:
(x +4)^2 = 14
Step-by-step explanation:
The constant on the left wants to be the square of half the coefficient of the linear term:
(8/2)^2 = 16
In order for it to be that value, we need to add 4 to the equation.
x^2 +8x +12 +4 = 10 +4
x^2 +8x +16 = 14 . . . . collect terms
(x +4)^2 = 14 . . . . . . . write as a square
Answer:
(x+4)² - 14 =0
Step-by-step explanation:
x² + 8x + 12 =10
(x²+4²) - 4²+12 = 10
(x+4)² -4-10 = 0
(x+4)² - 14 =0
Note: When completing squares, in the equation above.
We square the half of 8.We add the result to x² , and subtract it with 12.A rectangular container that has a length of 30 cm, a width of 20 cm, and a height of 24 cm is filled with water to a depth of 15 cm.How many more mL of water could be added to the container before it overflows?
Answer:
[tex]5400cm^{3}[/tex] more water could be added to the container before the container overflows
Step-by-step explanation:
The volume of the rectangular container is got by multiplying its given dimensions: Length X breadth X height
This will be 30 X 20 X 24 = [tex]14400 cm^{3}[/tex]
To find the volume of water inside the rectangular container, we will use the new height for our computation of volumes, keeping the length and breadth of the cylinder the same.
This will be [tex]30 \times 20 \times 15 =9000 cm^{3}[/tex]
The volume of water needed to be added until the container overflows will be got by subtracting the volume of water present in the container from the total volume of the container
[tex]14400 - 9000 =5400cm^{3}[/tex]
Note 1 [tex]cm^{3}= 1 ml[/tex]
Question 5 (1 point)
Administrators surveyed students enrolled in a new school in order to choose the school mascot. There are 480 students enrolled in the
school. What is the proportion needed to calculate the average number of students that chose the lion for the mascot?
A. 20/22 = x/480
B. 21/72 = x/480
C. 72/21 = x/480
D. 42/72 = x/480
Answer:
Step-by-step explanation:
answers A jus did itt
Answer: A. yo is welcome bro
Step-by-step explanation:
Perimeter of an isosceles triangle is 90 m. If the length of the two equal sides is three fourth of the unequal side , find the dimensions of the triangle
Answer:
The length of the equal side is 27 meters each and that of the unequal side is 36 meters
Step-by-step explanation:
An isosceles triangle is a triangle with two sides being equal (also two equal base angles).
Let us assume the length of the two equal sides to be x meters each, and the length of the unequal side to be y meter. Since the perimeter of the triangle is 90 m, it can be expressed as:
x + x + y = 90
2x + y = 90
But the length of the equal side is three fourth of the unequal side, i.e x = 3/4y
Therefore:
2(3/4y) + y = 90
3/2y + y = 90
2.5y = 90
y = 90/2.5
y = 36 meters
Also x = 3/4 * 36 = 27 meters
The length of the equal side is 27 meters each and that of the unequal side is 36 meters
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
The arc length is a quarter of the circumference of the full circle, so 2πr/4.
The straight sides are both radii, so each length r.
Total perimeter
p = 2πr/4 + r + r = r(π/2 + 2)
We put in r=2, π=3.14 and get
p = (2(3.14/2 + 2)) = 3.14 + 4 = 7.14
Answer: 7.14 km
The perimeter is also known as the circumference. The formula for the circumference is C = pi x diameter.
Step 1) Find the diameter
d = r x 2
d = 2 x 2 = 4 km
Step 2) Find the whole circumference
C = pi x 4
C = 4pi km
Step 3) Find 1/4 of the circumference
4pi x 1/4 = 1pi
1pi = 3.14
Step 4) Add the sides not part of the arc
3.14 + 2 + 2 = 7.14
C = 7.14 km
Hope this helps! :)
What is the slope of a line parallel to the line whose equation is 5x – y = –9. Fully
reduce your answer.
Answer: y= 5x+9
Step-by-step explanation: you subtract the 5x from both sides where it becomes a negative. then you divide everything by -1 and you come out with y=5x+9
The slope is:
⇨ 5Work/explanation:
This equation is almost in perfect slope intercept. Let's rearrange it just a little.
[tex]\sf{5x+y=-9}[/tex]
[tex]\sf{-y=-5x-9}[/tex]
[tex]\sf{y=5x+9}[/tex]
Now, parallel lines have equal slopes. This means that whatever the slope of line A is, the slope of line B will be the same, if lines A and B are parallel.
The slope of [tex]\sf{y=5x+9}[/tex] is 5.
So the slope of the line parallel to it is 5.Extra info
Slope intercept is y = mx + b where the slope is m and the y-intercept is b.
h(x) = -(x + 1)(x - 7)
What is the maximum height that the ball will reach?
Answer:
16
Step-by-step explanation:
All we have to do is write this in vertex form of a quadratic. It is now in factored form. To get it into vertex form we must complete various steps. Here you can skip it using desmos graphing calculator:
Answer: 16 units.
Step-by-step explanation:
To find the vertex, first simplify the quadratic equation into its standard form:
[tex]h(x)=-(x+1)(x-7)\\h(x)=(-x-1)(x-7)\\h(x)=-x^2+6x+7\\[/tex]
Using this formula, we can then find the axis of symmetry by using the formula S = -b/2a:
[tex]S=\frac{-6}{-2}[/tex]
The axis of symmetry lies on x = 3.
You can then substitute x for 3 in the equation to find the vertex of the parabola:
[tex]h(3)=-9+18+7\\h(3)=16[/tex]
The ball will be 16 units high after travelling 3 units horizontally. This is the maximum height the ball will reach before falling.
What is the perimeter of the triangle
Answer:
I think its 46...
Step-by-step explanation:
Answer:
the answer is 40
Step-by-step explanation:
15+8+17=40
Gavin is building a dresser. He built drawers that all have a volume of of a cubic foot. The expression below represents the total volume of all the drawers in the dresser if there are b drawers across, and c drawers high. If the dresser is 6 drawers high and 3 drawers wide, what is the total volume of all the drawers in the dresser?
The total volume of all the drawers in the dresser, which has 6 drawers high and 3 drawers wide, is found by multiplying these two values. Therefore, the total volume of all the drawers in the dresser is 18 cubic feet.
Explanation:This problem involves the calculation of volume in a real-world context. We know that each drawer has a volume of 1 cubic foot, and the total volume of all the drawers can be obtained by multiplying the number of drawers across (width) by the number of drawers high (height). From the question, we know the dresser is 6 drawers high and 3 drawers wide. Therefore, the total volume is obtained by multiplying 6 (height) by 3 (width), which yields 18 cubic feet. Hence, the total volume of all the drawers in the dresser is 18 cubic feet.
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Use the interactive graph to plot each set of points. Which sets represent proportional relationships? Check all that apply. A.(1, 4), (3, 8), (5, 9) B.(3, 2), (6, 4), (9, 6) C.(2, 2), (4, 4), (6, 6) D.(1, 3), (2, 7), (3, 8) E.(0, 0), (1, 2), (2, 4), (4, 8)
The sets that represent proportional relationships are: B, C, and E.
Here's how we can determine which sets of points represent proportional relationships:
Set A:
Plot the points (1, 4), (3, 8), and (5, 9) on the graph.
Calculate the ratio of y to x for each point:
(4/1) = 4
(8/3) = (8/3)
(9/5) = (9/5)
As you can see, the ratios are not the same. Therefore, set A does not represent a proportional relationship.
Set B: (attachment 1)
Plot the points (3, 2), (6, 4), and (9, 6) on the graph.
Calculate the ratio of y to x for each point:
(2/3) = (2/3)
(4/6) = (2/3)
(6/9) = (2/3)
In this case, the ratios are all the same, which is 2/3. Therefore, set B represents a proportional relationship.
Set C: (attachment 2)
Plot the points (2, 2), (4, 4), and (6, 6) on the graph.
Calculate the ratio of y to x for each point:
(2/2) = 1
(4/4) = 1
(6/6) = 1
All the ratios are equal to 1. Therefore, set C represents a proportional relationship.
Set D:
Plot the points (1, 3), (2, 7), and (3, 8) on the graph.
Calculate the ratio of y to x for each point:
(3/1) = 3
(7/2) = (7/2)
(8/3) = (8/3)
The ratios are not the same. Therefore, set D does not represent a proportional relationship.
Set E: (attachment 3)
Plot the points (0, 0), (1, 2), (2, 4), and (4, 8) on the graph.
Calculate the ratio of y to x for each point:
(0/0) = undefined (division by zero)
(2/1) = 2
(4/2) = 2
(8/4) = 2
Ignoring the undefined ratio at (0, 0), we see that the ratios are all equal to 2. Therefore, set E represents a proportional relationship.
Complete and correct question:
Use the interactive graph to plot each set of points. Which sets represent proportional relationships? Check all that apply.
A.(1, 4), (3, 8), (5, 9)
B.(3, 2), (6, 4), (9, 6)
C.(2, 2), (4, 4), (6, 6)
D.(1, 3), (2, 7), (3, 8)
E.(0, 0), (1, 2), (2, 4), (4, 8)
Which of these four sets of side lengths will form a right triangle?
Set 1
6 cm, 7 cm, StartRoot 12 EndRoot cm
Set 2
8 in., StartRoot 29 EndRoot in., StartRoot 35 EndRoot in.
Set 3
StartRoot 3 EndRoot mm, 4 mm, StartRoot 5 EndRoot mm
Set 4
9 ft, StartRoot 26 EndRoot ft, 6 ft
Only Set 3 forms a right triangle as it satisfies the Pythagorean theorem, with side lengths matching the equation (√3)^2 + 4^2 = (√5)^2.
The question is about determining which set of side lengths will form a right triangle. To form a right triangle, the side lengths must satisfy the Pythagorean theorem, where the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).
Let's check each set of side lengths:
Set 1: 62 + 72
eq (√12)2 (Not a right triangle)
Set 2: 82 + (√29)2
eq (√35)2 (Not a right triangle)
Set 3: (√3)2 + 42 = (√5)2 (Right triangle)
Set 4: 92 + (√26)2
eq 62 (Not a right triangle)
Therefore, only Set 3 forms a right triangle because it is the only set that satisfies the Pythagorean theorem.
If sin theta= 12/13 and θ is in quadrant II, cos 2 theta= and cos theta = .
Answer:
cos2θ = -0.7041
Cos θ = -0.3847
Step-by-step explanation:
Firstly, we should understand that since θ is in quadrant 2, the value of our cosine will be negative. Only the sine is positive in quadrant 2.
Now the sine of an angle refers to the ratio of the opposite to the adjacent. And since there are three sides to a triangle, we need to find the third side which is the adjacent so that we will be able to evaluate the cosine of the angle.
What to use here is the Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the adjacent and the opposite.
Since Sine = opposite/hypotenuse, this means that the opposite is 12 and the hypnotist 13
Thus the adjacent let’s say d can be calculated as follows
13^2 = 12^2 + d^2
169 = 144 + d^2
d^2 = 169-144
d^2 = 25
d = √25 = ±5
Since we are on the second quadrant, the value of our adjacent is -5 since the x-coordinate on the second quadrant is negative.(negative x - axis)
The value of cos θ = Adjacent/hypotenuse = -5/13
Cos θ = -5/13
Cos θ = -0.3846
Using trigonometric formulas;
Cos 2θ = cos (θ + θ) = cos θ cos θ - sin θ sin
θ = cos^2 θ - sin^2 θ
Cos 2θ = (-5/13)^2 - (12/13)^2
Cos 2θ = 25/169 - 144/169
Cos 2θ = (25-144)/169 = -119/169
Cos 2θ = -0.7041
There are four quadrants in a coordinate geometry.
The cosine values are [tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex] and [tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]
The given parameter is:
[tex]\mathbf{sin(\theta) = \frac{12}{13}}[/tex]
Using trigonometry ratio, we have:
[tex]\mathbf{sin^2(\theta) + cos^2(\theta)= 1}[/tex]
Substitute [tex]\mathbf{sin(\theta) = \frac{12}{13}}[/tex]
[tex]\mathbf{(\frac{12}{13})^2 + cos^2(\theta)= 1}[/tex]
Expand
[tex]\mathbf{\frac{144}{169} + cos^2(\theta)= 1}[/tex]
Collect like terms
[tex]\mathbf{ cos^2(\theta)= 1-\frac{144}{169}}[/tex]
Evaluate fraction
[tex]\mathbf{ cos^2(\theta)= \frac{25}{169}}[/tex]
Take square roots of both sides
[tex]\mathbf{ cos(\theta)= \pm \frac{5}{13}}[/tex]
The angle is in the second quadrant.
So, we have:
[tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex]
Also, we have:
[tex]\mathbf{ cos(2\theta) = cos^2(\theta) - sin^2(\theta)}[/tex]
So, the equation becomes
[tex]\mathbf{ cos(2\theta) = \frac{25}{169} - \frac{144}{169}}[/tex]
Take LCM
[tex]\mathbf{ cos(2\theta) = \frac{25-144}{169}}[/tex]
[tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]
Hence, the values are:
[tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex] and [tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]
Read more about quadrants at:
https://brainly.com/question/7196054
jim says that the output of the floor function is the number before the decimal point in the input true or false?
Answer:
its correct for positive numbers
Answer:
Jim’s statement is correct for all numbers greater than or equal to 0, and negative integers. It does not work for negative non-integer numbers. For example, the floor of –3.5 is –4, where –4 is not equal to –3, the number before the decimal point.
Step-by-step explanation: Math
can two distinct quadratic equations have two real solutions
Answer:
A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.
Step-by-step explanation:
Does that make sense?