Answer:
- high tide occurs at 12 noon and 12 midnight
- Low tide occurs at 6 a.m and 6 p.m
- maximum depth value = 20 ft
- Minimum depth value = 15 ft
Step-by-step explanation:
The depth is modelled as;
y = 20 + 5 cos (πt/6)
We are told that t = 0 represents 12:00 midnight.
This is high tide because at t = 0, the cos function will be at it's maximum value of 1 since cos 0 = 1.
Max depth value is;
y = 20 + 5(0)
y = 20 ft
Minimum depth value will be the low tide and it will be when the cos function is equal to -1.
Thus;
y = 20 + 5(-1)
y = 15 ft
Since t represents number of hours and since at 12 midnight, t = 0, thus; high tide will occur again at;
12 noon
Also, let's check for low tide.
Let's try t = 6 which means 6 a.m
Thus;
y = 20 + 5 cos (π(6)/6)
y = 20 + 5 cos π
Cos π has a value of -1
Thus;
y = 20 + 5(-1)
y = 20 - 5
y = 15 ft
Thus;
Low tide occurs at 6 a.m and 6 p.m
solve the inequality |x +4|-4>0
The inequality form of the given expression is:
x < -8 or x > 0
The interval notation is : (−∞,−8)∪(0,∞)
Given, the expression is |x + 4| - 4 > 0
An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
Isolate the variable by dividing each side by factors that don't contain the variable.
⇒ |x + 4| - 4 > 0
⇒ |x + 4| > -4
Remove mod.
⇒ x + 4 > -4 or x - 4 > -4
⇒ x > -4 -4 or x > -4 +4
⇒ x <-8 or x > 0
Hence the internal notation is :
(−∞,−8)∪(0,∞)
The required graph is plotted.
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How many significant digits are in the given measurement:
6040.0050 m
7
0
8
4
Answer:
8 significant digits
Step-by-step explanation:
Let's count
6040.0050
⬇ ⬇⬇⬇.⬇ ⬇⬇ ⬇
1 234 567 8
therefore it's 8 significant figures
Prove the following inequality.
The proof of the inequality → (a + b)²/2 ≥ 2ab, is given below -
We have the following inequality -
(a + b)²/2 ≥ 2ab
We have to prove it.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
According to the question, we have -
Inequality -
(a + b)²/2 ≥ 2ab
Proof -
Starting from the inequality - (a - b)² ≥ 0
(a - b)² ≥ 0
a² + b² - 2ab ≥ 0
a² + b² - 2ab + 2ab ≥ 2ab
a² + b² ≥ 2ab
Add - 2ab on both sides, we get -
a² + b² + 2ab ≥ 4ab
(a + b)² ≥ 4ab
Divide both sides by 2, we get -
(a + b)²/2 ≥ 2ab
Hence Proved.
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Find the reciprocal of -1 1/17
Answer:
17/-11
Step-by-step explanation:
why,because reciprocal in mathematics means changing the numerator to the denominator and denominator to numerator.
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10. Two of the greatest rainfalls ever recorded were on, July 4, 1956.
In Unionville, Maryland it rained 1.23 in. in 1 min. In Curtea-de-
Arges, Romania on July 7, 1889 it rained 8.1 in. in 20 min. If it
had rained for 20 min in Unionville at its same record pace, what
would be the difference between the two rainfall amounts?
Answer:
The difference would be Unionville would have had 24.6 in. of rain and Arges only had 8.1 in
Step-by-step explanation:
tim has 74 socks, that are white or black. he has 1 more pair of white socks than black socks. how many individual socks of each color does he have?
Tim owns 74 socks, the colours of which are unknown.
He does, however, have an additional pair that is white rather than black.
Therefore, it suggests that we are working with the two hues white and black.
The result of dividing the total number of socks by two is:
= 74/2
= 37 socks, two pairs each for black and white.
But let's not forget that Tim has a pair of white socks in addition to his black pair.
The total number of white socks is equal to= 37+1= 38 socks.
Total black sock pairs= 37-1=36 socks.
Last but not least, the question asks us to count the number of single socks rather than pairs.
For white then:
There will be = (38x 2) socks per pair.
= 76 socks
For Black
The individual socks will be = (36 × 2)socks
= 72 socks
We can then deduce that there are 76 individual socks for white and 72 individual socks for black.
How many pairs of socks must you take to find a matching pair?The solution would have to be four. Despite the large number of socks in the drawer, there are only three different colours, so if you take four socks, you will undoubtedly find at least one pair that matches.
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List the numbers in order from least to greatest.
5/8, 1/2, 0.3 , -3/5 , -0.8 , -1/10
Answer:
-3/5, -1/10, -0.8, 0.3, 1/2, 5/8
Step-by-step explanation:
negatives are always less than positive numbers. As you can see the first numbers that are negative count down and then once it turns positive the numbers count up. For example, it goes -3,-1,-0 then 0,1,5
Please answer the 2 question in photo [ Brainliest + easy points ]
the density of a certain material is such that it weighs 3 grams per fluid ounce of volume. express this density in ounces per liter.
The density of the material in ounce per liter is 0.1059 ounce per liter.
How to express the density in ounce per liter?The ounce per liter conversion selector on this page selects the density measurement unit to convert to starting from ounces per liter (oz/L).
Given that,
Density = 3 grams per fluid ounce
Convert grams to ounce.
1 grams = 0.0353 ounce
Then
Density = 3 * 0.0353 ounce per fluid grams
= 0.1059 ounce per fluid grams
Convert fluid gram to liter
Density = 0.1059 ounce per 1000 liter
= 0.0001059 ounce per liter
Hence, the density in ounce per liter is 0.0001059 ounce per liter.
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Write 2.5 as a mixed number and as an improper fraction. Write your answers in simplest form.
Answer:5/2 and 2 1/2
Step-by-step explanation:
Answer:
Step-by-step explanation:
2.5 as a mixed number is 2 1/2 since 1/2 = 0.5
2.5 as an improper fraction is 5/2
if i drop a watermelon from the top of a water tower, and it takes 3.34 seconds to hit the ground, calculate how tall the tower is in meters.
The height of the water tower is found to be 54.66 meters.
What is acceleration due to gravity?A free-falling object is one that is falling solely due to gravity.
Some key features regarding the acceleration due to gravity are-
A free-falling component has a downward acceleration of 9.8 m/s/s (on Earth). This magnitude for the acceleration of a free-falling object is so significant that it has its own name. The acceleration of gravity is the acceleration of any object moving solely under the influence of gravity. In fact, the acceleration of gravity is so important quantity that scientists have a special symbol to represent it - the symbol g. The most precise numerical value for gravity's acceleration is 9.8 m/s/s.Now, according to the question;
It takes a watermelon 3.34 sec to reach the ground.
Use the equation of motion in straight line.
D = (1/2) x (gravity) x (time)²
D is the height of the water tower.
= (1/2) x (9.8 m/s²) x (3.34 sec)²
= (4.9 m/s²) x (11.16 sec²)
D = 54.66 meters.
Thus, the height of the water tower is estimated as 54.66 meters.
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Show graphically that the system of linear equations 5x – y = 14 ; x – 2y =1 has a unique solution. Write the coordinates where line x – 2y =1 intersects the X-axis. Write the solution.
The graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)
The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)
How to Determine the Solution to the System of Equations?Given the linear equations:
5x – y = 14 ---> equation 1
x – 2y = 1 ---> equation 2
Rewrite both equations in slope-intercept form as y = mx + b, where b represents the y-intercept of the line and m represents the slope.
5x - y = 14
-y = -5x + 14
y = 5x - 14 (slope is 5 and y-intercept is -14)
x - 2y = 1
-2y = -x + 1
y = 1/2x - 1/2 (slope is 1/2, and the y-intercept is -1/2).
Therefore, the graph of the system of linear equations is shown in the image below, where the solution is: (3, 1)
The coordinates where x - 2y = 1 intersects the x-axis (horizontal axis) is: (-14, 0)
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Let g(x) = {2x + 4 if x < −1, x + 4 if x ≥ −1.
Find the value of g^-1(-1)
The inverse of a function when x = -1 is g^-1(-1) = -5/2
Inverse of a functionLinear functions are function that has a leading degree of 1. Given the expression below;
g(x) = 2x + 4
Determine the inverse
y = 2x + 4
Replace y with x
x = 2y + 4
Make y the subject of the formula
2y = x - 4
y = (x-4)/2
g^-1(x) = (x-4)/2
Substitute x = -1 into the equation
g^-1(x) = (-1-4)/2
g^-1(-1) = -5/2
Hence the inverse of a function when x = -1 is g^-1(-1) = -5/2
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How many times larger is 7 x 10^5 than 2 x 10^3?
Answer:
698,000
Step-by-step explanation:
7×10^5=700000
2×10^3=2000
700,000-2000=698,000
The given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.
Given that,
To determine, how many times larger is 7 x 10^5 than 2 x 10^3.
What is the Ratio?The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
We have two values, here we have to determine the relationship between the two values.
[tex]ratio = 7*10^5 / 2 * 10^3\\Ratio = 3.5 * 10 ^2[/tex]
Implies,
[tex]7*10^5 = 3.5*10^2 (2 * 10^3)[/tex]
Thus, the given 7 * [tex]10^5[/tex] is 3.5*10² times larger than 2 * 10³.
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russell runs 9/10 miles in 5 minutes. at this rate how many miles can he run in one minute
Answer:
I´m pretty sure it is 1.8 miles
Step-by-step explanation:
Please Help I will give Brainlist !!! Its a Math Problem !! Given that the length of two sides of a triangle are 3 cm and 2 cm, which of the below is the only measure that could possibly be a length of the last unknown side?
Question options:
2 cm
5 cm
6 cm
9 cm
Answer:
2
Step-by-step explanation:
Triangle side theorem states the sum of the lengths of any two sides of a triangle must be greater than the remaining side
3 + 2 = 5 third side would have to be LESS than 5
so the only answer is 2 cm
during math class, you find the length of a right triangle's hypotenuse with a theorem created long ago. who do you have to thank for that theorem?
The length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = the hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
We need to find the length of a right triangle's hypotenuse with a theorem created long ago.
What is a Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
The Pythagoras theorem equation is expressed as, c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Therefore, the length of a right triangle's hypotenuse with a theorem created long ago is c² = a² + b², where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
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Gary, the school chef, needs to make 40
tacos for every 15 students. How many tacos
would Gary need to prepare for 3 students?
The number of tacos that is needed for 3 students is 8 tacos.
How many tacos would be needed for 3 students?
The first step is to determine the number of tacos that is needed for one student. To determine this value, divide the total number of tacos by the total number of students.
Division is the mathematical operation that is used to determine the quotient of two or more numbers. Division entails splitting a number into equal groups using another number. The sign used to denote division is ÷
Tacos that should be prepared for one student = total tacos / number of students
= 40 / 15
In order to determine the number of tacos needed for 3 students, multiply the result gotten in the previous step by 3. Multiplication is the process used in determining the product of two or more numbers. The sign used to denote multiplication is x .
Tacos needed for 3 students = (40 / 15) x 3 = 8
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if angle 2 equals (2x+5)degrees and angle 3 equals 85degrees, what is the value of x
Based on the information given, the value of x is 40 degrees
What are corresponding angles?Corresponding angles are defined as any pair of angles which on the same side of one or two lines, there is a cut through by a transversal.
It is also important to note that when a transversal intersects two parallel lines, the corresponding angles of the lines would be equal.
Given the angles;
Angle 2 equals (2x+5) degrees Angle 3 equals 85 degreesWe have that;
Angle 2 = Angle 3
Substitute the values
2x + 5 = 85
collect like terms
2x = 85 - 5
2x = 80
Make 'x' the subject by dividing both sides by 2
2x/ 2 = 80/ 2
x = 40 degrees
Thus, the value of x is 40 degrees
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which expression shows the prime factorization of 36? 2 × 2 × 3 2 × 2 × 3 2 × 3 × 3 2 × 3 × 3 2 × 2 × 2 × 3 × 3 2 × 2 × 2 × 3 × 3 2 × 2 × 3 × 3
Answer:
36 = 2 x 2 x 3 x 3
Answer:
2 2/3 * 2 2/3 = 64/9 = 7 1/9 ≅ 7.1111111
Step-by-step explanation:
The result:
2 2/3 * 2 2/3 = 64/
9
= 7 1/
9
≅ 7.1111111
Spelled result in words is sixty-four ninths (or seven and one ninth).
How do we solve fractions step by step?
Conversion a mixed number 2 2/
3
to a improper fraction: 2 2/3 = 2 2/
3
= 2 · 3 + 2/
3
= 6 + 2/
3
= 8/
3
To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/
3
= 6/
3
b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8
c) Write a previous answer (new numerator 8) over the denominator 3.
Two and two thirds is eight thirds
Multiple: 8/
3
* 8/
3
= 8 · 8/
3 · 3
= 64/
9
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(64, 9) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eight thirds multiplied by eight thirds is sixty-four ninths.
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write an equation of the line . through (1,-2);parallel to 2x=3y+4
Answer:
y = 2/3x - 8/3
or 2x = 3y + 8
Step-by-step explanation:
2x = 3y + 4
3y = 2x - 4
y = 2/3x - 4/3
If two lines are parallel, their slopes are equal
if m = 2/3, y = -2, x = 1
y = mx + b
-2 = 2/3(1) + b
-2 = 2/3 + b
b = -2 - 2/3 = -8/3
y = 2/3x - 8/3
or 3y = 2x - 8
or 2x = 3y + 8
The measure of an angle is 56.3°. What is the measure of its complementary angle?
Answer:
33.7
Step-by-step explanation:
Complementary angles are angles that when added, sum up to 90*
First, make the equation, x being the missing angle
90*= x + 56.3
Rewrite the equation to find the missing angle
90 - 56.3 = x
x= 33.7
Answer:33.7°
Step-by-step explanation:
To find the complement of an angle, subtract that angle's measurement from 90 degrees. The result will be the complement
90° - 56.3°
=33.7°
find the indicated value for the given function. f(4) =|2x-7|
Answer: 1
I did this problem a couple times and got 1 every time
Best painters charges $100 to paint a room and $15 per can of paint used. Top Painters charges $75 to paint a room and $30 per can of paint used. Which equation could be used to find the number of cans of paint (p) for which the cost of the two companies is the same?
a) 45p = 175
b) p(100 + 15) = p(75 + 30)
c) 100p + 15 = 75p + 30
d) 15p + 100 = 30p + 75
d. 15p + 100 = 30p + 75
What clockwise angle rotations, if any, between 0 degrees and 360 degrees make the figure rotate onto themselves?
A clockwise 360 degrees angle rotation will make the figure rotate onto themselves.
Any angle rotations other than a 0 degree or a 360 degree will change the figure and so does not rotate onto themselves.
To rotate onto themselves, which means the figure should not be changed after the rotation transformation, we have to rotate it 360 degrees.
We are asked for a clockwise angle rotation, so the require angle rotation is of 360 degrees.
0 degree angle rotation will not make a rotation. So we will go with a 360 degree rotation. Any figure after a 'full circle' clockwise rotation will goes onto themselves.
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Which graph shows the function f(x) = x with an input of f ?
A coordinate plane with a line passing through (negative 4, negative 1), (negative 3, 0), and (0, 3).
A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).
A coordinate plane with a line passing through (negative 1, negative 3), (0, 0), and (1, 3).
A coordinate plane with a line passing through (negative 3, negative 2), (0, 0), and (3, 1).
Using translation concepts, the graph that shows that function f(x) = x with an input of f(x - 3) is given by:
A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).
What is the missing information?The input of the function, of f(x - 3), is missing.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the function is:
f(x) = x.
The translation is in the input, f(x - 3), meaning that the function is shifted 3 units right and defined by:
f(x - 3) = x - 3.
Hence three points on the graph are:
x = -2, f(x) = -5.x = 0, f(x) = -3.x = 3, f(x) = 0.Hence the correct description is:
A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).
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Answer:
D
Step-by-step explanation:
The price of a watch was increased by 20% to £162.
What was the price before the increase?
Answer:
120% = 162
10% = 13.5
100% = 135
so it's £135
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A parallelogram has an AREA of 7 square units. If the height that corresponds to a base is 14 units, what is the base?
Answer:
b = 0.5
Step-by-step explanation:
a = b x h
7 = 14b Divide both sides by 14
0.5 = b
Determine the inverse function of f(x)=1/7x-1/7
The inverse of the function → y= f(x) = 1/7x - 1/7 is -
f⁻¹(x) = 7x + 1.
We have -
y = f(x) = x/7 - 1/7
We have to find its inverse function.
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.
Step 2 - Rewrite the equation by solving for 'y'.
Step 3 - Replace 'y' with f⁻¹(x).
According to the question, the equation given is as follows
y = f(x) = x/7 - 1/7
Replace 'y' with 'x', we get -
x = y/7 - 1/7
Now, solve for y -
y/7 = x + 1/7
y = 7(x + 1/7)
y = 7x + 1
Replace 'y' with f⁻¹(x) -
f⁻¹(x) = 7x + 1
Hence, the inverse of the function → f(x) = 1/7x - 1/7 is -
f⁻¹(x) = 7x + 1.
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Please answer this math equation.
The table that represents the linear function is table (B)
How to determine the linear function?As a general rule, a linear function is any function that has a constant rate of change
This means that as the function independent value changes by a constant, the function dependent value changes by a constant
In other words, as the function x value changes by a constant, the function y value changes by a constant
Using the above as a guide, we can see the table B represents a linear function
This is so because, as x increases by 3, the y value decrease by -2
Hence, the table that represents the linear function is table (B)
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