To find the equation of a line parallel to y = x - 5 that goes through (7,0), we need to use the fact that parallel lines have the same slope.
The slope of the line y = x - 5 is 1, since the coefficient of x is 1. Therefore, the slope of the parallel line we want to find is also 1.
Using the point-slope form of a line, we can write the equation of the parallel line as:
y - y1 = m(x - x1)
where (x1, y1) is the point (7,0) and m is the slope of the line, which we know is 1.
Plugging in the values, we get:
y - 0 = 1(x - 7)
Simplifying, we get:
y = x - 7
Therefore, the equation of the line parallel to y = x - 5 that goes through (7,0) is y = x - 7.
Answer:
y = x - 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 5 ← is in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes , then
y = x + c ← is the partial equation
to find c substitute (7, 0 ) into the partial equation
0 = 7 + c ( subtract 7 from both sides )
- 7 = c
y = x - 7 ← equation of parallel line
Triangle
P
Q
R
PQR is a right triangle. The triangle has vertices at
P
(
−
2
,
4
)
,
Q
(
3
,
4
)
P(−2,4), Q(3,4) and
R
(
−
2
,
−
2
)
R(−2,−2). Graph the triangle on the triangle on the coordinate plane. To graph a triangle, plot all the vertices on the coordinate plane.
The graph of the triangle PQR is created by connect the three vertices.
What is triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is a clοsed, 2-dimensiοnal shape with 3 sides, 3 angles, and 3 vertices. A triangle is alsο a pοlygοn.
To graph the triangle PQR, we first plot the three vertices P(-2,4), Q(3,4), and R(-2,-2) on a coordinate plane:
Now, we connect the three vertices to form the triangle PQR:
Thus, the graph of the triangle ΔPQR is shown in the attachment..
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is 4/9 half of 8/18 shaw how you know
Answer:
To show this, we can simplify both fractions to a common denominator and compare them.
First, we can simplify 8/18 to 4/9 by dividing both the numerator and denominator by 2.
Then, we can compare 4/9 to 4/9.
Since both fractions are equal, we know that 4/9 is half of 8/18.
Alternatively, we can cross-multiply and simplify to compare the fractions:
4/9 = (1/2) * 8/18
4/9 = 4/9
loretta wants to put a circular mirror on a wall. the mirror has a radius of 23 inches. how many square inches of space will the mirror take up on the wall?
5,761.28 square inches of space will require the mirror to take up on the wall when Loretta wants to put a circular mirror on a wall.
We can find the space that the mirror takes up on the wall by using the area of a circle. it is given by:
A = πr^2
where
A = area of a circle
r =radius of a circle
Given data
radius of the mirror = 23 inches
The area of the mirror is:
A = π(23)^2
= 1,661π
where assume π =3.14159:
A = 1,661(3.14159)
A = 5,761.28 square inches
Therefore, the mirror will take up approximately 5,761.28 square inches of space on the wall.
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can yall for real help ?
The box plot below represents some data set. What percentage of the data values are greater than 65?
Answer: Unfortunately, without further context, I can't answer your question. Please post the box plot from the question first.
The line plot displays the cost of used books in dollars.
A horizontal line starting at 3 with tick marks every one unit up to 8. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 4, 5, and 7. There are four dots above 6.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are outliers present.
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The measure οf the center that is mοst apprοpriate tο represent the data in the line plοt graph is -
Optiοn A: The median is the best measure οf center because there are nο οutliers present.
What is line plοt?A line plοt is a graph that uses symbοls tο represent data abοve a frequency number line tο indicate the frequency οf each value. It is emplοyed tο arrange the data simply and is very simple tο understand.
Since the data is displayed using a line plοt and the plοt shοws the frequency οf data values, it is clear that the data is discrete.
In this case, the apprοpriate measure οf center wοuld be the median, which is the middle value when the data is arranged in οrder.
The fact that there are sοme dοts abοve certain values suggests that these values οccur mοre frequently in the data set.
Hοwever, this dοes nοt necessarily mean that there are οutliers present. Outliers are extreme values that are far away frοm the majοrity οf the data and can skew the results when using the mean as a measure οf center.
Therefοre, the median is the mοst apprοpriate measure οf center in this case because it is nοt affected by the presence οf οutliers and it represents the middle value οf the data set.
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I need help on this hope you guys can help
The measure of the angle in the angles is 151°
What is an angle?An angle is a figure in Plane Geometry which is formed by two rays or lines that share a common endpoint
the given angles are
<EFH = 44°
and <HFG 107°
This implies that <EFG = <EFH + <HFG
= 44 + 107 = 151°
In conclusion, the measure of angle <EFG = 151°
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a running shoe company wants to sponsor the fastest 3% of runners. you know that in this race, the running times are normally distributed with a mean of 7.2 minutes and a standard deviation of 0.56 minutes. how fast would you need to run to be sponsored by the company? g
Answer:
6.104
Step-by-step explanation:
Given that,
Mean, {eq}\mu = 6.8 {/eq}
Standard deviation, {eq}\sigma = 0.37 {/eq}
{eq}P(X < x) = 0.03\\ P(\dfrac{X - \mu}{\sigma} < \dfrac{x - \mu}{\sigma}) = 0.03\\ P(Z < \dfrac{x - 6.8}{0.37}) = 0.03\\ P(Z < z) = 0.03 {/eq}
Excel function for the value of z:
=NORMSINV(0.03)
{eq}z = -1.881\\ \dfrac{x - 6.8}{0.37} = -1.881\\ x = 6.8-1.881\times 0.37\\ \color{blue}{x = 6.104 \ minutes} {/eq}
To be sponsored by the running shoe company as one of the fastest 3% of runners, one would need to run faster than the upper 3rd percentile of runners. This can be calculated using the z-score formula which is given as; z = (x - μ) / σ where x is the value we want to find the percentile of, μ is the mean and σ is the standard deviation.
The z-score formula can be rearranged to solve for x which is the running time needed to be sponsored by the company as follows;x = z * σ + μWe want to find the upper 3rd percentile, which corresponds to a z-score of 1.88 (from z-tables or calculator).
Therefore;1.88 = (x - 7.2) / 0.56. Rearranging to solve for x;x = 1.88 * 0.56 + 7.2x = 8.1888 (rounded to 4 decimal places)Therefore, one would need to run faster than 8.1888 minutes to be sponsored by the running shoe company as one of the fastest 3% of runners.
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I need a answer for this
The graph that represents a function is the absolute value graph
Identifying the graph that represents a functionThe vertical line test is a way to determine whether a graph represents a function or not.
To apply the vertical line test, we draw a vertical line through the graph.
If the vertical line intersects the graph at more than one point, then the graph does not represent a function. If the vertical line intersects the graph at only one point, then the graph represents a function.The graph that represents a function using the above as a guide is the absolute value graph in option a
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A petri dish contains 4 viruses. Each hour, the number of viruses increases, as shown in the table. The population change can be modeled by a geometric sequence. Write a recursive formula and an explicit formula that can model this sequence. Use the formulas to predict how many viruses will be in the dish by the 7th hour.
We predict that there will be 512 viruses in the dish after 7 hours.
What is the model of the population?To model the population growth of the viruses in the dish, we can use a geometric sequence with a common ratio of 2, because the number of viruses doubles every hour.
Let Vn be the number of viruses in the dish after n hours. Then we have:
Recursive formula: Vn = 2Vn-1, with V0 = 4 (since we start with 4 viruses).
Explicit formula: Vn = 4 × 2n.
To predict how many viruses will be in the dish by the 7th hour, we can plug n = 7 into the explicit formula:
V7 = 4 × 27 = 4 × 128 = 512.
Therefore, we predict that there will be 512 viruses in the dish after 7 hours.
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Express the trig ratios as fractions in simplest terms
Help asap please!!!!
The value of the identities are;
cos F = 19/20
sin E= √39/20
sin E and cos F are not equal
How to determine the value of the identitiesThe different trigonometric identities in mathematics also have their different ratios. They are;
sinecosinetangentsecantcosecantcotangentTheir ratios are fractions given as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
cos F =
Opposite = 19
Hypotenuse = 20
cos F = 19/20
The value of sin E
sin E = 39/20
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Hassan travels by bus to work every morning.
The bus is either green or blue or yellow.
The table shows information about the probabilities of each colour.
Calculate the value of x
Work out the probability that Hassan’s bus is either blue or yellow
Answer:
3/5
Step-by-step explanation:
Total= 2x + 2x + x= 5x
Total of Blue and yellow= 2x + x= 3x
So.. 3x/5x which is equivalent to 3/5
FIFA has made a football of a leather of diameter 21 cm. If 10% leather is wasted and the cost of leather includings labor cost is Rs. 25 per sq.cm. find the total cost of leather bought to make a football.
The total cost of leather bought used to make a football is given as follows:
Rs 1,524.
How to obtain the surface area of a sphere?The surface area of a sphere of radius r is given by the equation presented as follows:
S = 4πr².
FIFA has made a football of a leather of diameter 21 cm, hence the radius is given as follows:
r = 10.5 cm.
Then the surface area is given as follows:
S = 4π x 10.5²
S = 1385.44 cm².
The cost is of Rs 25 per cm², with an additional 10% due to waste, hence the total cost is given as follows:
1.1 x 1385.44 = Rs 1,524.
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a cable of density p pounds per foot is used to lift w pounds of coal up a mineshaft that is 632 feet deep. how much work is done in this process?
The work done in the process of lifting coal up a mineshaft that is 632 feet deep is found to be 650,000 ft/lb.
For a cable of density, work = ∫k*y dy from 0 to b.
where k is the linear density of the cable (in lb/ft in this case), y is the distance from the top of the cable, and b is the total distance the weight has to travel to the bottom of the cable.
With this setting, the top of the cable should be labeled y=0 and the bottom of the cable (connected to the coal weight) should be labeled y=b. In this case, k = 2 ft/lb and b = 500 ft.
The 800 lb coal weight is additional information that we have not yet calculated.
Since pounds are a unit of force and the force to lift the coal is constant at 800 pounds, you can add the weight of 800 pounds to the integral and the work done to lift the coal is force * distance . The final integral is:
work = ∫(2y + 800) dy from 0 to 500.
integral:
Work = y2 + 800y | 0 to 500
= (500)2 + 800(500)
So, the work done is 650,000 ft/lb.
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Complete question - A cable that weighs 2 lb/ft is used to lift 800 lb of coal up a mine shaft 500 ft deep. Find the work done.
Suki says the area of the triangle is 12 cm². Emilia says the area of the triangle is 10 cm². Find the area of the triangle and explain any errors the girls might have made.
helpppp
Answer:
Let’s call the base of the triangle b and its height h. The area of a triangle is given by the formula A = 1/2 * b * h.
If Suki says that the area of the triangle is 12 cm², then we can write:
12 = 1/2 * b * h
Similarly, if Emilia says that the area of the triangle is 10 cm², then we can write:
10 = 1/2 * b * h
We can solve for one of the variables in terms of the other by dividing both sides of each equation by 1/2:
b * h = 24
b * h = 20
Now we have two equations with two variables. We can solve for one variable in terms of the other by dividing both sides of one equation by the other:
(b * h) / (b * h) = 24 / 20
1 = 6/5
This is a contradiction, so there is no solution that satisfies both equations.
Step-by-step explanation:
Select the correct answer.
This table represents value of a cubic polynomial function.
Based on the information in the table, which sentence best describes the interval [-2, 1]?
A. The function is increasing on the interval [-2, 1].
B. The function is both increasing and decreasing on the interval [-2, 1].
C. The function is decreasing on the interval [-2, 1].
D. The function is constant on the interval [-2, 1].
The function is both increasing and decreasing on the interval [-2, 1]. The y values decrease from 12 to 0 and then increase to 7.5 through 6. Therefore option B is correct answer.
In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences. German mathematician Peter Dirichlet first offered the modern definition of function in 1837.
Y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x). The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), other abbreviated symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or unspecified.
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Each big square below represents one whole.
A big square with 100 of the 100 equal pieces shaded
A big square with 5 of the 100 equal pieces shaded
Express the shaded area as both a fraction and a decimal.
Fraction:
Decimal:
A big square with 100 squares in the whole square. 5 of those squares are shaded. The shaded area as both a fraction and a decimal is expressed as:
Fraction: 5/100
Decimal: 0.05
What are decimals and fractions?In the form of a numerator and a denominator, fractions express a portion of a whole. Decimals are used to express fractions with a denominator of a power of ten, such as 10, 100, or 1000, in numerical form. Arithmetic is the representation of fractions in their decimal form, where the denominator is 10 or a power of 10 more, such as 100, 1000, or 10,000, etc.
Given:
Area of the whole square = 10 by 10
= 10×10 = 100unit²
The shaded area expressed as a fraction = 5unit²/100unit²
= 51/100
Shaded area expressed as a decimal = 5/100
Then take the number 5 and carry the point by two decimal place from the right
= 0.05
Shaded area expressed as a percent of the whole = (5/100) × 100
= (5×100)/100
= 5%
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f(x) = 12x - 4.8x²
find the average rate of change over the interval 0
To find the average rate of change of a function over a given interval, we need to calculate the change in the function over that interval, and divide by the length of the interval.
In this case, we want to find the average rate of change of the function f(x) = 12x - 4.8x^2 over the interval [0,5].
First, we need to find the value of the function at the endpoints of the interval:
f(0) = 12(0) - 4.8(0)^2 = 0
f(5) = 12(5) - 4.8(5)^2 = -72
Next, we calculate the change in the function over the interval:
Change in f(x) = f(5) - f(0) = -72 - 0 = -72
Finally, we divide the change in the function by the length of the interval:
Average rate of change = (Change in f(x)) / (Length of interval) = (-72) / (5-0) = -14.4
Therefore, the average rate of change of the function f(x) = 12x - 4.8x^2 over the interval [0,5] is -14.4.
what if you were not restricted to using just rectangles to fill up the space between the curve and the x-axis? suggest a different geometric shape that you think might give us a more accurate estimate for this area? justify why you think your new geometric shape would yield a more accurate result.
If you were not restricted to using just rectangles to fill up the space between the curve and the x-axis, a different geometric shape that might give a more accurate estimate for this area is a trapezoid.
Using trapezoids would likely yield a more accurate result because they can better approximate the curve's shape.
Here's a step-by-step explanation of how using trapezoids can provide a more accurate estimate:
Divide the interval on the x-axis into equal subintervals.
In each subinterval, form a trapezoid by connecting the endpoints of the subinterval to the curve and then closing the shape by drawing a horizontal line from the curve to the x-axis
Calculate the area of each trapezoid using the formula: A = (1/2) * (base1 + base2) * height, where base1 and base2 are the lengths of the parallel sides of the trapezoid (the lengths along the x-axis and the curve), and the height is the length of the vertical line connecting the two bases (the width of the subinterval)
Sum the areas of all trapezoids to approximate the total area between the curve and the x-axis.
The reason trapezoids can provide a more accurate estimate is that they can closely follow the shape of the curve, especially when the curve is not a straight line. Since trapezoids have two different base lengths, they can better accommodate the changes in the curve's slope within each subinterval. This results in a closer fit to the curve compared to using rectangles, which can overestimate or underestimate the area depending on the curve's concavity.
Overall, using trapezoids for estimating the area under a curve can provide more accurate results, especially as the number of subintervals increases.
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A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval ?The exponential function decays at one-half the rate of the quadratic function.The exponential function decays at the same rate as the quadratic function.The exponential function decays at two-thirds the rate of the quadratic function.The exponential function decays at three-fourths the rate of the quadratic function.
PLEASE HELP!!
The circumference
What is the area of the green sector?
of the circle above is 24 cm and the area is 42 cm².
7
cm²
What is the arc length of the edge of the green sector?
cm.
Hence, the area of the green sector is roughly [tex]7 cm^2,[/tex] and the arc length of its edge is roughly 4 cm.
what is area ?Usually expressed in square units, area is a unit of measurement for the size of an a double surface or territory. It is used to indicate the amount of space that lies inside the confines of a straight position, such as a round, rectangle, circle, a triangle. Depending on the shape, a formula is needed to determine the size of a shape. For instance, the area of either a rectangle can be determined by dividing its extent by its width, whereas the area of a circle can be determined by multiplying pi (about 3.14), by the square of its radius. Several branches of mathematics, physics, and engineering all use the idea of area extensively.
given
(Area of Green Sector / Area of Circle) 360 degrees is the formula for the Green Sector's Central Angle.
green sector's centre angle is equal to (7 cm2 / 42 cm2) 360 degrees.
60 degrees is the green sector's midpoint (rounded to the nearest degree)
We may apply the following formula to determine the arc length of the green sector:
circumference (central angle / 360 degrees) = arc length
arc length is equal to 24 cm when divided by 60 degrees.
4-cm-long arc (rounded to one decimal place)
Hence, the area of the green sector is roughly [tex]7 cm^2,[/tex] and the arc length of its edge is roughly 4 cm.
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A 6 inch by 10 inch rectangle is dilated by a factor of 2. What is the area of the dilated rectangle?
please help.
see below
Answer:
A
Step-by-step explanation:
in any right triangle the sine ratio of an angle Θ is
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex]
Which square root of 225 has a negative value?
The two square roots of 225 are +15 and -15.
However, since negative values are usually not considered answers for practical purposes, the principal square root of 225 is +15 (i.e., √225 = 15).
Can someone please help me ASAP it’s due today!! I will give brainliest if it’s all done correctly.
Answer part A, B, and C for brainliest!!
(a) The experimental probability of rolling a 3 is approximately 8%.
(b) The experimental probability of rolling a 6 is 25%.
(c) The experimental probability of rolling a number less than 4 is 50%.
What is the experimental probability of rolling a 3?
The experimental probability of rolling a 3 can be determined from the result presented in the table as shown below.
from the result presented, there a total outcome of 12
number of rolling a 3 in the result = 1
P(3) = 1/12 = 0.083
P(3) ≈ 8%
The experimental probability of a rolling a 6 is calculated as;
number of 6 obtained in the result = 3
P(6) = 3/12
P(6) = 0.25
P(6) = 25%
The experimental probability of rolling a number less than 4:
P ( less than 4) = P(1) + P(2) + P(3)
P ( less than 4) = 17% + 25% + 8%
P ( less than 4) = 50%
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Which one of the following is not equal reast
A 2 of 15
B 3/2 of 400
C 5 of 60
D 6 of50%
Answer:Option(a)
Step-by-step explanation: A) 2 of 15
the total number of sides in 2 regular polygons is 13, and tge titak number of diagonals is 25. how many sides is each polygon
One polygon has 6 sides and the other has 7 sides.
Polygons are closed 2D shapes made up of straight lines. Regular polygons have sides of equal length and angles of equal measure. In this problem, we are given information about two regular polygons.
We are told that the total number of sides in both polygons is 13. Let's call the number of sides in one polygon "n" and the number of sides in the other polygon "m". Then, we know that:
n + m = 13
Next, we are given the total number of diagonals in both polygons, which we can calculate using the formula:
d = (n(n-3) + m(m-3))/2
where "d" is the total number of diagonals. We are told that d = 25. Substituting this value and the equation for n + m into the diagonal formula, we get:
25 = (n(n-3) + m(m-3))/2
25 = (n² - 3n + m² - 3m)/2
50 = n² - 3n + m² - 3m
We can use the equation n + m = 13 to solve for one variable in terms of the other. For example, we can solve for "m" by subtracting "n" from both sides:
m = 13 - n
Substituting this into the previous equation, we get:
50 = n² - 3n + (13-n)² - 3(13-n)
50 = n² - 3n + 169 - 26n + n² - 36 + 3n
Simplifying this equation, we get:
2n² - 26n + 45 = 0
We can use the quadratic formula to solve for "n":
n = (26 ± √376)/4
n ≈ 5.61 or n ≈ 8.39
Since we are dealing with whole numbers of sides, "n" must be either 6 or 8. Plugging each value into the equation n + m = 13, we find that the other polygon must have the opposite value.
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if a cylinder has a height of 7 inches and a volume of 2908.33in3 guns it’s diameter
The diameter of the cylinder is approximately 22.98 inches.
To find the diameter of the cylinder, we need to first find the radius using the formula for the volume of a cylinder:
Volume = π × r² × h
Given:
Volume (V) = 2908.33 in³
Height (h) = 7 inches
We will rearrange the formula to find the radius (r):
r² = Volume / (π × h)
Now, plug in the given values:
r² = 2908.33 / (π × 7)
r² ≈ 131.95
Now, find the square root to get the radius:
r ≈ √131.95
r ≈ 11.49 inches
Since the diameter is twice the radius, we can find the diameter (d) by:
d = 2 × r
d = 2 × 11.49
d ≈ 22.98 inches.
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A ladder PQ, of length 5 m, is leaning against a vertical wall. The lower end Q of the ladder is sliding away from the wall at a constant rate of 0.6 m/s. Find the velocity of the upper end P when Q is 4m from the wall.
Answer:
The velocity of the upper end P when Q is 4 m from the wall is -0.8 m/s
Step-by-step explanation:
Let's denote the distance of the lower end Q from the wall as x and the distance of the upper end P from the ground as y. We are given that the ladder has a length of 5 m, and thus by the Pythagorean theorem, we have:
x^2 + y^2 = 5^2 = 25
Now, we're given that the lower end Q is sliding away from the wall at a constant rate of 0.6 m/s. This means that the rate of change of x with respect to time (dx/dt) is 0.6 m/s. We need to find the rate of change of y with respect to time (dy/dt) when x = 4 m.
Differentiate both sides of the Pythagorean equation with respect to time (t):
d(x^2)/dt + d(y^2)/dt = d(25)/dt
2x(dx/dt) + 2y(dy/dt) = 0
We can plug in the known values and solve for dy/dt when x = 4 m:
2(4)(0.6) + 2y(dy/dt) = 0
To find the value of y when x = 4 m, we can use the Pythagorean equation:
4^2 + y^2 = 25
16 + y^2 = 25
y^2 = 9
y = 3 (since the height must be positive)
Now, we can substitute y = 3 into the equation we derived earlier:
2(4)(0.6) + 2(3)(dy/dt) = 0
4.8 + 6(dy/dt) = 0
Now, solve for dy/dt:
6(dy/dt) = -4.8
(dy/dt) = -4.8 / 6
(dy/dt) = -0.8 m/s
Thus, the velocity of the upper end P when Q is 4 m from the wall is -0.8 m/s. The negative sign indicates that the upper end P is moving downward.
a bowl contains 10 red balls and 10 blue balls. a woman selects balls at random without looking at them. what is the minimum number of balls she must select to be sure of having at least three blue balls?
The minimum about of balls she should pick is 13.
So, the woman consider all the balls and picks the balls without looking,
To have a clear chance of picking at least 3 blue balls from the bowl she has to first eliminate the possibility of picking red balls.
Therefore,
She first picks 10 balls from the bowl, which gradually eliminates the possibility of picking a red ball.
now, she picks 3 more balls from the rest of the available balls which increases the changes of the balls being blue.
then,
=> 10 + 3 = 13
The minimum about of balls she should pick is 13.
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