To find if two lines are parallel, the slope must be the same.
so m=m
for P(1,2); L: 3x-2y=1
First, solve the equation for y:
3x-2y=1
Subtract both sides by 3x
3x-2y=1
3x-3x-2y =1-3x
-2y=1-3x
Now, divide both sides by -2y
-2y/-2 = 1-3x
y =1/-2 +3x/2
The parallel line using the point P(1,2)
y-y1 =m(x-x1)
Replace the values and solve for y.
y-2=3x/2 -1
y=3x/2+2
So the parallel lines is y=3x/2+2
To find a perpendicular line, when you multiply the slopes the result must be equal to -1.
So:
m1*m2 = -1
Replace m1=3/2
m1*m2 = -1
3x/2* m2 = -1
m2 = -1/(3x/2)
m2 = -2/3
To find the line use:
y-y1 =m(x-x1)
y-2=-2/3(x-1)
y-2=-2x/3 +2/3
y= -2x/3 +8/3
So y= -2x/3 +8/3 is the perpendicular line.
Math help!!! Only a tutor that can give me answers to 9 and 10!!
9.
Alternative interior angles are congruent
Therefore;
5x + 42 = 18x -12
collect like term
5x - 18x = -12 - 42
-13 x = -54
Divide both-side of the equation by -13
x=4.15
The total movie attendance in a country was 1.16 billion people in 1990 and 1.40 billion in 2008. Assume that the pattern in movie attendance is linear function of time. (Need to answer questions a-d for this question - pic attached)
a)
In order to find a function M(t), first let's identify two ordered pairs that are solutions to the equation.
From the given information, we have the ordered pairs (1990, 1.16) and (2008, 1.4).
Using these ordered pairs, let's find the slope-intercept form of a linear equation (y = mx + b)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1.4-1.16}{2008-1990}=\frac{0.24}{18}=0.01333 \\ \\ y=mx+b \\ 1.16=1990\cdot0.01333+b \\ b=-25.3667 \\ \\ y=0.01333x-25.3667 \end{gathered}[/tex]So the equation is M = 0.01333t - 25.3667
The independent variable represents the year (correct option: first one)
b)
The slope represents the change in M over the change in t, that is, it represents the change in attendance over a year (correct option: first one)
c)
For t = 2015, we have:
[tex]\begin{gathered} M=0.01333\cdot2015-25.3667 \\ M=26.86-25.37 \\ M=1.49 \end{gathered}[/tex]d)
For M = 1.5, we have:
[tex]\begin{gathered} 1.5=0.01333\cdot t-25.3667 \\ 0.01333t=26.8667 \\ t=2015.5 \end{gathered}[/tex]True or false if a set of points all lie on the same plane they are called collinear
We have that a group of points can be:
Coplanar: if they lie in the same plane
Collinear: if they lie in the same line
Answer- False: they are called coplanarA
Y
+
B
X
Z
Given the diagram shown with AB|| XZ
AY = 7
AX = 6
AB= 14
find XZ.
Step-by-step explanation:
due to AB being parallel to XZ, we know that ABY and XZY are similar triangles.
therefore, they have the same angles, and there is one common scale factor for all side lengths from one triangle to the other.
so,
AY / XY = AB / XZ
XY = AY + AX = 7 + 6 = 13
7/13 = 14/XZ
XZ×7/13 = 14
XZ×7 = 14×13
XZ = 14×13/7 = 2×13 = 26
Drag the tiles to the boxes to form correct pairs.Match each operation involving fx) and g(x) to its answer.(T) = 1 - 22 and g(x) = V11 – 40(gx )(2)(8 - 1)(-1)(9 + )(2)-373V3 - 30V15
1.
[tex](g\times f)(2)[/tex]It means multiply f(x) and g(x) and then put "2" into it. The solution is what we are looking for. So,
[tex]\begin{gathered} (g\times f)(2)=\sqrt[]{11-4x}\times1-x^2 \\ =\sqrt[]{11-4(2)}\times1-(2)^2 \\ =\sqrt[]{3}\times-3 \\ =-3\sqrt[]{3} \end{gathered}[/tex]2.
[tex](g-f)(-1)[/tex]For this we subtract f from g and put -1 into the expression. So
[tex]\begin{gathered} (g-f)(-1)=\sqrt[]{11-4x}-1+x^2 \\ =\sqrt[]{11-4(-1)}-1+(-1)^2 \\ =\sqrt[]{15}-1+1 \\ =\sqrt[]{15} \end{gathered}[/tex]3.
[tex](g+f)(2)[/tex]We simply add f and g and put 2 into the final expression.
[tex]\begin{gathered} (g+f)(2)=\sqrt[]{11-4x}+1-x^2 \\ =\sqrt[]{11-4(2)}+1-(2)^2 \\ =\sqrt[]{3}-3 \end{gathered}[/tex]4.
[tex]\begin{gathered} (\frac{f}{g})(-1) \\ \end{gathered}[/tex]We divide f by g and put -1 in the final expression. Shown below:
[tex]\begin{gathered} (\frac{f}{g})(-1)=\frac{1-x^2}{\sqrt[]{11-4x}} \\ =\frac{1-(-1)^2}{\sqrt[]{11-4(-1)}} \\ =\frac{0}{\sqrt[]{15}} \\ =0 \end{gathered}[/tex]Now, please match each answer with each choice.
The graph of function g is a vertical stretch of the graph of function f by a factor of 3. Which equation describes function g?
g(x)=f(x/3)
g(x)=3f(x)
g(x)=f(3x) ,
g(x)=1/3f(x)
Answer:
B) g(x) = 3f(x)Step-by-step explanation:
What is a vertical stretch?Given a function f(x), a new function g(x) = cf(x), where c is a constant, is a vertical stretch of f(x) when c > 1.
In our case the function f(x) is stretched by a factor of 3.
It means c = 3 and therefore:
g(x) = 3f(x)Correct choice is B
Need help asap !! Thank you
The coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.
What is a linear equation?A connection between a set of variables results in a linear system when presented on a graph. The variable will have a degree of only one.
The linear equation is given below
- 2x - 3y = 6
For the x-intercept, the value of the y will the zero. Then we have
- 2x - 3(0) = 6
-2x = 6
x = -3
The x-intercept is at (-3, 0).
For the y-intercept, the value of the x will the zero. Then we have
- 2(0) - 3y = 6
-3y = 6
x = -2
The y-intercept is at (0, -2).
Thus, the coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.
More about the linear equation link is given below.
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which equation matches the graph A. y= 2x + 3 B. y= -2x + 3 C. y= -4x + 2 D. y= 4x + 2
From the given graph the line is passing through the points (-2,0) and (0,3).
Let,
[tex]\begin{gathered} (x_1,y_1)=(-1.5,0) \\ (x_2,y_2)=(0,3) \end{gathered}[/tex]From the option the equation of the line is y=2x+3
Since on subtituting (0,3) in the above expression the condition satisfys, also on substituting (-1.5,0) in the given expression the condition satisfys.
Thus, the correct option is option A.
Ninety percent of a large field is cleared for planting. Of the cleared land, 50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?*
For the given question, let the size of the original field = x
Ninety percent of a large field is cleared for planting
So, the size of the cleared land = 90% of x = 0.9x
50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants.
So, the size of the land planted with blueberry plants and strawberry plants =
[tex]0.5\cdot0.9x+0.4\cdot0.9x=0.45x+0.36x=0.81x[/tex]The remaining will be = 0.9x - 0.81x = 0.09x
Given: the remaining 360 acres of cleared land is planted with gooseberry plants
so,
[tex]0.09x=360[/tex]divide both sides by (0.09) to find x:
[tex]x=\frac{360}{0.09}=4,000[/tex]So, the answer will be:
The size of the original field = 4,000 acres
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:A graph is titled Distance Vs. Time is shown. The x axis is labeled Time in minutes and shows numbers 0, 1, 2, 3, 4, 5. The y axis is labeled Distance from Ocean Surface in meters. A straight line joins the points C at ordered pair 0,66, B at ordered pair 1, 110, A at ordered pair 2, 154, and the ordered pair 3, 198.Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)Part B: What are the initial value and slope of the graph, and what do they represent? (
We are given a graph that shows the depth in meters (y) as a function of the time in minutes (x).
Part A:
Points A, B, and their projection in the point (2, 110) form a similar triangle with the triangle formed by points A, C, and the point (2, 66).
Which of these describes the transformation of triangle ABC shown below?A) reflection across the x-axisB) reflection across the y-axisC) reflection across the line y=xD) translation
From the figure, we have the coordinates of the vertices:
ABC ==> A(2, 1), B(5, 1), C(1, 5)
A'B'C' ==> A'(-2, 1), B'(-5, 1), C(-1, 5)
Let's determine the type of transformation that occured here.
Apply the rules of rotation.
For a rotation acorss the y-axis, only the x-coordinates of the points will change to the opposite. i.e from negative to positive or from positive to negative.
For a rotation across the y-axis, we have:
(x, y) ==> (-x, y)
From the given graph, we can see that the only the x-coordinates changed from positive to negative.
Therefore, the transformation that occured here is the reflection across the y-axis.
ANSWER:
B) Reflection across the y-axis.
What’s the correct answer answer asap for brainlist
Answer:
your answer is B
Step-by-step explanation:
Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire
Two systems of equations are given below For each system, choose the best description of its solution If applicable, give the solution 7 System The system has no solution The system has a unique solution 5x-*= -1 5x+y=1 The system has infinitely many solutions Systeme The system has no solution The system has a unique solution: *+ 2y 13 -* + 2y = 7 The system has infinitely many solutions.
If we sum both equations, we have the next result:
[tex]0\text{ = 0}[/tex]Since we have this, we can say that the system has infinite solutions. We sum both equations, and we finally get that 0 = 0. In this case, the system has infinite solutions.
All these solutions are expressed by (solving for y):
[tex]y=\text{ 1 + 5x}[/tex]For example, for a value of x = 1, y is a function of x; then, y = 1 + 5 = 6, or (1, 6), and so on.
For the next system of equations:
[tex]\begin{gathered} x\text{ + 2y = 13} \\ -x\text{ + 2y = 7} \end{gathered}[/tex]Adding both equations, we finally have:
[tex]4y\text{ = 20}\Rightarrow\text{ y = 5}[/tex]Then, solving for x, we have (using the first equation):
[tex]x\text{ + 2(5) = 13 }\Rightarrow x\text{ = 13 - 10 }\Rightarrow x\text{ = 3}[/tex]Then, this last system has a unique solution, which is (3, 5) or x = 3 and y = 5.
The height of a tree is x feet. If it grows ½ times the original height, choose the correct expression that denotes the situation.
ANSWER
1.5(x)
EXPLANATION
The tree is originally x feet tall. If it grows 1/2 this height it means that now it is 1/2x taller, or we can express this as a decimal, 0.5x. If we add these two heights we'll have the new height of the tree:
[tex]x+0.5x=(1+0.5)x=1.5x[/tex]Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x.
(x ^4 - 3x^3 + 3x^2 - 3x + 6) / (x - 2)
SOLUTION
We want to perform the following division using synthetic division
[tex]\frac{x^4-3x^3+3x^2-3x+6}{x-2}[/tex]This becomes
First we write the problem in a division format as shown below
Next take the following step to perform the division
Now, we have completed the table and we obtained the following coefficients, 1, -1, 1, -1, 4
Note that the first four ( 1, -1, 1, -1) are coefficients of the quotient, while the last one (4) is the coefficient of the remainder.
Hence the quotient is
[tex]x^3-x^2+x-1[/tex]And the remainder is 4.
Hence
[tex]\frac{x^4-3x^3+3x^2-3x+6}{x-2}=x^3-x^2+x-1+\frac{4}{x-2}[/tex]How many angles and sides are there in a Heptagon?ANGLES:SIDES:
The heptagon is a polygon of 7 sides and 7 angles
The heptagon is a closed figure formed from 7 sides
Since every 2 sides connected to form an angle, then
It contains also 7 angles
Then the answer is :
Angles: 7
Sides: 7
Jaylen used a 20% discount on a pair of jeans that cost $70 before tax. The sales tax is 6%. How much does the pair of jeans cost after tax? Show your work
If Jaylen used a 20% discount on a pair of jeans that cost $70 before tax, then the price of the jeans will be $70 - 20%.
Let's calculate the 20% of $70.
[tex]70\times20\%=14[/tex]So, the discounted price of the jeans before tax is $70 - $14 = $56.
Generally, sales tax is applied to the discounted price, so let's calculate the 6% of $56.
[tex]6\%\times56=3.36[/tex]The sales tax is $3.36.
Therefore, the cost of the pair of jeans after tax is $59.36.
[tex]56+3.36=59.36[/tex]Maura and her brother are at a store shopping for a beanbag chair for their school's library. The store sells beanbag chairs with different fabrics and types of filling. Velvet Suede Foam 2 7 Beads 2 7 What is the probability that a randomly selected beanbag chair is filled with beads and is made from velvet? Simplify any fractions.
The store sells a total of 18 types of chairs (this is the sum of all the types of chairs in the two way frequency table). From this table we notice that only two of them are filled with beads and made from velvet. Then the probability of choosing this is:
[tex]P=\frac{2}{18}=\frac{1}{9}[/tex]Therefore the probability is 1/9
#2 Funding the perimeter and area of the composite figure.
1)
We can find the circumference using the formula
[tex]C=2\pi r[/tex]but remember that the diameter is 2 times the radius
[tex]d=2r[/tex]So we can use the formula using radius or diameter, the problem gives us the diameter, so let's use it, so the formula will change a little bit
[tex]C=\pi d[/tex]Where "d" is the diameter.
d = 40 yd, and π = 3.14, so the circumference will be
[tex]\begin{gathered} C=\pi d \\ C=3.14\cdot40=125.6\text{ yd} \end{gathered}[/tex]And to find out the area we can use this formula
[tex]A=\frac{\pi d^2}{4}[/tex]Or if you prefer use the radius
[tex]A=\pi r^2[/tex]Let's use the formula with the diameter again
[tex]\begin{gathered} A=\frac{\pi d^2}{4} \\ \\ A=\frac{3.14\cdot(40)^2}{4} \\ \\ A=1256\text{ yd}^2 \end{gathered}[/tex]Then the circumference is 125.6 yd and the area is 1256 yd^2
2)
Here we have a compounded figure, we have half of a circle and a triangle, so let's think about how we get the perimeter and the area.
The perimeter will be the sum of the sides of the triangle and half of a circumference, we already know the length of the triangle's side, it's 10.82, we got to find the half of a circle circumference and then sum with the sides.
We know that
[tex]C=\pi d[/tex]And we can see in the figure that d = 12 mm, then
[tex]C=\pi d=3.14\cdot12=37.68\text{ mm}[/tex]But that's a full circumference, we just want half of it, so let's divide it by 2.
[tex]\frac{C}{2}=\frac{37.68}{2}=18.84\text{ mm}[/tex]Now we have half of a circumference we can approximate the perimeter of the figure, it will be
[tex]\begin{gathered} P=10.82+10.82+18.84 \\ \\ P=40.48\text{ mm} \end{gathered}[/tex]The area will be the area of the triangle sum the area of half of a circle
Then let's find the triangle's area first
[tex]A_{}=\frac{b\cdot h}{2}[/tex]The base "b" will be the diameter of the circle, and the height "h" will be 9 mm, then
[tex]A_{}=\frac{12\cdot9}{2}=54\text{ mm}^2[/tex]And the half of a circle's area will be
[tex]A=\frac{1}{2}\cdot\frac{\pi d^2}{4}=\frac{3.14\cdot(12)^2}{8}=$$56.52$$\text{ mm}^2[/tex]Then the total area will be
[tex]A_T=56.52+54=110.52\text{ mm}^2[/tex]Therefore, the perimeter and the area is
[tex]\begin{gathered} P=40.48\text{ mm} \\ \\ A=110.52\text{ mm}^2 \end{gathered}[/tex]Find the perimeter of the following quadrilateral.The bottom side measures 2 ft.
The perimeter of a quadrilateral is given by the sum of all the sides.
In order to add mixed numbers, let's rewrite them as a sum of the integer part and the fraction part.
So we have:
[tex]\begin{gathered} P=1\frac{5}{12}+3\frac{3}{4}+2\frac{1}{6}+2 \\ P=1+\frac{5}{12}+3+\frac{3}{4}+2+\frac{1}{6}+2 \\ P=(1+3+2+2)+(\frac{5}{12}+\frac{9}{12}+\frac{2}{12}) \\ P=8+\frac{16}{12} \\ P=8+1+\frac{4}{12} \\ P=9+\frac{1}{3} \\ P=9\frac{1}{3}\text{ ft} \end{gathered}[/tex]Therefore the perimeter is 9 1/3 ft.
The histogram below shows the number of hurricanes making landfall in the United States for a period of 108 years. On average, there have been 1.72 hurricanes per year with a standard deviation of 1.4 hurricanes per year. Is the distribution approximately normal?
(A) No, the distribution is skewed to the right.
(B) No, the distribution is skewed to the left.
(C) Yes, the distribution has a single peak.
(D) Yes, the percentage of values that fall within 1, 2, and 3 standard deviations of the mean are close to 68%, 95%, and 99.7%, respectively.
Using the Empirical Rule, the correct option regarding the skewness of the distribution is given as follows:
(A) No, the distribution is skewed to the right.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of 68%.The percentage of scores within two standard deviations of the mean of the distribution is of 95%.The percentage of scores within three standard deviations of the mean off the distribution is of 99.7%.In the context of this problem, the mean and the standard deviation are given as follows:
Mean: 1.72.Standard deviation: 1.4.A huge percentage is within one standard deviation of the mean, and the distribution is not symmetric, hence it is not normal.
Since most values are at the lower bounds of the histogram, the distribution is right skewed and option a is correct.
More can be learned about the Empirical Rule at https://brainly.com/question/10093236
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H = -16t^2 + 36t + 56 Where H is the height of the ball after t seconds have passed.
we have the equation
H = -16t^2 + 36t + 56
This equation represents a vertical parabola open downward, which means, the vertex is a maximum
The time t when the ball reaches its maximum value corresponds to the x-coordinate of the vertex
so
Convert the given equation into vertex form
H=a(t-h)^2+k
where
(h,k) is the vertex
step 1
Complete the square
H = -16t^2 + 36t + 56
Factor -16
H=-16(t^2-36/16t)+56
H=-16(t^2-36/16t+81/64)+56+81/4
Rewrite as perfect squares
H=-16(t-9/8)^2+76.25
the vertex is (9/8,76.25)
therefore
the time is 9/8 sec or 1.125 seconds when the ball reaches its maximum4. Which inequality is represented by the graph?8642S-6428X4-6laO4x - 2y > 12O4x - 2y < 12O4x + 2y > 12O4x + 2y < 12
Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.
First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:
We can easily find the points (0, -6) and (2, -2).
With this, we can find the equation of the line using the point-slope formula:
[tex]y-y_0=m\cdot(x-x_0)[/tex]Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]Plugging the coordinates of the points, we get:
[tex]m=\frac{-2-(-6)}{2-0}=\frac{-2+6}{2}=\frac{4}{2}=2[/tex]Such that:
[tex]\begin{gathered} y-(-6)=2\cdot(x-0) \\ y+6=2x \end{gathered}[/tex]Rearranging it in the ax + by = c form,
[tex]2x-y=6[/tex]Multiply both sides of the equation by a factor of 2
[tex]4x-2y=12[/tex]Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:
[tex]4x-2y>12[/tex]All the point (x, y) satisfying this inequality are contained in the shaded region.
zero and negative exponentswrite in simplest form without zero or negative exponents
We have the following rule for exponents:
[tex]a^0=1[/tex]then, in this case we have:
[tex](-17)^0=1[/tex]If tan A = ã and tan B=16calculate and simplify the following:?tan(A - B) = +
SOLUTION
[tex]\begin{gathered} In\text{ Trigonometry} \\ \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\text{ tan B}}_{} \end{gathered}[/tex]Given:
[tex]\begin{gathered} \tan \text{ A= }\frac{5}{6} \\ \tan \text{ B= }\frac{1}{6} \end{gathered}[/tex]Now substitute these given into the expression above:
[tex]\tan (A-B)=\frac{\frac{5}{6}-\frac{1}{6}}{1+(\frac{5}{6}\times\frac{1}{6})}[/tex]Simplifying further:
[tex]=\frac{\frac{2}{3}}{1+\frac{5}{36}}[/tex][tex]\begin{gathered} =\frac{\frac{2}{3}}{\frac{41}{36}} \\ =\frac{2}{3}\times\frac{36}{41} \\ =\frac{72}{123} \\ =\frac{24}{41} \end{gathered}[/tex]The answer therefore is:
[tex]\frac{24}{41}[/tex]is y=10 a solution to the inequality y + 6 < 14
The inequality given is
[tex]y+6<14[/tex]Collecting like terms we will have
[tex]\begin{gathered} y+6<14 \\ y<14-6 \\ y<8 \end{gathered}[/tex]With the above solution, we can conclude that y=10 is not a solution to the inequality because the values of y are less than 8
Hence, The answer is NO
distance of (-5,-3) and (-9,4)
Answer:11
Step-by-step explanation:
Am I correct? I need some clarification on this practice problem solving I have attempted this problem but for some reason I feel like I may be wrong
Solution:
The modulus of a complex number;
[tex]z=a+bi[/tex]is denoted by;
[tex]|z|=|a+bi|=\sqrt[]{a^2+b^2}[/tex]Thus, given the complex number;
[tex]2-6i[/tex]The modulus is;
[tex]\begin{gathered} a=2,b=-6 \\ |2-6i|=\sqrt[]{2^2+(-6)^2} \\ |2-6i|=\sqrt[]{4+36} \\ |2-6i|=\sqrt[]{40} \\ |2-6i|=\sqrt[]{4\times10} \\ |2-6i|=\sqrt[]{4}\times\sqrt[]{10} \\ |2-6i|=2\times\sqrt[]{10} \\ |2-6i|=2\sqrt[]{10} \end{gathered}[/tex]ANSWER:
[tex]2\sqrt[]{10}[/tex]Hallum hardware created flyers to advertise a carpet sale . A portion of the flyer is shown below. Based on the chart, which statement describes the relationship between area and the cost of carpet?
The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.
Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.
Ratio = cost / area
750 / 500 = 1.50
1500 / 1000 = 1.50
2,250 / 1500 = 1.50
3000 / 2000 = 1.50
Since the ratios are constant, the relationship is proportional.
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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.
9 mVolume = 75 n mm3RadiusG
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]In this problem
we have
V=75pi mm^3
h=9 m------> convert to mm
h=9,000 mm
substitute in the given equation
[tex]\begin{gathered} 75\cdot\pi=\frac{1}{3}\cdot\pi\cdot r^2\cdot9,000 \\ \text{simplify} \\ 75=r^2\cdot3,000 \\ r^2=\frac{75}{3,000} \\ \\ r^2=\frac{1}{40} \\ \\ r=\frac{1}{\sqrt[\square]{40}} \\ \\ r=\frac{\sqrt[\square]{40}}{40} \\ \text{simplify} \\ r=\frac{2\sqrt[\square]{10}}{40} \\ \end{gathered}[/tex][tex]r=\frac{\sqrt[\square]{10}}{20}\text{ mm}[/tex]