The equation that models the data in the table is:
[tex]c=22d[/tex]
Step-by-step explanation:The table that represent the days and cost is given by:
Days Cost
2 44
3 66
5 110
6 132
We see that the cost is a constant multiple of the number of days.
i.e. the equation is given by:
c=22d
i.e. the relationship is linear.
( Since, when d=2
we have: c=22×2=44
when d=3 we have:
c=22×3=66
and so on )
A particle moves along the curve below. y = 24 + x3 as it reaches the point (1, 5), the y-coordinate is increasing at a rate of 4 cm/s. how fast is the x-coordinate of the point changing at that instant?
To find the rate of change of the x-coordinate at the point (1, 5) with a given y-coordinate rate of change, we use the chain rule to differentiate the equation y = 24 + [tex]x^3[/tex] with respect to time, and solve for dx/dt.
Explanation:The student's question involves the relationship between the rates of change of the x-coordinate and y-coordinate of a particle moving along a curve. Given the equation y = 24 +[tex]x^3[/tex], we need to find how fast the x-coordinate is changing at the point (1, 5), given that the y-coordinate is increasing at a rate of 4 cm/s. To find this, we can use the chain rule from calculus to relate the rates of change. Differentiating both sides with respect to time t, we get dy/dt = 3[tex]x^2[/tex] dx/dt. Solving for dx/dt, we find the rate of change of the x-coordinate when x = 1 and dy/dt = 4 cm/s.
At the point (1, 5), [tex]\( \frac{{dx}}{{dt}} = \frac{4}{3} \)[/tex] cm/s when [tex]\( \frac{{dy}}{{dt}} = 4 \)[/tex] cm/s.
To find how fast the x-coordinate is changing [tex](\( \frac{{dx}}{{dt}} \))[/tex] when the y-coordinate is increasing [tex](\( \frac{{dy}}{{dt}} \)),[/tex] we'll use implicit differentiation.
Given [tex]\( y = 24 + x^3 \),[/tex] differentiate both sides with respect to time [tex](\( t \)):[/tex]
[tex]\[ \frac{{dy}}{{dt}} = \frac{{d}}{{dt}}(24 + x^3) \][/tex]
Given that [tex]\( \frac{{dy}}{{dt}} = 4 \)[/tex], and when [tex]\( x = 1 \) and \( y = 5 \),[/tex] we can find [tex]\( \frac{{dx}}{{dt}} \):[/tex]
[tex]\[ 4 = 0 + 3x^2 \cdot \frac{{dx}}{{dt}} \][/tex]
[tex]At \( x = 1 \):[/tex]
[tex]\[ 4 = 3(1)^2 \cdot \frac{{dx}}{{dt}} \][/tex]
[tex]\[ 4 = 3 \cdot \frac{{dx}}{{dt}} \][/tex]
[tex]\[ \frac{{dx}}{{dt}} = \frac{4}{3} \][/tex]
So, the x-coordinate of the point is changing at a rate of [tex]\( \frac{4}{3} \)[/tex] cm/s at that instant.
Can someone clearly explain and workout Q20? Much appreciated
Two geometric figures that are identical in shape, although not necessarily the same size, are called ____.
for a=3-5c when c=-0.5, what does a equal?
Plug in -0.5 for c
a = 3 - 5(-0.5)
Multiply -5 with (-0.5)
a = 3 + 2.5
Simplify
a = 5.5
a = 5.5 is your answer
hope this helps
In the formula 'a = 3-5c', 'a' becomes 5.5 when c=-0.5. This is derived by substituting -0.5 as 'c' in the given formula yielding the result of 5.5 after the calculation.
Explanation:The subject of your question is mathematics and it's about finding the value of 'a' in the formula: a = 3-5c when c=-0.5.
To answer your question, we'll substitute the value of 'c' into the formula:a = 3 - 5*(-0.5). When you multiply -5 with -0.5, the answer is 2.5.
Therefore, when you add 3 and 2.5, the answer is 5.5. So, when c = -0.5, the value of 'a' will be 5.5.
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Which of the following rational numbers is equal to 2 point 8 with bar over 8 ? twenty two over nine, twenty four over nine, twenty six over nine, twenty eight over nine
The rational number that equals to 2.8 (a decimal number that has repeating 8), from the options given, is twenty six over nine (26/9) because when converted to decimal it gives 2.89, which is closest to 2.8
Explanation:The question is asking which rational number is equal to 2.8 where the bar over the number indicates that it is repeating. The dot over the 8 implies that the number is actually 2.8888..., where the 8 is repeated indefinitely. So we need to find which fraction out of your given options: twenty two over nine, twenty four over nine, twenty six over nine, twenty eight over nine, equals to this decimal number.
To convert these fractions to decimal form:
22/9 = 2.44,
24/9 = 2.67,
26/9 = 2.89,
28/9 = 3.11
By comparing these values, we can see that twenty six over nine (26/9) is the decimal equivalent to 2.8 as it gives us 2.89 which is closest to it.
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What is the simplest form of this?
A line has slope 56 and y–intercept −3. Which answer is the equation of the line? y=−3x+5/6 y=5/6x−3 y=3x+5/6 y=5/6x+3
Answer:
The answer is the second one for sure y=5/6x−3.
Step-by-step explanation:
The equation of the line is y = (5/6)x - 3 which is the correct answer would be option (B).
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
We have been given a line that has a slope of 5/6 and a y-intercept is -3.
Let the required line of the equation would be as
y = mx + c
Where m is the slope of the line
We have given the y-intercept is -3 which means the x-coordinates will be zero.
Substitute the value of x = 0 and y = -3 in the above equation to get c.
⇒ -3 = m(0) + c
⇒ -3 = c
The slope of the line m = 5/6 which is given in the question,
Substitute the value of m = 5/6 and c = -3 in the equation y = mx + c
⇒ y = (5/6)x - 3
Therefore, the equation of the line is y = (5/6)x - 3.
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Find the point of intersection of the pair of straight lines. 2x + 6y = 26 −9x + 7y = 2
Vanessa has scored 45 32 and 37 are three math quizzes she will take one more quiz and she wants a quiz average of at least 40 what is the minimum score Vanessa needs to earn her 4th quiz
4 total quizzes,
for a 40 average on 4 quizzes she needs 40*4 = 160 total points
for 3 quizzes she has 45 +32 +37 = 114 points
160-114 = 46, she needs at least a 46 on the 4th quiz
Using the approximation 3.14 for pi, what is the radius of a circle with circumference 28.3 m?
Using π ≈ 3.14, the radius of a circle with circumference 28.3 m is approximately 4.5 meters.
Step 1:
Write down the formula for the circumference of a circle.
The formula for the circumference (C) of a circle is given by:
[tex]\[ C = 2 \pi r \][/tex]
Step 2:
Substitute the given value for the circumference into the formula.
Given [tex]\(C = 28.3\)[/tex] m, we use the approximation [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[ 28.3 = 2 \times 3.14 \times r \][/tex]
Step 3:
Solve for the radius (r).
Divide both sides of the equation by [tex]\(2 \times 3.14\)[/tex]:
[tex]\[ r = \frac{28.3}{2 \times 3.14} \][/tex]
Step 4:
Calculate the value of (r).
[tex]\[ r = \frac{28.3}{6.28} \][/tex]
[tex]\[ r \approx 4.5 \text{ m} \][/tex]
So, the radius of the circle with a circumference of 28.3 m, using the approximation [tex]\(\pi \approx 3.14\)[/tex], is approximately 4.5 meters.
5.95, 5.90, 5.85, 5.80, 5.75, 5.75, 5.75, 5.65, 5.65, 5.65, 5.55, 5.55, 5.55, 5.55, 5.55, 5.55
The men's pole vault finals' scores for the 2004 Olympic games in Athens are shown. Is the mean a good descriptor of this set?
Answer:
Step-by-step explanation:
Yes because their are no outlier
PLEASE HELP ME!!!! 20 PNTS!!!!!
Simplify the expression:
[tex] \frac{ \sqrt{ - 16} }{(3 - 3i) + (1 - 2i)} [/tex]
A.
[tex] \frac{ - 20 - 16i}{9} [/tex]
B.
[tex] \frac{8 + 4i}{15} [/tex]
C.
[tex] \frac{8 - 4i}{15} [/tex]
D.
[tex] \frac{ - 20 + 16i}{41} [/tex]
A ladder is leaned against a building. the bottom of the ladder is 11 feet from the building. the top of the ladder is 19 feet above the ground. what is the slope of the ladder?
b. what does the slope of the ladder mean in the real world?
c. if the ladder were set closer to the building, would it be harder or easier to climb? explain in terms of the slope of the ladder.
Given that the rise and run of a ladder are 19 feet and 11 feet respectively:
a. Slope of the ladder = 19/11 = 1.7
b. Slope = inclination of the ladder
c. The slope will be steeper and difficult to climb if the ladder was set closer to the wall of the building.
Recall:
Slope = vertical distance along a line / horizontal distance = rise/runa. run = 11 feet
rise = 19 feet
Slope of the ladder = [tex]\frac{rise}{run} = \frac{19}{11}[/tex] = 1.7
b. The slope of the ladder refers to the inclination of the ladder to the wall.
c. If the ladder was set close to the wall of the building, the more steeper the slope would be. This would make it difficult to climb compared to a gentle slope.
In summary, given that the rise and run of a ladder are 19 feet and 11 feet respectively:
a. Slope of the ladder = 19/11 = 1.7
b. Slope = inclination of the ladder
c. The slope will be steeper and difficult to climb if the ladder was set closer to the wall of the building.
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What is the difference between 150.2 and 146.4?
Which expression represents the phrase, "one fifth the sum of 14 and a number"?
a) 15(14+x)
b) 15(14)+x
c) 15+14+x
d) 15x+14
Let
x--------> the number
we know that
1) the phrase, "the sum of 14 and a number"
represent the expression --------> [tex](14+x)[/tex]
and
2) the complete phrase, "one fifth the sum of 14 and a number"
represent the expression --------> [tex]\frac{1}{5}(14+x)[/tex]
therefore
the answer is
[tex]\frac{1}{5}(14+x)[/tex]
Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 2 miles from her home. The football field is 8 miles from the library.
Using Pythagoras theorem, we can find that the library is approximately 7.746 miles from the football field, which forms a right-angled triangle with Kristen's home and the park.
Explanation:This problem is a classic example of use of Pythagoras theorem in right-angle triangle. Here, the distances of Kristen's home, the park, and the football field form a right-angle triangle, with the distance from the park to the library acting as the altitude of the triangle. To find the distance from the library to the football field, we can use the relation:
[tex]\text{(Hypotenuse)}^2 = \text{(Base)}^2 + \text{(Perpendicular)}^2[/tex]According to the problem, The library is 2 miles from her home (Base), The football field is 8 miles from the library (Hypotenuse). So the distance from the library to the football field can be calculated as:
[tex]\text{Perpendicular} = \sqrt{(\text{Hypotenuse})^2 - (\text{Base})^2} = \sqrt{(8\text{ miles})^2 - (2\text{ miles})^2} = \sqrt{60} \approx 7.746 \text{ miles}[/tex]
So, the library is approximately 7.746 miles from the football field.
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The measures of the interior angles in a polygon are consecutive integers. the smallest angle measures 136 degrees. how many sides does this polygon have?
Please help! What is the solution of 4|x-3|-8=8?
A) x=-1 or x=7
B) x=19/4 or x=7
C) x=-1 or x=19/4
D) x=3/4 or x=19/4
John bikes 22km per hour and starts at mile 10. Gwynn bikes 28 km per hour and starts at mile 0. Which system of linear equations represents this situation?
Answer:
[tex]d=22t+10...(1)[/tex]
[tex]d=28t...(2)[/tex]
Step-by-step explanation:
Let t represent the number of hours and d represent the total distance after t hours.
We have been given that John bikes 22 km per hour and starts at mile 10. This means that slope of line will be 22 and y-intercept will be 10. So total distance covered by John in t hours will be:
[tex]d=22t+10...(1)[/tex]
We are also told that Gwynn bikes 28 km per hour and starts at mile 0. This means that slope of line will be 28 and y-intercept will be 0. So total distance covered by Gwynn in t hours will be:
[tex]d=28t+0[/tex]
[tex]d=28t...(2)[/tex]
Therefore, our required system of linear equations will be:
[tex]d=22t+10...(1)[/tex]
[tex]d=28t...(2)[/tex]
If you triple a number and add 11 you get 200 what is the number
A student scored 83 and 91 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive ...?
PLEASE HELP!!!!!!!!!!!
Susan makes 5 fruit cups for the picnic.In each cup,she has 5 strawberries and 3 kiwi. Joanna uses the same number of total fruits to make her strawberry and kiwi fruit cups,but she uses 4 cups. In each cup she uses 8 strawberries.
How many are in each fruit cup Joanna makes?
The bottom of a ladder must be placed 4 feet from a wall. the ladder is 12 feet long. how far above the ground does the ladder touch the wall? round your number to the nearest tenth.
There are 11.3 feet far above the ground does the ladder touch the wall.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
The bottom of a ladder must be placed 4 feet from a wall. the ladder is 12 feet long.
Now, Let the length of the ladder above the ground does the ladder touch the wall = x
Hence, We get;
x² = 12² - 4²
x² = 144 - 16
x² = 128
x = √128
x = 11.3 feet
Thus, the length of the ladder above the ground does the ladder touch the wall = 1.3 feet
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How would I solve 2x - 3 = x + 2?
Answer: 2x-3=x+2
. -x -x
1x -3=2
+3 +3
1x=5
1x divide by 1x, 5 divide by 1x
Which will be:
X=5
The expression 6s2 represents the surface area of a cube with edges of length s. what is the cube's surface area when s = 8?
Anyone? I’m so stuck
A = 180-110 = 70
angle A is 70 degrees
7t + 4 is less than or equal to 3t
A random sample of n = 4 scores is obtained from a population with a mean of m = 80 and a standard deviation of s = 10. if the sample mean is m = 90, what is the z-score for the sample mean
At the movie theatre, child admission is $5.40 and adult admission is $9.20 . on thursday, twice as many adult tickets as child tickets were sold, for a total sales of $785.40 . how many child tickets were sold that day
which natural phenomenon is the best example of periodic behavior
Answer: The answer is the number of hours of daylight each day.
Step-by-step explanation: We are to give the best example of a natural phenomenon of periodic behavior.
A periodic behavior means the behavior which repeats itself in equal intervals of time or periods. Since we are talking about a natural phenomenon, so the rotation of earth around the sun can be an example.
In other words, we can say the number of hours of daylight each day will be the proper example, because the sun gives light for almost same number of hours each day.
Thus, the natural phenomenon is the number of hours of daylight each day.