Using the trigonometric ratios Cos and Tan we can find Cos A = 0.8 and Tan C = 0.75 from the given diagram.
What are Trigonometric ratios?Trigonometric ratios are mathematical functions used to relate the angles and sides of a right-angled triangle. The three primary trigonometric ratios are:
Sine : It is the ratio between the opposite side of the right triangle and the hypotenuse of the right triangle.
Cosine : It is the ratio between the adjacent side of the right triangle and the hypotenuse of the right triangle.
Tangent : It is the ratio between the opposite side of the right triangle and the adjacent side of the right triangle.
We know that Cos A = adjacent side of the right triangle/ hypotenuse of the right triangle
That is Cos A = AB/AC = 32/40 = 0.8
Similarly Tan C = opposite side of the right triangle/ adjacent side of the right triangle
That is Tan C = BC/AB = 24/32 = 0.75
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a man can hit his target 25% of the time if he fires 4 shots in succession what is the probability that he will hit his target
The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.
The probability of missing all 4 shots is (0.75)^4 = 0.3164.
Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:
1 - 0.3164 = 0.6836 or 68.36%.
So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.
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A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
Answer: First choice 480t = 300t + 900
Step-by-step explanation:
A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
ANS
Let say t is time in hrs for Which Both Assembly line worked
M made 300 toys per hr on Tuesday
Toys made on Tuesday at Assembly line M = 300 × t = 300t toys
N made 480 toys per hr on Tuesday
Toys made on Tuesday at Assembly line N = 480 × t = 480t toys
Toys Made by N on Tuesday = Toys made by M on Tuesday + Toys made by M on Monday
480t = 300t + 900
=> 180 t = 900
=> t = 900/180
=> t = 5 hr
N capacity on tuesday Per hour * t = M capacity on tuesday per hour * t + Toys made by M on Monday
N = N capacity on tuesday Per hour
M = M capacity on tuesday Per hour
=> t (N - M ) = 900
=> t = 900/(N-M)
i need some help with this problem i don’t really understand it
Answer:
-34x+29
Step-by-step explanation:
[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]
The length of one leg of a right triangle is 2 times the length of the other, and the
length of the hypotenuse is 12. What is the length of the longest leg?
Answer:
[tex]\frac{24\sqrt{5} }{5}[/tex]
Step-by-step explanation:
Let's start by assigning one of the unknown legs with the variable x.
We know that the other leg is 2 times the length of x, so we can write:
2x
We also know that the length of the hypotenuse is 12.
From here, we can use the Pythagorean Theorem.
Recall that the Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.
Let's substitute the values. We have:
[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]
Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:
[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]
Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]
Let's solve for 2x:
[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]
So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]
A 30 pack of copy paper cost $48.30 a 32 pack cost $49.60 which is the better buy (help me explain it)
Answer:
Step-by-step explanation:
the 32 pack because it costs just slightly more
*MATH* PLS HELP! THE PROBLEM IS IN THE IMAGE!
(PLEASE show your work or explain how you got that answer)
The scale factor that takes triangle C to triangle D is 3/10.
What is scale factor?Scale factor is a number by which the size a geometrical figure or shape can be changed with respect to its original size.
To find the scale factor that takes triangle C to triangle D, we use the formula below
Formula:
S.F = Length of triangle D/Corresponding Length of triangle CWhere:
S.F = Scale factorFrom the diagram in the question,
Given:
Hypotenus of triangle D = 3.36Hypotenus of triangle C = 11.2Substitute these values into equation 1
S.F = 3.36/11.2S.F = 0.3 = 3/10Hence, the scale factor is 3/10.
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the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes hours for a car moving at . how long does the trip take for a car moving at ?
The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.
Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.
The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]
Distance(d) = Speed(r)×Time(t)Time(t) = Distance(d)/Speed(s)Now, Speed of car (s) = 50 miles per hour
Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]
=> x = 4 × 50 miles
=> x = 200 miles
Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]
=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]
= 5 hours.
Hence, required value of time is 5 hours.
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Complete question :
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?
the ricardo household used w cubic feet of water during a summer month express the number of ccf of water they used algebraically
Ricardo used w/100 Ccf of water.
Given that, Ricardo household used w cubic feet of water in a month of summers,
we need to express the number of ccf of water they used algebraically,
Ccf = A CCF is a unit of measurement of volume.
The CCF is used to measure gas consumption, used in the billing of natural gas and water delivered to households.
1 CCF = 100 cubic feet
CCF means Centum Cubic Feet.
1 cubic feet = 0.01 Ccf
Therefore,
w cubic feet = 0.01 × w Ccf
= w / 100
Hence, Ricardo used w/100 Ccf of water.
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Please use Triangle Inequality to solve, I'm having a bit of trouble. I'd also appreciate if you just help me.
The value of x for the given triangle through which the perimeter of the given relation is satisfied is 10.
What about perimeter of triangle?
The perimeter of a triangle is the total length of its boundary, which is the sum of the lengths of its three sides. The perimeter can be thought of as the distance around the triangle, and it is measured in units of length such as centimeters, meters, or feet. The perimeter of a triangle is an important geometric property that is used in many practical applications, such as calculating the amount of fencing needed to enclose a triangular-shaped garden or determining the length of wire required to form a triangular circuit.
According to the given information:
The perimeter of triangle is sum of all sides of the triangle
In which,
2x + 4 + 3x - 8 + x - 2 = 54
6x - 6 = 54
6x = 60
x = 10
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Find the number of permutations with of the letters in each word
The trigonometry functions when calculated are sin(A) = 18/34 and cos(A) = 30/34
Calculating the trigonometry functionsFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where we have
Opposite = 18Adjacent = 30Hypotenuse = 34Using the above as a guide, we have the following:
sin(A) = 18/34
cos(A) = 30/34
Hence, the values are sin(A) = 18/34 and cos(A) = 30/34
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Solve for all values of x by factoring.
x² + 6x-41 = 6x - 5
The solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.
Solving for all values of x by factoring.To solve for all values of x by factoring x² + 6x - 41 = 6x - 5, we can first simplify the equation by combining like terms:
x² + 6x - 41 = 6x - 5
x² - 41 = -5
Next, we can bring all the terms to one side of the equation:
x² - 41 + 5 = 0
x² - 36 = 0
Now we can factor the left side of the equation:
(x - 6)(x + 6) = 0
Setting each factor equal to zero and solving for x, we get:
x - 6 = 0 or x + 6 = 0
x = 6 or x = -6
Therefore, the solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.
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I NEED HELP ON THIS ASAP!! PLEASE IT'S DUE TODAY!
The exponential function to represent the number of new participants of the challenge as a function of the day number, is f(x) = 12 × 4ˣ.
How to find the exponential function ?Let f(x) be the number of new participants on day x.
On day 0 (today), Aliyah, Kim, and Reese are the only participants. They each send selfies to 4 friends, so there will be 3 x 4 = 12 new participants on day 1.
From day 1 onwards, each new participant will send selfies to 4 friends. Therefore, the number of new participants will quadruple each day. This gives us an exponential growth function:
f(x) = 12 × 4ˣ
where f(x) represents the number of new participants on day x.
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The volume of a volleyball is approximately 113 in ^3. What is its diameter? Round your answer to the nearest whole number.
A. 13 in
B. 6 in
C. 2 in
D. 5 in
will give brainliest
If the volume of a volleyball is approximately 113 in³, then the diameter of the volleyball is approximately option (D) 5 inches.
The formula for the volume of a sphere is
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.
We are given the volume of the volleyball as 113 in³, so we can solve for the radius as follows
113 = (4/3)πr³
r³ = 113 / ((4/3)π)
r³ ≈ 21.50
r ≈ 2.8
To find the diameter, we double the radius:
d = 2r ≈ 5.6
Rounding this to the nearest whole number
d = 5 in
Therefore, the correct option is (D) 5 in
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Complete the table using the information given.
Using the above information, we can calculate the missing figures in the table and this is shown on the table attached.
What is the table about?For the "Shorts" row: It's given that 42 people were wearing shorts.
Since it's mentioned that twice as many people were wearing closed-toed shoes as open-toed shoes, and 30 people were wearing open-toed shoes, we can deduce that 30 people were also wearing closed-toed shoes.So, the total number of people wearing closed-toed shoes is 30, and the total number of people wearing shorts is also 42, since they are the same group of people.Therefore, the "Close-Toed Shoes" column in the "Shorts" row is also 42, and the "Total" column is the sum of open-toed and closed-toed shoes, which is 84.
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See text below
30 people surveyed were wearing open-toed shoes.
1/3 of the people with open-toed shoes were wearing
pants.
• 42 people were wearing shorts.
Twice as many people were wearing closed-toed shoes
than open-toed shoes.
Complete the table using the information given.
Open-Toed Shoes Close-Toed Shoes Total
Shorts ------- ------ --------
Pants ------ ---------- ------
Total ------ ---------- ---------
Q4: The walking distance that is saved by cutting across the lot is?
The walking distance that is saved by cutting across the lot is 55.
What is a right angle triangle?A right triangle, also known as a right-angled triangle, is a triangle that has one angle that measures 90° (a right angle). The remaining two angles are acute, or less than 90°
Apply right angle triangle rules;
⇒ 38² = (x+14)² + x²
⇒ 1444 = x² + 196 + 28x + x²
⇒ 2x² + 28x - 1248 = 0
⇒ x = 19 and x = -33
Therefore, the walking distance that is saved by cutting across the lot is:
⇒ x + x + 14
⇒ 19 + 19 + 14
⇒ 52
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Fruit Smoothle
O E. Talia can use 1
cup orange juice
cup yogurt
8 cup strawberries
8 cup blueberries
cup of ice
Blend all ingredients. Serve cold.
Makes 1 serving.
Which statement about the recipe is true? Mark all that apply.
cup strawberries to double the recipe.
O A. Talia can use
OB. Talia can use
OC. Talia can use
12 cup yogurt to make 3 servings.
cup blueberries to make 4 servings.
OD. Talia can use
1
cups orange juice to make 4 servings.
cup of ice to make 5 servings.
A. Talia can use 1 and 3/4 cup strawberries to double the recipe. B. Talia can use 1 and 1/3 cup yogurt to make 3 servings. D. Talia can use 2 cups orange juice to make 4 servings.
What is proportion?In statistics, a proportion is a fraction or a percentage that reflects the proportion of a population's or sample's members who share a particular attribute to the population's or sample's overall size. It is a kind of ratio where the denominator is the entire population or sample size and the numerator is the number of people who possess a specific trait or attribute.
From the given ingredients and the serving size we can see that the correct statement is:
A. Talia can use 1 and 3/4 cup strawberries to double the recipe.
B. Talia can use 1 and 1/3 cup yogurt to make 3 servings.
D. Talia can use 2 cups orange juice to make 4 servings.
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The complete question is:
4. The radius of a cylinder is 3x-2 cm. The height of the cylinder is x +3 cm. What is the
surface area of the cylinder? Use the formula A=2x²+2xrh.
02x (3x2+10x-8)
O 27(12x+7x-2)
O 27(12x²-2x+13)
O 27(12x²-5x-2)
Answer:
D: 27(12x² - 5x - 2).
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πr² + 2πrh
Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:
A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
A = 24πx² - 10πx - 4π
A = 2π(12x² - 5x - 2)
Therefore, the answer is option D: 27(12x² - 5x - 2).
Answer:
D
Step-by-step explanation:
Given a circle has a center at (-6, 14) and a diameter of 30, write the equation of the circle
Answer:
The center of the circle is at (-6, 14), and the radius is 15, so we have this equation:
[tex] {(x + 6)}^{2} + {(y - 14)}^{2} = 225 [/tex]
In the figure, the curve y=x² + 7x + 6 cuts the
x-axis at two points A and B, and the y-axis at the
point C. Calculate the coordinates of A, B and C.
A
y
B
O
C
-X
Answer:
A(-6,0) B(-1,0) C(0,6)
Step-by-step explanation:
PLEASE HELP. Lesson 15.3 Tangents and Circumscribed Angles
Proof of Circumscribed Angle Theorem
Given: ZAXB is a circumscribed angle of circle C.
Prove: ZAXB and ZACB are supplementary.
Complete the proof.
A
B
C
If ZAXB is a circumscribed angle of circle C, XA and XB are
Select an answer to the circle
Therefore, angles ZACB and ZAXB are congruent, and since they are complementary to angles ZAO and ZBO, respectively, they must be supplementary.
What is Circumscribed Angle Theorem?The Circumscribed Angle Theorem states that an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs. More formally, if two chords of a circle intersect at point P, then the measure of the angle formed by the chords (let's call it angle ABC) is equal to half the sum of the measures of the arcs intercepted by the angle.
Here,
To prove that ZAXB and ZACB are supplementary, we need to show that the sum of their measures is 180 degrees. Here's the proof:
Given: ZAXB is a circumscribed angle of circle C.
To Prove: ZAXB and ZACB are supplementary.
Proof:
Draw circle C with center O and circumscribed angle ZAXB.
Draw radii OA, OB, and OC to the points of intersection A, B, and C.
Since XA and XB are tangent to circle C at points A and B, respectively, we know that angles OAX and OBX are right angles.
Therefore, angles ZAO and ZBO are complementary to angles ZAC and ZBC, respectively.
By the Inscribed Angle Theorem, we know that angles ZAO and ZBO are congruent to angle ZAXB.
Therefore, angles ZACB and ZAXB are congruent, and since they are complementary to angles ZAO and ZBO, respectively, they must be supplementary.
Thus, we have proven that ZAXB and ZACB are supplementary.
Therefore, the proof is complete.
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2㏒_[6](2)+3㏒_[6](3)+㏒_[6](12)
Answer: 4
Step-by-step explanation:
Given:
[tex]2log_62+3log_63+log_612[/tex]
Rewrite using the power property:
[tex]log_62^2+log_63^3+log_612[/tex]
Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:
[tex]log_6(2^2*3^3*12)[/tex]
Simplify by multiplying:
[tex]log_6(4*27*12)[/tex]
[tex]log_6(1,296)[/tex]
Evaluate the logarithm:
[tex]log_6(1,296)[/tex]
4
One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 17 feet, a width of 15 feet, and a height of 12 feet? Write your answer as a decimal. Gal
We need at least 3.465 gallons of paint to paint the walls of this room.
The area of the two rectangular faces on either end of the prism is:
length x height = 17 x 12 = 204 square feet
The area of the two rectangular faces on the sides of the prism is:
width x height = 15 x 12 = 180 square feet
The area of the top and bottom faces of the prism is:
length x width = 17 x 15 = 255 square feet
The total surface area of the prism is:
2(204) + 2(180) + 2(255) = 1386 square feet
Now, we divide surface area by coverage of one gallon of paint:
1386 / 400 = 3.465
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What is the equation of the line 2x+3y+1=0 after it has been reflected across y=-1 and rotated about o(2,3) by 180
The equation of the line 2x + 3y + 1 = 0 after it has been reflected across y = -1 and rotated about O(2,3) by 180 degrees is -2x + y = 15.
To reflect the line 2x + 3y + 1 = 0 across the line y = -1, we need to subtract twice the y-coordinate of each point on the line from the equation of the line.
This is because the reflection of a point across a line is obtained by reflecting it across the line's perpendicular bisector, which is also the line with the same x-coordinates and twice the distance from the point to the line.
Subtracting twice the y-coordinate, we get:
2x + 3(-2y - 1) + 1 = 0
Simplifying the equation, we get:
2x - 6y - 5 = 0
Now, to rotate the line about the point O(2,3) by 180 degrees, we can use the rotation formula:
x' = 2a - x
y' = 2b - y
where (x,y) are the coordinates of a point on the original line, and (x',y') are the coordinates of the same point after rotation about the point (a,b).
Substituting the coordinates of two points on the line, we get:
(0,-1) → x' = 2(2) - 0 = 4, y' = 2(3) - (-1) = 7
(-1/2,0) → x' = 2(2) - (-1/2) = 4 1/2, y' = 2(3) - 0 = 6
Now, we can use the two points (4,7) and (4 1/2,6) to find the equation of the rotated line using point-slope form:
slope = (6-7) / (4 1/2 - 4) = -2
y - 7 = -2(x - 4)
y = -2x + 15
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A pre-image has coordinates A(3, -5), B(3, 1) and C(-2, 0). The image has coordinates A'(3, 5), B'(3, -1) and C'(-2, 0). What type of reflection occurred? Explain how you know.
For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the x-axis refection.
Explain about the reflection about x axis:The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given data:
pre-image coordinates - A(3, -5), B(3, 1) and C(-2, 0).
Image coordinates A'(3, 5), B'(3, -1) and C'(-2, 0).
As its is clear from the given coordinates that value of x is same while the value of y gets change by negative.
(x,y) ---> (x, -y) , shows the refection about the x axis.
Thus, For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the refection about the x axis.
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.
Which equation is a step in solving the equation |5 − 3x| + 2 = 19?
A.
5 − 3x = -17
B.
|5 − 3x| = -17
C.
5 + 3x = -17
D.
|5 + 3x| = 17
Answer:
Step-by-step explanation:
The absolute value (or modulus) | 5 - 3x | of a real number 5 - 3x is the non-negative value of 5 - 3x without regard to its sign.
| 5 - 3x| + 2 = 19
| 5 + 3x | = 19 - 2
| 5 + 3x | = 17
Ans: D
Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 90° counterclockwise.
U′(0, −2), V′(−1, −3), W′(−3, −3)
U′(0, −2), V′(1, −3), W′(3, −3)
U′(2, 0), V′(3, −1), W′(3, −3)
U′(−2, 0), V′(−3, 0), W′(3, −3)
Answer:
The vertices of the image after rotating triangle uvw 90 degrees counterclockwise are u′(0, −2), v′(1, −3), w′(3, −3).
Step-by-step explanation:
the mean weight of an adult is 62 kilograms with a variance of 144 . if 195 adults are randomly selected, what is the probability that the sample mean would be greater than 59.5 kilograms? round your answer to four decimal places.
The probability is 0.9835 where the sample mean would be greater than 59.5 kilograms.
The central limit theorem can be used to approximate the sampling distribution of the sample mean as a normal distribution.
where the mean equals the population mean (μ = 62 kg) and the standard deviation equals the population standard deviation divided by the square root of sample size (σ/sqrt (n) = sqrt(144 / 195) = 2.4287 kg).
Next, find the probability that the sample mean is greater than 59.5 kilograms.
z = (59.5 - 62) / (2.4287 / square (195)) = -2.1295
Using an ordinary regular table or calculator, we know that the probability of a Z-score less than -2.1295 is 0.0165.
Therefore, the probability that the sample mean exceeds 59.5 kilograms is
1 - 0.0165 = 0.9835
Rounding to four decimal places gives a probability of 0.9835.
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
The optimal measure of variability is the IQR, which equals 4. The proper measure of variability for the data is C.
How is IQR the best measure of variability?The difference among the third and the first quartile is defined by the interquartile range. The entire series is divided into four equally sized pieces by the partitioned values referred to as quartiles. Three quartiles are present.
The spread of the middle 50% of the data, which is less susceptible to outliers than the range, is measured by the interquartile range (IQR), which is the best measure of variability for these data.
The IQR is calculated by deducting the third quartile ([tex]Q_3[/tex]) from the first quartile ([tex]Q_1[/tex]). We can see from the box plot that [tex]Q_1[/tex] is roughly
17 and [tex]Q_3[/tex] is roughly 21.
Therefore,
[tex]IQR=Q_3-Q_1\\\\IQR=21-17\\\\IQR=4[/tex]
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How do you find the period of a cosine function of the form y = cos bx?
The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.
This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.
it represents the distance along the x-axis for the cosine function to complete one full oscillation.
The period of a cosine function of the form y = cos bx, first identify the coefficient b.
Use the formula T= 2π/b to calculate the period 'T'.
For example,
Consider cosine function y = cos 2x,
The coefficient of x is 2.
Using the formula above, the period is equal to
Period = 2π/2
= π
So the period of the function y = cos 2x is π.
This implies that the cosine function completes one full oscillation every π units along the x-axis.
Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.
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Timmy is building a model of a building in his town that is 180 meters. He is using a scale of 1.5 cm. = 3.5 meters. How tall will his model be?
Answer: 77
Step-by-step explanation: You could set up a proportion for this question. 1.5 centimeters = 3.5 meters x centimeters = 180 meters 1.5 x 180 / 3.5 Rounded to the nearest whole number, the answer is 77.