The answer is , the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.
What is Integer?An integer is a whole number that can be positive, negative, or zero, but does not have any fractional or decimal parts. Integers can be represented on the number line, with zero at the center and positive integers to the right and negative integers to the left.
We use technique called "stars and bars" to solve this problem.
Using this approach, the number of positive integers less than 1000 with a digit sum of 4 is equal to the number of ways to arrange 4 stars and 3 bars. We can choose the positions of the bars in 7 ways (i.e., there are 7 places where we can place a bar), so the total number of such arrangements is 7 choose 3 (i.e., we choose 3 places for the bars out of the 7 possible places), which is:
7 choose 3 = 7! / (3! * (7-3)!) = 35
Note that we need to subtract the number of solutions that have 0 as the first digit, since we are only looking for positive integers. We can choose the positions of the bars in 6 ways (i.e., we cannot place a bar before the first star), so the number of such arrangements is 6 choose 3, which is:
6 choose 3 = 6! / (3! * (6-3)!) = 20
Therefore, the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.
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PLEASE SOMEONE HELP.
Functions are in the world all around us. You have used functions to model phenomena and to
make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you
can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or
even with the same function. A composition of functions is useful when a change in one function
will create a change in another function, which, in turn, affects a third function. For example,
suppose that humans build a housing development on land that was previously used as a corn
field. This change in land usage causes the number of birds in the area to decrease, which causes
the number of mosquitos to increase. You could model the increase in the number of mosquitoes
as a function of the number of birds in the area, which is a function of the number of humans that
live on that land.
You can also use the composition of functions to show that one function is the inverse of another
function. Recall that the graphs of inverse functions are reflections of each other over the line .
Think about these ideas as you read through the scenario below.
Last night it started raining as Hibah was closing up the store where she works. By 3 am, the roof
of the store developed a small hole and water began to leak onto the sales floor. The water
created a circular puddle on the floor. At any time, t,
in minutes, the radius of the puddle increases by 0.1
cm. The rain continued through the night, but stopped
by the time the morning shift arrived at the store at 7
am.
When the employees arrived at work, the leak and
water puddle were discovered. The employees
cleaned up the water puddle and placed a tall circular
bucket underneath the leak, which was still slowly
dripping. The capacity of the bucket can be expressed
as () = 83 + 42 − 6 + 5. By 10 am, the
amount of water in the bucket is () = 23 + 2 − 4 + 7.
Use the information given to explore some of the mathematical concepts you have practiced so
far by answering the questions below.
Answer:
Hibah's store developed a leak in the roof during a rainstorm, causing a circular puddle to form on the sales floor. The radius of the puddle increased by 0.1 cm per minute. The rain stopped by 7 am, when the morning shift arrived and discovered the puddle. The employees cleaned up the puddle and placed a bucket under the leak.
I hope that's what your looking for :)
1.
Find the area of the kite.
253.92 m²
380.88 m²
126.96 m²
190.44 m²
6.9 m
9.2 m
9.2 m
13.8 m
Step-by-step explanation:
Area of a kite = D1 × D2/2
D1 = 6.9 + 13.8 = 20.7m
D2 = 9.2 + 9.2 = 18.4m
Area =. 20.7 × 18.4
------------------
2
= 190.44m²
What is the period of the parent cosine function, y = cos(x)?
degrees
What is the period of the cosine function shown in the graph?
degrees
On a coordinate plane, a cosine curve is shown. The period of the cosine function is 1080 degrees.
The period of the parent cosine function, y = cos(x) is 1
Calculating the period of the parent cosine function, y = cos(x)?From the question, we have the following parameters that can be used in our computation:
The parent cosine function, y = cos(x)
For a parent cosine function, y = cos(x), the period is always 1
This is the general rule of the cosine sinusoidal function
Hence, the period of the parent cosine function, y = cos(x) is 1
The graph of the cosine function is added as an attachment
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PLS HELP WITH THIS MATH PROBLEM! Attached is the math problem.
The expression (x³y⁴)⁻²/(x⁻²y) is the same as x⁻⁴y⁻⁹
What are Exponents:Exponents are a way of expressing the repeated multiplication of a number by itself.
Here are the rules of exponents:
Product Rule: aᵇ × aⁿ = a⁽ᵇ⁺ⁿ⁾Quotient Rule: aᵇ / aⁿ = a⁽ᵇ⁻ⁿ⁾Power Rule: (aᵇ)ⁿ = aᵇⁿNegative Exponent Rule: a⁻ⁿ = 1/aⁿHere we have
The expression (x³y⁴)⁻²/(x⁻²y)
The above expression can be simplified as follows
Using the above exponent rules
=> (x³y⁴)⁻²/(x⁻²y)
=> (x³⁽⁻²⁾y⁴⁽⁻²⁾) /(x⁻²y) [ By the Power Rule: (aᵇ)ⁿ = aᵇⁿ ]
=> (x⁻⁶y⁻⁸) /(x⁻²y)
=> (x⁻⁶ · x² · y⁻⁸ · y⁻¹) [ By the Quotient Rule: aᵇ / aⁿ = a⁽ᵇ⁻ⁿ⁾ ]
=> (x⁻⁶⁺² y⁻⁸⁻¹) [ By the Product Rule: aᵇ × aⁿ = a⁽ᵇ⁺ⁿ⁾ ]
=> (x⁻⁴y⁻⁹)
Therefore,
The expression (x³y⁴)⁻²/(x⁻²y) is the same as x⁻⁴y⁻⁹
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A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet.
The letter selected will be recorded as the outcome.
Consider the following events.
Event X: The letter selected comes before "D".
Event Y : The letter selected is found in the word "CAGE".
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
a) The only outcome that satisfies both events X and Y is the letter C.
b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.
c) The complement of event X is {D, E, F, G}.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
The outcomes for each of the following events are:
(a) Event "X and Y": {C}
To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.
(b) Event "X or Y": {A, B, C, E, G}
The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.
(c) The complement of event X: {D, E, F, G}
The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.
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A girl who is flying a kite lets out 200 feet of string which makes an angle of 50° with the ground. Assuming that the string is stretched out, find, to the nearest foot, how high the kite is above ground.
The height of the kite from the ground when the angle is 50 degrees is 232 feet.
What is trigonometry?The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.
Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.
To find the height of the kite above the ground we use the trigonometric identity of tangent.
Thus, we have:
tan(50°) = h/200
Now, using cross multiplication:
h = 200 tan(50°) ≈ 232 feet
Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.
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2a. Find the volume of the model of Saturn.
2
Eliza made sphere-shaped
models of the Earth and Saturn
out of playdough for a science
project. The model of Earth has
a diameter of 4.8 cm and the
model of Saturn has a diameter
of 45.6 cm.
The volume of the modelled Saturn is 2176.40 cm³.
How to find the volume of the spherical Saturn?Eliza made sphere-shaped models of the Earth and Saturn out of playdough for a science project. The model of Earth has a diameter of 4.8 cm and the model of Saturn has a diameter of 45.6 cm.
Therefore, the volume of the spherical Saturn can be found as follows:
volume of the Saturn = 4 / 3 πr³
where
r = radius
Therefore,
r = 45.6 / 2 = 22.8 cm
volume of the Saturn = 4 / 3 × 3.14 × 22.8²
volume of the Saturn = 4 / 3 × 3.14 × 519.84
volume of the Saturn = 6529.1904 / 3
volume of the Saturn = 2176.3968
volume of the Saturn = 2176.40 cm³
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How do I solve this equation?? With the steps given below
Answer:
Step-by-step explanation:
What is the measure of angle B?
Answer:
36°
Step-by-step explanation:
angle a= 180-117
angle a=63°. because angles on straight line add to 180°
angle b= 180-81-63
angle b=36°. because angles in triangle add to 180°
need help offering 15 points
Answer: C
Step-by-step explanation:
your typical equation for varies inversely is y=k/x
here E = k/d² from the wording of problem. plug in numbers to solve for k.
120=k/20²
k=48000
plug k back in to get generic E equation.
E=48000/d²
What is the place value of 1 of 574.8931.
What’s the range of f(x)=6x/(x^2-9)
The range of a function refers to the set of all possible output values that the function can produce for its corresponding input values. In this case, the function is:
f(x) = 6x / (x^2 - 9)
To find the range of this function, we need to consider the restrictions on the denominator (x^2 - 9) that would make the function undefined.
The denominator (x^2 - 9) can be factored as a difference of squares:
x^2 - 9 = (x + 3)(x - 3)
So, the function is undefined when the denominator is equal to zero, i.e., when:
(x + 3)(x - 3) = 0
This occurs when x = -3 or x = 3.
Now, we need to consider the behavior of the function as x approaches these values. As x approaches -3 or 3 from the left, the function becomes increasingly negative, and as x approaches -3 or 3 from the right, the function becomes increasingly positive. This is because the numerator (6x) remains constant while the denominator approaches zero, resulting in a very large positive or negative value for f(x).
Since the function can approach arbitrarily large positive or negative values as x approaches -3 or 3, respectively, the range of the function is (-∞, ∞), which represents all real numbers except for the values -3 and 3. In interval notation, the range of the function can be written as:
Range of f(x): (-∞, ∞) \ {-3, 3}
What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, increases in value. As x increases in value, increases in value. B. As x decreases in value, decreases in value. As x increases in value, increases in value. C. As x decreases in value, increases in value. As x increases in value, decreases in value. D. As x decreases in value, decreases in value. As x increases in value, decreases in value.
The correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.
What is a function and equation?A mathematical object called a function accepts inputs (often represented by the symbol x) and creates outputs (typically represented by the symbol y or f(x)). An equation can be used to describe a function, although a function is not always defined by an equation.
It may incorporate one or more variables, but it does not always indicate how those variables are related.
For instance, even if the equation 2x + 3 = 7 involves the variable x, it does not define a function.
Given the function starts at (-3, 0) and extends upwards and to the right.
Thus, if x approaches negative infinity, the function cannot take on negative values, so the graph approaches the x-axis but never touches or goes below it.
Hence, the correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.
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divide. State the quotient in simplest form. 4x^5/
Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.
what is ratio ?In addition, ratios can be used to compare components of an ensemble, such as the ration of a circle's surface area to its circumference. As it is a linear correlation that cannot be reduced, the ratio in this instance is not simplified. In mathematics, science, economics, and many other disciplines, ratios are frequently employed to explain and study the quantitative relationships between various values.
given
The ratio is:
[tex]4x^5 / (2x^3)[/tex]
We can divide the numerator by the denominator to simplify the quotient.
By dividing 4x5 by 2x3, we obtain:
[tex](4x^5) / (2x^3) = 2x^(5-3) = 2x^2[/tex]
Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.
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how do i solve this. step by step
The equation of the line is
y = (-1/2)x + 3How to find the equation of the lineTo find the equation of the line passing through the points (2,2) and (-2,0), we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where
m is the slope of the line, and
(x1, y1) are the coordinates of one of the points on the line.
First, we need to find the slope of the line. The slope is given by:
m = (0 - 2) / (-2 - 2) = -1/2
substituting the points
y - 2 = (-1/2)(x - 2)
Expanding the right side and simplifying, we get:
y - 2 = (-1/2)x + 1
y = (-1/2)x + 3
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Quadrilateral ABCD is the result of a reflection of quadrilateral EFGH over the line.
Which line segment in the image corresponds to EH⎯in the pre-image?
Responses
CD⎯
BC⎯
AB⎯
AD⎯
The answer of the given question based on the quadrilateral is , the line segment corresponding to EH⎯ is AD⎯.
What is Line segment?A line segment is a part of a line that consists of two endpoints and all the points between those endpoints that are collinear (lying on the same straight line). In other words, a line segment is a straight line that is bounded by two distinct points. A line segment is usually denoted by drawing a line over the two endpoints and labeling it with a single letter representing the segment name or by labeling the endpoints with capital letters and drawing a bar over them to indicate the segment between them.
A line segment has a finite length and can be measured using a ruler or a measuring tape. The length of line segment is distance between its two endpoints.
In the pre-image, the line segment corresponding to EH⎯ is AD⎯.
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PLEASE HELP!
A wool tapestry is 32 years older than a linen tapestry. Twenty years ago, the wool tapestry was twice as old as the linen tapestry. Find the present age of each.
Answer choices:
a. 83, 51
b. 84, 52
c. 85, 53
d. 86, 54
e. 87, 55
Explain in detail how you got to the answer.
Let's use the variables w and l to represent the current ages of the wool and linen tapestries, respectively.
From the problem, we know that:
w = l + 32 (the wool tapestry is 32 years older than the linen tapestry)
w - 20 = 2(l - 20) (twenty years ago, the wool tapestry was twice as old as the linen tapestry)
We can simplify the second equation by distributing the 2:
w - 20 = 2l - 40
Now we can substitute the first equation into the second equation to eliminate w:
(l + 32) - 20 = 2l - 40
Simplifying this equation, we get:
l + 12 = 2l - 40
Adding 40 to both sides:
l + 52 = 2l
Subtracting l from both sides:
l = 52
Now we can use the first equation to find w:
w = l + 32 = 52 + 32 = 84
Therefore, the present age of the wool tapestry is 84 years old, and the present age of the linen tapestry is 52 years old.
So the answer is option (b) 84, 52.
Which number line shows the solution set for |8-2p|= 6?
Answer:
p = 1 or p = 7
So first number line is the answer we are looking for.
Step-by-step explanation:
|8-2p| = 6
We are asked to find the absolute value for this equation.To do that, we need to get rid of the brakes and rewrite equation in two forms:
One in positive state and the other in negative.8 - 2p = 6
or
8 - 2p = -6
For the first state:
8 - 2p = 6
Subtract 8 from the both sides.- 2p = -2
Since both sides are in negative form, they will have positive value.2p = 2
Divide both sides by 2.p = 1
Now, the second state:
8 - 2p = -6
Subtract 8 from both sides.- 2p = -14
Again, both sides are negative and 2 negatives = 1 positive.2p = 14
Divide both sides by 2.p= 7
Marco planted 288 strawberry plants
in 12 rows. If each row had the same
number of plants, how many plants
were in each row?
offering 15 points help
Answer:
Step-by-step explanation: X=1
An angle measure 57 degrees. Find the second angle that will make the 2 angles complementary and supplementary angles. (need answer ASAP)
i. The second angle that will make the 2 angles complementary is 33^o.
ii. The second angle that will make the 2 angles supplementary is 123^o.
What are complementary and supplementary angles?Complementary angles are measure of given angles whose addition gives a right angle i.e 90^o. While two or more angles are supplementary when their addition produces 180^o.
a. To find the second angle that will make the 2 angles complementary, we have;
let the second angle be represented by x, then;
x + 57 = 90
x = 90 - 57
= 33
x = 33^o
b. To find the second angle that will make the 2 angles supplementary, we have;
let the second angle be represented by y; so that;
y + 57 = 180
y = 180 - 57
= 123
y = 123^o
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Consider a political discussion group consisting of 10 democrats, 9 republicans, and 3 independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting no republicans
The probability of selecting no Republicans is approximately 0.2102, or about 21.02%.
What is probability?
Probability is a measure of the likelihood of an event occurring.
There are a total of 22 members in the group, consisting of 10 Democrats, 9 Republicans, and 3 Independents.
To find the probability of selecting no Republicans, we need to consider the possible ways in which two members can be selected without any Republicans being chosen.
There are two cases to consider:
The first person selected is not a Republican, and the second person selected is also not a Republican.
The first person selected is a Republican, and the second person selected is not a Republican.
Case 1: The probability of selecting a non-Republican member on the first draw is (10 + 3)/22, since there are 10 Democrats and 3 Independents out of 22 members. After the first member is selected, there are 21 members left, including 9 Republicans. The probability of selecting another non-Republican member on the second draw is (10 + 3 - 1)/(22 - 1), since there is one fewer member in the group after the first draw. Therefore, the probability of selecting no Republicans in this case is:
(10 + 3)/22 * (10 + 3 - 1)/(22 - 1) = 13/77
Case 2: The probability of selecting a Republican member on the first draw is 9/22, since there are 9 Republicans out of 22 members. After the first member is selected, there are 21 members left, including 10 Democrats and 3 Independents. The probability of selecting a non-Republican member on the second draw is (10 + 3)/(22 - 1), since there is one fewer member in the group after the first draw and we cannot select the Republican member again. Therefore, the probability of selecting no Republicans in this case is:
9/22 * (10 + 3)/(22 - 1) = 27/418
The total probability of selecting no Republicans is the sum of the probabilities in the two cases:
13/77 + 27/418 = 0.2102 (rounded to four decimal places)
Therefore, the probability of selecting no Republicans is approximately 0.2102, or about 21.02%.
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4. Kiara opened an investment account at a bank that pays 4% interest compounded annually. The table shows the activity in the account for 3 years. Year 1 2 3 Beginning Balance for Year $0.00 $1040.00 $1081.60 New Amount Deposited at Balance Beginning of Year $1000.00 $0.00 $0.00 $1000.00 $1040.00 $1081.60 Interest Interest Rate Earned 4% 4% 4% $40.00 $41.60 $43.26 Ending Balance for Year $1040.00 $1081,60 $1124.86 Which statement explains why the balance in this account has grown?
The balance in this account has grown because of the interest earned on the account, which is compounded annually. Each year, the interest is calculated based on the beginning balance for the year, which includes the previous year's balance plus any new deposits made at the beginning of the year. The interest rate is then applied to this balance, and the resulting interest is added to the balance. This process is repeated each year, causing the balance to grow over time. Additionally, in this particular example, new deposits were made in the first year, which further increased the balance and contributed to its growth.
Use completing the square to solve this quadratic equation. Check all that apply. x2 – 8x + 16 = 2
A.
x = 4 –
B.
x = –4 –
C.
x = 4 +
D.
x = –4 +
The correct options are- B. x = –4 – √2 and D. x = –4 + √2 are the roots of the given quadratic equation.
Define about the completing the square:When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.
Given quadratic equation:
x² – 8x + 16 = 2
This can be written as:
x² – 2*4x + 4² = 2
(x + 4)² = 2
Taking square root both sides:
√(x + 4)² = √2
(x + 4) = ±√2
x = ±√2 - 4
Or x = -4 + √2 and x = -4 - √2
Thus, the roots of the quadratic equation found by using the method of completing the square are - x = -4 + √2 and x = -4 - √2
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Complete question:
Use completing the square to solve this quadratic equation. Check all that apply. x² – 8x + 16 = 2
A. x = 4 –√2
B. x = –4 – √2
C. x = 4 + √2
D. x = –4 + √2
A ball is kicked straight up into the air from a height of 12 ft with an initial velocity of 64ft/s
Answer: the ball reaches a maximum height of 76 ft, and it takes 2 seconds to reach the highest point.
Step-by-step explanation: The acceleration induced by gravity is estimated to be approximately -32 ft/s^2, with the negative value indicating its downward direction.
At the apogee of the ball's trajectory, its vertical velocity experiences a momentary cessation.
The duration required for the ball to attain its maximum height can be determined through employment of the equation t = Vf / a, in which Vf denotes the attained final velocity (which is zero in the present scenario) and a denotes the gravitational acceleration. Upon substitution of the given numerical values, the resulting value of t is determined to be equal to 2 seconds, achieved through the utilization of the equation t = 64 / 32.
The determination of the maximum height achieved by the ball can be achieved through utilization of the formula h = hi + Vit + 1/2at^2, with hi denoting the initial height (12 ft), Vi representing the initial velocity (64 ft/s), a signifying the acceleration due to gravity (-32 ft/s^2), and t representing the time it takes for the ball to reach the apex of its trajectory (2 seconds). Upon entering the provided numerical values into the formula, the resulting value for the height of the object can be determined as h = 12 + 64(2) + 1/2(-32)(2)^2, which equates to 76 feet.
We saw that about 34% of
all students received at least one referral. Suppose we have concerns about the number of
disciplines in one particular school - it seems very high, and we've had concerns from parents at the school. In one particular year, 162 out of the 340 students at that school had a referral.
a. If we selected a random sample of 340 students, would the sample proportion that are
disciplined be approximately normally distributed? Why or why not?
b.
Use the normal distribution to find the probability of randomly selecting a sample of 340
students and finding that 162 of them or more have received a referral during that
particular year.
C. Would we think that is unusual? Explain your reasoning.
The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.
what is probability ?It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.
given
The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.
Calculating the sample proportion is necessary:
The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:
P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031
Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:
[tex]z = (0.476 - 0.34) / 0.031 = 4.39[/tex]
The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.
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Please help me im in the middle of a makeup quizzz. SHOW WORKK
Answer:
Hey
So my brother posted this on Yahoo
Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.
What you do now is the following:
Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)
So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°
The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.
Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°
= 88.8/360*π*7² - 24.5*sin 88.8°
≃ 13.5 cm²
(using area of ∆ = ½.a.b.sin C for the triangle)
b)
volume of water = cross-sectional area * length
≃ 13.5 * 30 cm³
≃ 404 cm³
Hoped it Helped
Step-by-step explanation:
Hey
So my brother posted this on Yahoo
Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.
What you do now is the following:
Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)
So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°
The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.
Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°
= 88.8/360*π*7² - 24.5*sin 88.8°
≃ 13.5 cm²
(using area of ∆ = ½.a.b.sin C for the triangle)
b)
volume of water = cross-sectional area * length
≃ 13.5 * 30 cm³
≃ 404 cm³
Hoped it Helped
3 x 3/8 simplify the expression
Answer:9/8
Step-by-step explanation:
Answer:
Step-by-step explanation:
3 x 3/8 = 1 1/8
Please help with this equation i’ll give brainliest!!
Answer:
The Correct answer is C
y>7
11.find the values of c that satisty the Mean Value Theorem. Show steps
Note that the value of C that satisfies the mean value theorem is -11/6
What is the mean value theorem?
The mean value theorem in mathematics says that for each given planar arc between two end points, there exists at least 1 point where the tangent to the arc is parallel to the secant between its ends. It is one of the most significant findings in real - world analysis.
To apply the mean value theorem, we need to check 2 conditions
f(x) is continuous on [-3, -1]
f(x) is differentiable on (-3, -1)
f(x) = (x^2-1/3x) satisfies both conditions.
Now, let's find the value of c that satisfies the mean value theorem:
f(-1) - f(-3) = f'(c)(-1 - (-3))
(2/3) - (-26/3) = f'(c)(2)
f'(c) = -4
To find the value of c, we need to solve for c in f'(c) = -4 ...
f '(x) = d/d x(x² -1/3x)
= 2x - 1/3
2c - 1/3 = -4
2c = -4 + 1/3
c = -11/6
So we can state that the value of c that satisfies the mean value theorem is -11/6
Larn more about the Mean Value Theorem:
https://brainly.com/question/30403137
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