The height of the water increasing at a rate of 0.05 m/min
The Volume of a cylinder is
[tex]V = \pi r^{2}h[/tex]
where r is the radius and h is the height of the cylinder.
Given that the radius r of cylinder is 5m and the water is filled at the rate of 4 [tex]m^{3} /min[/tex]
[tex]V = 25\pi h[/tex] ...(1)
Now, differentiating (1) with respect to time t,
[tex]\frac{dV}{dt} = 25\pi \frac{dh}{dt}[/tex]
Substituting the value of [tex]\frac{dV}{dt}[/tex]
4 = [tex]25\pi \frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}[/tex] = [tex]\frac{4}{25\pi }[/tex]
[tex]\frac{dh}{dt}[/tex] = 0.05 m/min
Hence, the water is increasing at the rate of 0.05 m/min
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1/6 (x-3) = 1/3 (x+2)
The value of x in the equation given as 1/6(x - 3) = 1/3(x + 2) is 7
How to evaluate the equation?The equation is given as
1/6(x - 3) = 1/3(x + 2)
From the question, we can see that the equation is a linear equation with one variable
As a general rule: linear equations are equations that have constant average rates of change.
We start by multiplying both sides of the equation by 6
So, we have the following equation
6 * 1/6(x - 3) = 1/3(x + 2) * 6
Next, we evaluate the products
So, we have the following equation
x - 3 = 2x + 4
Next, we collect the like terms
So, we have the following equation
2x - x = 3 + 4
Evaluate the like terms in the above equation
x = 7
This means that the solution of the equation is 7
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One of the legs of a right triangle measures 13 cm and the other leg measures 11 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
17.03 cm
Step-by-step explanation:
Use the Pythagorean theorem, which states a^2+b^2=c^2. 13^2+11^2=290, sqrt290 cannot be simplified down into a whole number, therefore the next closes rounded to the nearest tenth is 17.03.
Which function has a minimum of -4?
A. y = (x - 5)² – 4
B. y = -(x-4)² - 5
C. y = (x-4)² +5
D. y = -(x - 5)² + 4
8. (15 pts) Explain clearly why Graph A IS a function, while Graph B is NOT a function. (Youcan indicate where the graphs pass or fail and reference that in your explanation)
We can see two graphs and we need to determine the reason why graph A IS a function, and graph B is NOT a function.
To achieve that, we can proceed as follows:
1. A function is a relation in which for each element of the domain we have only (exactly) one element of the range.
2. The domain of a function is the values for x for which the function is defined, and the range is those values for y that result when the function takes values for x and after following the rule of the function (the values for which the function is defined).
3. To determine if a graph is a function, we can use the vertical line test. Given the above definitions, this test tells us that if a vertical line passes through a graph at more than a point, then the relation is NOT a function.
4. Now we can use the Vertical Line Test on each graph as follows:
Graph A:As we can see from the graph, the vertical line passes through only one point (one value for y associated to x). We can see that the open circle indicates that the function is not defined for the value while the solid circle indicates that the function is defined for that value.
For instance, for x = -1 the value of the function is y = 0 (and not y = -1 - see the open circle). We have a similar case for x = 1 (y = 1) (not y = 0).
Therefore, graph A IS a function.
Graph B
In this case, we can say that the vertical line passes through more than one point in most of the values. However, we can say that there are some values where the line passes through one point - from x = -3 to x = -2 (included) -, and for values greater than 2 (x>2).
However, since the vertical line test indicates that the line passes through more than a point (there are more than a value, y, for each x) then Graph B is NOT a function.
Therefore, in summary, we can say that using the method of the vertical line test, Graph A IS a function, while Graph B is NOT a function.
my daughter is working on expression problems. i cant remember how to do this...the problem is 12(3y+x)please help me tell her how to write and solve this.
EXPLANATION
Given the expression 12(3y+x).
Let's solve it:
Applying the distributive property:
12*3y + 12*x
Multiplying like terms:
36y + 12x
The answer is 36y + 12x
What value of x satisfies the equation 4x + 2 = 22?
A 3.5
B 5.0
C 6.0
D 7.5
Answer:
B
Step-by-step explanation:
4x + 2 = 22 ( subtract 2 from both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Convert the angle \frac{13\pi}{4} 413π radians to degrees.
1 rad x 180/pi =57.296 deg
so the answer is 744.845
Distributive property -(6v-4u-1)
STEP - BY - STEP EXPLANATION
What to do?
Apply the distributive property on the given expression.
Given:
[tex]-\left(6v-4u-1\right)[/tex]Step 1
Explain what the distributive property mean.
Distributing -1 implies multiplying -1 by each term.
Step 2
Apply the distributive property.
[tex]-\left(6v-4u-1\right)=-6v+4u+1[/tex]ANSWER
-6v + 4u +1
How does slavery and oppression of other people impact you?
Slavery and oppression of other people impact others as it brings about discrimination and fear.
What is slavery?In the olden days, slavery was so lucrative that the Mississippi River valley produced more millionaires per capita than any other region of the country. With cash crops like tobacco, cotton, and sugar cane, the southern states of America developed into the country's economic engine.
In Africa, the slave trade had a terrible impact. A culture of lawlessness and violence was encouraged by the financial incentives provided to warlords and tribes to participate in the slave trade. Economic and agricultural development in a large portion of western Africa was virtually impossible due to depopulation and a persistent fear of enslavement.
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I have a calculus question about limit functions. Pic included.
Answer:
Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.
Explanation:
P(25, 10) lies on the curve:
[tex]y=\sqrt{x}+5[/tex]Q is the point (x, √x+5).
For any value of x, the slope of the secant line PQ is determined using the formula:
[tex]\text{ Slope of secant PQ}=\frac{(\sqrt{x}+5)-10}{x-25}[/tex](a)When x=25.1
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{25.1}+5)-10}{25.1-25}=0.0999[/tex](b)When x=25.01
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{25.01}+5)-10}{25.01-25}=0.09999[/tex](c)When x=24.9
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{24.9}+5)-10}{24.9-25}=0.1001[/tex](d)When x=24.99
[tex]\text{Slope of secant PQ}=\frac{(\sqrt{24.99}+5)-10}{24.99-25}=0.10001[/tex]Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.
A trapezoid has bases 4 and 12 and area of 40m^2 find the height
Step 1
State the formula for the area of a trapezoid
[tex]\begin{gathered} The\text{ area of a trapezoid=(}\frac{a+b}{2})\times height(h) \\ \text{Where a= base 1=4}m \\ b=\text{base 2=12m} \\ \text{The area of the trapezoid=40m}^2 \end{gathered}[/tex]Step 2
Find the height
[tex]\begin{gathered} 40=(\frac{4+12}{2})\times h \\ 40=\frac{16}{2}\times h \\ 80=16h \\ h=\frac{80}{16} \\ h=5m \end{gathered}[/tex]Hence, the height = 5m
Wha What is 12 tens in standard form
the following equation is used by scientists to relate the pressure, volume, amount and temperature of gas solve for r in terms of p,v,n and t
The equation is PV = nRT.
What is a ideal gas law?The calculations for the ideal gas law are comparison of the Pressure and Volume of gas based upon amount and temperature.
The basic formula is PV = nRT where
P = Pressure in atmospheres (atm)
V = Volume in Liters (L)
n = number of moles (mol)
R = the Ideal Gas Law Constant
T = Temperature in Kelvin (K)
The value of n is the amount of the gas measured as moles.
One may need to convert a mass to moles by dividing the given mass of the gas by the molar mass of the gas to get moles.
Hence, The equation is PV = nRT.
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I need help graphing this piecewise function!
The piecewise function on the graph is,
f(x) = { 1 -3x ; if x ≤ 2
{ 4-x ; if x > 2
The graph of a piecewise function is given. The left function is defined on the interval x ≤ 2 and the right function is defined on the interval x > 2.
To find the functions we need two points on each function since both functions are straight lines.
First we will find the left function defined on x ≤ 2.
So the two points are (x₁, y₁) = (0,1) and (x₂, y₂) = (2, -5).
Now slope of the left function, m₁ = (y₂ - y₁)/(x₂ - x₁)
= -5 - 1/2 - 0
= -6/2
= -3
So the equation of the left function is,
y - y₁ = m(x-x₁)
⇒ y - 1 = -3(x-0)
⇒ y = 1 -3x
Thus the left function is f(x) = 1 -3x
Consider the right function.
The two points on the graph of the right function are (x₁, y₁) = (4,0) and (x₂, y₂) = (6, -2).
So slope of the second function, m₂ = (y₂ - y₁)/(x₂ - x₁)
= -2 - 0/6-4
= -2/2
= -1
Now equation for the right function is,
y - y₁ = m(x-x₁)
⇒ y - 0 = -1(x-4)
⇒ y = 4 -x
So the right function is f(x) = 4-x
Hence the piecewise function is,
f(x) = { 1 -3x ; if x ≤ 2
{ 4-x ; if x > 2
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The management of the UNICO department store has decided to enclose a 903 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.
The dimensions of the enclosure that can be erected at minimum cost are 21.25 feet by 42.50 feet
How to determine the dimensions of the enclosure that guarantees the minimum costFrom the question, the given parameters are
Area = 903 square feet
Shape = rectangle
From the question, we understand that:
One side of the area would be enclosed by the external wall of the store
If the dimensions of the area are Length (L) and Width (W), then we have
Area = LW
Perimeter = 2L + W
Rewrite as
A = LW
P = 2L + W
Substitute 903 for A in A = LW
LW = 903
Make W the subject
W = 903/L
Substitute W = 903/L in P = 2L + W
P = 2L + 903/L
Differentiate the equation
So, we have
P' = 2 - 903/L²
Set to 0
2 - 903/L² = 0
So, we have
903/L² = 2
This gives
L² = 903/2
Divide
L² = 451.5
Take the square roots
L = 21.25
Substitute L = 21.25 in W = 903/L
W = 903/21.25
Evaluate
W = 42.50
Hence, the dimensions of the enclosure are 21.25 feet by 42.50 feet
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Simplify the complex rational expression. When typing your answer for the numerator and denominator be sure to type the term with the variable first with no spaces between characters. If an exponent is needed use the carrot key (^) by pressing shift and 6 at the same time.\frac{\left(\frac{2}{a}+\frac{7}{b}\right)}{b}The numerator is AnswerThe denominator is Answer
The given expression is
[tex]\frac{(\frac{2}{a}+\frac{7}{b})}{b}[/tex]To add 2 fractions we have to give them the same denominators
In the up part (numerator) we have 2 different denominators a and b
Then the common denominator of the 2 fractions must be the product of them
[tex]\frac{2}{a}+\frac{7}{b}=\frac{2b}{ab}+\frac{7a}{ab}=\frac{2b+7a}{ab}[/tex]Then the fraction will be
[tex]\frac{\frac{2b+7a}{ab}}{b}[/tex]Now, we will multiply the denominator of up by the denominator of the first fraction (ab x b)
[tex]\frac{\frac{2b+7a}{ab}}{b}=\frac{2b+7a}{b(ab)}[/tex]Multiply b by b to simplify, then
[tex]\frac{2b+7a}{b(ab)}=\frac{2b+7a}{ab^2}[/tex]The numerator is 2b + 7a
The denominator is ab^2
what is the sum?17.34 8.03+0.009
In order to add these numbers, first let's write all of them with the same number of decimal places:
17.34 = 17.340
8.03 = 8.030
0.009 = 0.009.
Then, let's add all algarisms that are in the same position in each number:
0 + 0 + 9 = 9
4 + 3 + 0 = 7
3 + 0 + 0 = 3
7 + 8 + 0 = 15 (5 plus 1 to next algarism)
1 + 0 + 0 (+ 1) = 2
So the final result is 25.379.
PLEASE HURRY ASAP
What is the product of (−4)(23)(−7)?
Answer:
644
Step-by-step explanation:
-4x23=-92
-92x-7=644
hope this helped :)
Answer:
644
Step-by-step explanation:
if you multiply -4 by 23 it equals -92 and then if you multiply -92 by -7 it comes out to a positive 644 because if multiplying a negative by a negative it becomes a positive.
thank you for your question and let me know if it is right or wrong
blessings!
To estimate the height of a stone figure Anya holds a small square up to her eyes and walks backwards from the figure she stops when the bottom of the figure aligns with the bottom edge of the square and the top of the figure aligns with the top edge of the square her eye level is 1.84m from the ground she is 3.50m from the figure what is the height of the figure to the nearest hundredth of a meter
SOLUTION
Let us make a sketch that will help us solve the question
From the image I provided, let the Height of the figure be H.
Then this means that the height of the figure H is
[tex]H=x+1.84[/tex]Note that I have splitted the triangle into two.
Now, we need to find the two acute angles
[tex]\begin{gathered} \alpha\text{ and }\theta\text{ in the bigger triangle.} \\ \text{Note that }\alpha+\theta+90^o=180^o\text{ (sum of angles in the big triangle)} \end{gathered}[/tex]Now, from the triangles splitted in the right side, both are right-angles just like the first (biggest) triangle.
So we will use the trig-ratio, SOHCAHTOA to find the acute angles.
From the smallest triangle in the image,
[tex]\begin{gathered} \tan \alpha=\frac{opposite}{\text{adjacent }} \\ \tan \alpha=\frac{3.5}{\text{1.84 }} \\ \alpha=\tan ^{-1}\frac{3.5}{\text{1.84 }} \\ \alpha=62.27^o \end{gathered}[/tex]Now, the second acute angle becomes
[tex]\begin{gathered} \text{ }\alpha+\theta+90^o=180^o \\ 62.27+\theta+90=180 \\ \theta+152.27=180 \\ \theta=180-152.27 \\ \theta=27.73^o \end{gathered}[/tex]The other triangle that is the bigger one which was splitted has opposite side of 3.5m and adjacent side x, hence
[tex]\begin{gathered} \tan \theta=\frac{opposite}{\text{adjacent}} \\ \tan 27.73=\frac{3.5}{x} \\ x\times\tan 27.73=3.5 \\ x=\frac{3.5}{\tan 27.73} \\ x=6.65804m \end{gathered}[/tex]Now H becomes
[tex]\begin{gathered} H=x+1.84 \\ H=6.65804+1.84 \\ H=8.49804 \end{gathered}[/tex]Hence, the height of the figure is 8.50 m to the nearest hundreth
How do you simplify (9^12)^7 is it
9^84
81^84
81^19
9^19
(9¹²)⁷
Use the rules of exponents to simplify the expression. To raise a power to another power, multiply the exponents.
9¹² ˣ ⁷
Multiply 12 by 7.
9⁸⁴
Answer: 9^84 is the answer!
Step-by-step explanation:
What is the value of x in the geometric sequence x, 3, — ‚ .A. -27B. -9C. -1D. -3
Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get
[tex]\frac{x}{3}[/tex]if we do that with the second and third numbers, we get
[tex]\frac{3}{\text{ -}\frac{1}{3}}=\text{ -}\frac{3\cdot3}{1\cdot1}=\text{ -9}[/tex]this two numbers should be equal. So we get
[tex]\frac{x}{3}=\text{ -9}[/tex]if we multiply both sides by 3, we get
[tex]x=3\cdot\text{ -9= -27}[/tex]so option A is the correct option.
The average number of babies born at a private hospital's maternity wing is 6 per hour. What is the probability that three babies are born during a particular 1-hour period in this maternity wing?
If the average number of babies born at a private hospital's maternity wing is 6 per hour. The probability that three babies are born during a particular 1-hour period in this maternity wing is 0.09.
How to find the Probability?Mean = 6 per hours
Number of babies = 3 babies
Hence,
Now let determine the probability
Let x represent the probability
Pr(X=3) = e^-6 × 6^3 ÷ 3!
Pr(X=3) =0 .535410 ÷ 6
Pr(X=3) = 0.089
Pr(X=3) =0.09 (Approximately)
Therefore we can conclude that 0.09 is the probability.
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I'll give brainliest!
The square roots would not be between 9 and 10 is [tex]\sqrt{80}[/tex].
[tex]\sqrt[]{80}=8.944\\ \sqrt[]{90}=9.486\\ \sqrt[]{95}=9.746\\ \sqrt[]{88}=9.380[/tex]
What are square roots?
The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a, a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolized by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.
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Convert the following angle from degrees to radians. Express your answer in simplestform.285°
Answer:
19π/12
Explanation:
We know that
180 degrees = π radians
and we are asked
285 degrees = ? radians?
This can be treated as a ratio problem by saying that
[tex]\frac{180}{\pi}=\frac{285}{x}[/tex]where x is the angle in radians.
Cross multpication gives
[tex]180x=285\pi[/tex]dividing both sides by 180 gives
[tex]x=\frac{285\pi}{180}[/tex][tex]x=\frac{19}{12}\pi[/tex]where we have used the fact that 285/12 = 19/12.
A lifeguard is sitting in an observation chair at a pool. The lifeguard's eye level is 6.2. feet fromground. The chair is 15.4 feet from a swimmer. Calculate the measure if an angle forms when thelifeguard looks down at the swimmer.
We can represent this situation with a triangle, as shown below:
We need to calculate the angle that forms between the line of sight of the Life Guard and the swimmer. For that, we will have to use the tangent relation.
[tex]undefined[/tex]Graph the line that has an x-intercept at (1, 0) and a y-intercept at (0, - 4). What is the slope of this line?
during the winter olympics the us curling team scored 2 points more than the canadian team. the canadian curling team scored 4 points more than the norwegian team. altogether the three teams scored a total of 208 point. how many points did the canadian team scored?
Answer:
70 points
Step-by-step explanation:
u = US points
c = Canadian points
n = Norwegian points
u = c + 2
n = c - 4
208 = u + c + n
208 = ( c + 2 ) + c + ( c - 4 ) = 3c - 2
Isolate c:
208 = 3c - 2
210 = 3c
c = 70
I NEED HELPPPPPPPPP HELPPP MEEEE
a) triangle with measurement 1/2 of the original measurement.
b) rhombus with measurement 2 times the original measurement.
c) parallelogram with measurement 1/4 of the original measurement.
The polygon is 2- dimensional figure and is any closed curve made of continuous edges also called the sides without intersecting each other, the corner of a polygon is called the vertices, the are of basically two types regular and irregular, whereas The scale factor a polygon the ratio of one side of a polygon to the comparing side of the other is called the scale factor. The proportion of all parts of a polygon, including diagonals, perimeter, and heights is the same as the proportion of the sides.
a) the given scale factor is 1/2 and, we need to construct a scale copy of the triangle having sides measurements 1/2 of the original measurements.
b) the new polygon must have the measurements 2 times the original measurements of the polygon .
c) the new polygon must have dimensions 1/4 of the dimensions of the original measurements.
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Select the correct answer.What is the solution to this equation?loge + + log 3 = log (+ + 1)OA1 =IO HICOB.1 =O C.सेNICOOD. r = 1
Given the equation:
[tex]\log _6x+\log _63=\log _6(x+1)[/tex]Let's solve for x.
To find the solution, take the following steps:
Step 1:
Apply the product property of logarithm to the left side of the equation:
[tex]\begin{gathered} \log _6(x\ast3)=\log _6(x+1) \\ \\ \log _6(3x)=\log _6(x+1) \end{gathered}[/tex]Step 2:
Eliminate the log on both sides
[tex]\begin{gathered} 3x=(x+1) \\ \\ 3x=x+1 \end{gathered}[/tex]Step 3:
Subtract x from both sides
[tex]\begin{gathered} 3x-x=x-x+1 \\ \\ 2x=1 \end{gathered}[/tex]Step 4:
Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{1}{2} \\ \\ x=\frac{1}{2} \end{gathered}[/tex]Therefore, the solution to the given equation is:
[tex]x=\frac{1}{2}[/tex]ANSWER:
[tex]\text{ B. x = }\frac{1}{2}[/tex]5/6x+1/12= 15 1/3+1/3xsolve for x
Answer:
x = 61/2 = 30.5 = 60 1/2
Step-by-step explanation:
We have:
[tex]\frac{5}{6}x+\frac{1}{12}=15+\frac{1}{3}+\frac{1}{3}x[/tex]We have to find the Least Common Multiple to solve this question:
[tex]\begin{gathered} \frac{2\cdot5x+1=12\cdot15+4+4x}{12} \\ \frac{10x+1=180+4+4x}{12} \\ 10x+1=180+4+4x \\ 10x-4x=180+4-1 \\ 6x=183 \\ x=\frac{183}{6} \\ x=\frac{61}{2}=30.5=30\frac{1}{2} \end{gathered}[/tex]