Answer is h(x) =\(\frac{1}{2}\) cos (\(\frac{2}{3}\)π +\(\frac{2}{3}\)π ) - \(\frac{1}{2}\)
∵The maximum point (- 2π. 3 )
minimum point (- π / 2 , - 4)
and h(x) = a cos (b x + c)+ d
∴ a + d = 3 d = - 1/ 2
⇒
-a + d = -4 a = 7 / 2
{solve the equation}
and -2πb + c = 0 b = 2 / 3
⇒
- ( π/ 2) b + c = λ c = 4 / 3 π
∴ h(x) =\(\frac{1}{2}\) cos (\(\frac{2}{3}\)π +\(\frac{2}{3}\)π) - \(\frac{1}{2}\)
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant
here detail explanation:
Sine Function
Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:
Sin a =Opposite/Hypotenuse = CB/CA
Cos Function
Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.
Cos a = Adjacent/Hypotenuse = AB/CA
Tan Function
The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.
Tan a = Opposite/Adjacent = CB/BA
Also, in terms of sine and cos, tan can be represented as:
Tan a = sin a/cos a
Secant, Cosecant and Cotangent Functions
Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:
Sec a = 1/(cos a) = Hypotenuse/Adjacent = CA/AB
Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB
cot a = 1/(tan a) = Adjacent/Opposite = BA/CB
Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant.
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Solve the equation.
\( {3}^{4(m + 1)} + {3}^{4m} - 246 = 0 \\ \)
\(3^{4m+4}+3^{4m}=246\\ (3^{4}+1)*3^{4m}=246\\82*3^{4m}=246\\3^{4m}=3\\m=\frac{1}{4}\)
1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Answer:
z = 0.9
Step-by-step explanation:
1/3(6z + 7.2) = 0.5 (8z + 2) - 0.4
Step 1) (2z +2.4)=(4z+1) - 0.4
Step 2) (2z +2.4)=(4z+0.6)
Step 3) 1.8 = 2z
Step 4) 1.8/2 = z
Step 5) 0.9 = z
Answer:
.9
Step-by-step explanation:
it is 0.9 i did this assignment with my teacher
Tyrone buys a bicycle priced at $86. If the sales tax is 10%, how much tax will Tyrone pay?
Answer:
He will pat $94.60.
Step-by-step explanation:
Since you need to add 10% tax to your total, that is ten cents per dollar, and since you are adding it to the $86, you need to do 86 x 1.10, which is 94.60, and there you have it.
what’s the area and the perimeter and of the triangle?
Answer:
16.5
Step-by-step explanation:
7.5 x 2.2. formula of triangle = bh
A data set has 10 values. • The mean of the data in the set is 12. • The mean absolute deviation of the data in the set is 4. Which statement about the values in the data set must be true? Each value in the data set varies from 12 by exactly 4. Each value in the data set varies from 12 by an average of 4. No values in the data set are less than 8 or greater than 16. Half of the values in the data set are 8 and half of the values in the data set are 16.
Answer:
The statement that must be true about the values in the data set is: "No values in the data set are less than 8 or greater than 16."
Step-by-step explanation:
Mean is the average value of a dataset. In this case, the mean of the data set is given as 12.
Mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. In this case, the MAD is given as 4.
If each value in the data set varied from 12 by exactly 4, then the mean absolute deviation would be 4. However, in this case, the given mean absolute deviation is 4, which means the average deviation is 4, but individual values can deviate in both positive and negative directions.
The statement that half of the values in the data set are 8 and half of the values are 16 cannot be concluded based on the given information. The mean of 12 does not imply that half the values are 8 and the other half are 16.
Therefore, the only statement that can be confirmed as true based on the given information is: "No values in the data set are less than 8 or greater than 16."
True or False? Every quadrilateral is a rhombus. Every parallelogram is a quadrilateral. Every square is a quadrilateral. Every rhombus with four right angles is a square. X Ś True False O True False O True False True False ?
First of all it's important to note that all parallelograms, rhombuses and squares are quadrilateral and they meet the following properties:
- Rhombus: quadrilateral whose four sides have the same length.
- Parallelogram: quadrilateral that has two pairs of parallel sides.
- Square: quadrilateral whose four sides and internal angles have the same length/measure.
With these definitions in mind we can solve the True or False table in the picture.
The first statement is false not every quadrilateral is a rhombus. For example rectangles that are not squares are not rhombuses since their four sides aren't all equal.
The second is true, as we saw before parallelograms are quadrilaterals. The same reason applies to the third statement, squares are qudrilaterals.
Now let's see the last statement. A rhombus with four right angles is a quadrilateral that has four equal sides (because it's a rhombus) and four equal angles (all measuring 90°). These are the conditions required for a quadrilateral to be considered a square so this last statement is true.
AnswersThen the answers are:
F
at the local college, a study found that students used an average of 5.2 school books per semester. a sample of 39 students was taken. what is the best point estimate for the average number of school books per semester for all students at the local college?
The best point estimate for the average number of school books per semester for all students at the local college is 5.2.
The average number of school books per semester for all students at the local college is 5.2. A sample of 39 students was taken, i.e., n = 39. To find, The best point estimate for the average number of school books per semester for all students at the local college.
The best point estimate for the average number of school books per semester for all students at the local college is the sample mean which can be calculated.
Therefore, the best point estimate for the average number of school books per semester for all students at the local college is 5.2.
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describe the sampling distribution model of p. what assumptions must you make for this description to be reasonable?
The sampling distribution model of p is a probability distribution that describes the possible values of a population proportion (p) based on a sample proportion (p-hat) from a random sample of the population. The assumptions that must be made for this description to be reasonable are:
The sample must be randomly selected from the population.The sample size must be large enough (typically n > 30).The population proportion must be well-defined and fixed, and not depend on the sample selected.Independence of observations.The sample should not be too large, otherwise it will be close to the population proportion.Sample ProportionIf the sample is not randomly selected, it may not be representative of the population and the sample proportion may not accurately reflect the true population proportion.
A large sample size allows the sample proportion to be a good estimate of the true population proportion, this is due to the central limit theorem which states that as sample size increases, the distribution of the sample proportion becomes more normal and the standard deviation of the sampling distribution becomes smaller.
The population proportion must be well-defined and fixed for the sample proportion to be a good estimate of it. If the population proportion is not well-defined or changes based on the sample selected, then the sample proportion may not accurately reflect the true population proportion.
Independence of observations ensures that the outcome of one observation does not affect the outcome of another observation, this allows us to assume that the sample proportion is a good estimate of the population proportion.
If the sample is too large, it will be close to the population proportion, and therefore the sample proportion will not provide any new information.
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The city of London, England, has an
elevation of 11 meters.
Which of these describes the elevation
of London?
below sea level
at sea level
above sea level
Answer:
above sea level
Step-by-step explanation:
Length ams breadth and height of rectangle block. Ratio is 4:3:5 and its volume is 3840 cm3 calculate length, breadth, height
The length, breadth, and height of the rectangular block are 256 cm, 192 cm, and 320 cm respectively.
To calculate the length, breadth, and height of a rectangular block whose ratio is 4:3:5 and its volume is 3840 cm3,
follow the steps below:
The ratio of length, breadth, and height is 4:3:5 respectively.
Therefore, assume the length to be 4x, the breadth to be 3x, and the height to be 5x, where x is the common factor.
Then, the volume of the block is calculated as:
Volume = length × breadth × height= 4x × 3x × 5x= 60x³
Since the volume of the block is 3840 cm³, we can equate the equation above to 3840 and solve for x, then find the
length, breadth, and height.
60x³ = 3840 x³ = 3840/60 x³ = 64
Length = 4x = 4 × 64 = 256 cm
Breadth = 3x = 3 × 64 = 192 cm
Height = 5x = 5 × 64 = 320 cm
Therefore, the length, breadth, and height of the rectangular block are 256 cm, 192 cm, and 320 cm respectively.
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What is the result when 6a + (-4b) is subtracted from 12a + 13b?
Answer:
(First put the numbers with the same values together)
or, 6a - 12a + (-4b) + 13b
or, -6a - 4b + 13b
or, -6a + 9b ans.
1/2 minus (1/8+1/8) I need help can somebody give me advice on this
Answer: 38
Step-by-step explanation:
Subtract 1/8 from 1/2
12 - 18 is 38.
Steps for subtracting fractions
Find the least common denominator or LCM of the two denominators:
LCM of 2 and 8 is 8
Next, find the equivalent fraction of both fractional numbers with denominator 8
For the 1st fraction, since 2 × 4 = 8,
12 = 1 × 42 × 4 = 48
Likewise, for the 2nd fraction, since 8 × 1 = 8,
18 = 1 × 18 × 1 = 18
Subtract the two like fractions:
48 - 18 = 4 - 18 = 38
7. (x³ +7x² + 2)÷(x-1)
Answer:
(x³ + 7x² + 2)÷(x-1) = x² + 8x + 15 + 8/(x-1).
Suppose you are conducting a study to compare firefly populations exposed to normal daylight/darkness conditions with firefly populations exposed to continuous light (24 hours a day). You set up two firefly colonies in a laboratory environment. The two colonies are identical except that one colony is exposed to normal light/darkness conditions and the other is exposed to continuous light. Each colony is populated with the same number of mature fireflies. After 72 hours, you count the number of living fireflies in each colony. Questions: Is this an experiment or an observation study? Explain. Is there a control group and a treatment group? Identify each group.
The study outlined above is an experiment. In the study, two firefly colonies are set up in a laboratory environment and are subjected to different conditions. Therefore, it is an experimental design as the researcher is actively manipulating the independent variable which is the exposure of fireflies to light.
An observational study would involve recording data on a subject without manipulating their environment or situation. An observational study would have a less controlled environment in which the researcher does not interfere with the study subjects. There is a control group and a treatment group. The control group is the colony that is exposed to normal daylight/darkness conditions. The treatment group is the colony that is exposed to continuous light. The control group is used to provide a baseline measure or standard of comparison for the experiment.
It provides a way to compare the difference between the treatment group and the control group. Thus, the control group is the normal light/darkness colony, and the treatment group is the continuous light colony.
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which one of these are expressions?
12+4-3
12-4(3)
12/4=3
12=4x3
The expressions are options 1, 2, and 3.
Out of the given options, the expressions are:
12 + 4 - 3
12 - 4(3)
12 / 4 = 3
An expression is a mathematical statement that consists of numbers, variables, and mathematical operations. It represents a value or a computation.
Option 1, "12 + 4 - 3," is an expression because it combines addition and subtraction operations to compute a value.
Option 2, "12 - 4(3)," is also an expression. The parentheses indicate multiplication, and it involves subtraction as well.
Option 3, "12 / 4 = 3," is an expression representing a division operation and an equality statement.
Option 4, "12 = 4x3," is not an expression but an equation because it involves an equality sign and represents an equality relationship rather than a computation.
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PLS HELP DUE TODAY,25 POINTS TO BRAINLIEST
Answer:
I think it’s H
Step-by-step explanation:
Answer:
The answer is H bacause it has the most number of colours
Which category do all of these shapes belong to?
Help
Answer:
rectangles
Step-by-step explanation:
All of these shapes belong to rectangles category.
What is rectangular shape?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.
Given:
Three shapes in the form of quadrilateral are given.
From the diagrams,
the shapes have the opposite sides equal and parallel.
That means, the shapes are rectangles.
Therefore, the shapes are rectangles.
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comparison between signed and unsigned integer expressions
Signed and unsigned integer expressions differ in how they interpret and represent numerical values. Signed integers can represent both positive and negative values, while unsigned integers can only represent non-negative values.
1. Signed Integer Expressions: Signed integers are capable of representing positive, negative, and zero values. They allocate a bit for the sign, typically using the leftmost bit (the most significant bit). The remaining bits are used to represent the magnitude of the number. The sign bit is set to 0 for positive or zero values and set to 1 for negative values. This representation allows for a wider range of values, but half of the possible bit patterns are reserved for negative numbers, limiting the maximum positive value that can be represented.
2. Unsigned Integer Expressions: Unlike signed integers, unsigned integers do not allocate a bit for the sign. Instead, all bits are used to represent the magnitude of the number, allowing for a wider range of non-negative values. As a result, unsigned integers can represent larger positive values than their signed counterparts. However, they cannot represent negative values or zero, as there is no reserved bit to indicate the sign.
The choice between signed and unsigned integer expressions depends on the specific requirements of a program. Signed integers are typically used when negative values need to be represented or when arithmetic operations may result in negative values. On the other hand, unsigned integers are useful when dealing with quantities that are always expected to be positive, such as array indices or lengths of data structures. It's important to consider the range of values required and the potential impact of overflow or underflow when selecting between signed and unsigned integer expressions.
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7p−(−5)+(−1)=solve it
Answer:
\(7p - ( - 5) + ( - 1) \\ = 7p + 5 - 1 \\ = 7p + 4\)
Answer:7p+4 :)
Step-by-step explanation:
Which of the following number lines shows the correct sum of the number above and -5/2?
A.
B.
C.
D.
what can you conclude about the tangent lines and the diameter of a circle?
A. No relation
B. perpendicular
c. Skewed
D. Parallel
Answer:
B. perpendicular Hope this helps!
Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
Answer:
8.50667 or approximately 8.51 feet per second
Step-by-step explanation:
The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.
use analytic methods to find (a) the local ex- trema, (b) the intervals on which the function is increasing, and (c) the intervals on which the function is decreasing
Use analytic methods,
(a) The local extrema,
1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.
2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.
(b) The intervals on which the function is increasing
Write properties of function :
Increasing interval : ( - ∞ , 0 )
(c) The intervals on which the function is decreasing
Write properties of function :
Decreasing interval : ( 0 , ∞ )
Given that,
Use analytic methods (a) the local extrema, (b) the intervals on which the function is increasing, and (c) the intervals, then the function is,
A function's growing (or decreasing) periods match the periods when its derivative is positive (or negative). As a result, we can easily determine the intervals where a function increases or decreases by taking its derivative and analyzing it to determine if it is positive or negative.
(a) How do we find the local extrema?Let f be continuous on an open interval (a , b) that contains a critical x-value.
1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.
2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.
(b) The intervals on which the function is increasing
Write properties of function :
Increasing interval : ( - ∞ , 0 )
(c) The intervals on which the function is decreasing
Write properties of function :
Decreasing interval : ( 0 , ∞ )
Therefore,
Use analytic methods,
(a) The local extrema,
1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.
2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.
(b) The intervals on which the function is increasing
Write properties of function :
Increasing interval : ( - ∞ , 0 )
(c) The intervals on which the function is decreasing
Write properties of function :
Decreasing interval : ( 0 , ∞ )
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Write an exponential function whose graph passes through the given points (0, - 2) and (- 1, - 4)
Answer:
\(y = 2(0.5) {}^{x} \)
Step-by-step explanation:
Use the general formula of exponential equation
\(y = ab {}^{x} \)
Plug 0,2 into the function
\( - 2 = ab {}^{0} \)
\( - 2 = a \times 1\)
\(a = - 2\)
\(y = - 2b {}^{x} \)
\( - 4 = - 2b {}^{ - 1} \)
\(2 = b {}^{ - 1} \)
\( {2}^{ \frac{ 1}{ - 1} } \)
\(2 {}^{ - 1} = 0.5\)
B=0.5
\(y = 2(0.5) {}^{x} \)
the cost of a 12-ounce bag of cashews is $5.86 what is the cost per ounce of the cashews to the nearest penny
Answer:
Answer:5.86÷12=0.5 in nearest penny
Step-by-step explanation:this number kind of problem u solve it using inversely proportional method one one quantity is decreasing which is the ounce
Step-by-step explanation:
Answer:
0.5
Step-by-step explanation:
When exposed to water, sodium catches on firo. Chamural Nhange: 14. My car traveled 6.05 miles in 5.75 minutes. If I continue driving at the same pace, how long will it take to drive 246 miles? (3 points) D= Answer: 15. A gold nugget has a mass of 21.75 g. Pure gold has a density of 19.32 g/mL. What is the volume of the gold nugget? (2 points) Answer: 16. There are 993.0 miles between Philadelphia and Orlando. How many kilometers separate these cities? Note that 1mi=1.609 km
15. If your car traveled 6.05 miles in 5.75 minutes and you continue driving at the same pace, it will take approximately 262.17 minutes to drive 246 miles.
16. The volume of the gold nugget with a mass of 21.75 g and a density of 19.32 g/mL is approximately 1.125 mL.
15. Using the given information, we can set up a proportion to find the time it will take to drive 246 miles. The proportion can be set up as: (6.05 miles / 5.75 minutes) = (246 miles / x minutes), where x represents the unknown time. Cross-multiplying and solving for x, we find that x ≈ 262.17 minutes. Therefore, it will take approximately 262.17 minutes to drive 246 miles at the same pace.
16. To calculate the volume of the gold nugget, we can use the formula: volume = mass / density. Plugging in the given values, we get: volume = 21.75 g / 19.32 g/mL. Performing the division, we find that the volume is approximately 1.125 mL. Therefore, the volume of the gold nugget is approximately 1.125 mL.
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Mike throws a ball over a 20-foot fence to a baseball field. The height h of the bereal a tire tsessnes
can be modeled by the equation h = -16t? + 40t+ 5, What is the maximum height reached by the tall?
A. 21 feet
B. 25 feet
c. 30 feet
D. 1.25 feet
E. 0.5 feet
The maximum height reached by the ball is 30 feet. Option C
To find the maximum height reached by the ball, we need to determine the vertex of the parabolic function represented by the equation h = \(-16t^2 + 40t + 5.\)
The vertex of a parabola in the form y = ax^2 + bx + \(ax^2 + bx + c\) is given by the formula x = -b / (2a), which gives us the x-coordinate of the vertex. In this case, a = -16 and b = 40.
Using the formula, we can calculate the x-coordinate of the vertex:
x = -b / (2a) = -40 / (2*(-16)) = -40 / (-32) = 1.25
To find the corresponding y-coordinate (maximum height), we substitute the x-coordinate back into the equation:
h \(= -16(1.25)^2 + 40(1.25) + 5\) = -16(1.5625) + 50 + 5 = -25 + 55 = 30
Therefore, the maximum height reached by the ball is 30 feet.
The correct answer is option C) 30 feet.
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Wendy earned $14 per hour for x hours, plus a bonus of $50. Write an expression that represents how much Wendy earned. plz answer fast.
Answer:
W(x) = $50 + ($14/hr)x
Step-by-step explanation:
hope this helped
Pls help me it’s so hard imo thank you sm
Answer: 7e-5 millimeters, and the nanometer scale is more appropriate
Step-by-step explanation: PLEASE MARK ME BRAINLIEST!!!!!!
-divide the length value by 1e+6
-The millimeter scale and the centimeter scale are two huge, while the nanometer scale is too small. The nanometer scale is often used to measure atoms and viruses.
Answer:
a) The length of the virus in millimetres is 0.000 07 mm.
b) Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.
Step-by-step explanation:
SI is the abbreviation for The International System of Units.
The SI base unit for length is metres (m).
Milli and nano are SI prefixes used to form decimal multiples or submultiples of SI units.
1 millimetre (mm) = 1 × 10⁻³ metres = 0.001 m1 nanometre (nm) = 1 × 10⁻⁹ metres = 0.000 000 001 mTherefore, to convert nanometres to millimetres, multiply the nanometres by 10⁻⁶:
1 nm = 1 × 10⁻⁶ mmSo 70 nanometres is:
70 × 10⁻⁶ mm = 0.000 07 mmViruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.
Sherane rolls a standard, six-sided number cube. Find p (not composite).
Answer:
2/3
Step-by-step explanation:
A six sided number cube :
Sample space = (1, 2, 3, 4, 5, 6)
Non composite numbers on a six sided number cube = (1, 2, 3, 5)
Probability of an event = required outcome / Total possible outcomes
Required outcome = number of non composite numbers = 4
Total possible outcomes = sample space = 6
P(not composite) = 4 / 6 = 2/3