The Equation of a Line
The slope-intercept form of a line can be written as:
y = mx + b
Where m is the slope of the graph of the line and b is the y-intercept.
In the specific case where the line passes through the origin (0,0), we can find the value of b by substituting x=0 and y=0:
0 = m(0) + b
Solving for b:
b = 0.
Thus, the equation of the line reduces to:
y = mx
We only need to find the value of the slope.
That is where we need the second data. Our line is perpendicular to the line of equation 4x + 3y = 6.
Solving for y:
[tex]y=-\frac{4}{3}x+2[/tex]The slope of the second line is -4/3.
We must recall that if two lines of slopes m1 and m2 are perpendicular, then:
[tex]m_1\cdot m_2=-1[/tex]Substituting the value of m1 and solving for m2:
[tex]\begin{gathered} -\frac{4}{3}\cdot m_2=-1 \\ m_2=\frac{3}{4} \end{gathered}[/tex]The slope of our line is 3/4 and the required equation is:
[tex]y=\frac{3}{4}x[/tex]From this last equation, we need to find the general form of the line.
Multiply both sides of the equation by 4:
4y = 3x
Subtract 3x on both sides:
4y - 3x = 0
Reorder:
-3x + 4y = 0
Why is it incorrect to write {∅} to denote a set with no elements?
Answer:
It's incorrect because {∅} is saying that the set contains empty sets, which is not the same as saying the set is empty (which can be denoted by { } or ∅
Step-by-step explanation: It's all in the answer.
Linear Programming WorksheetGraph each feasible region. maximize or minimize each objective
Given:
x+2y = 8
x=2, y=0
Substitute x=2 then find value of x as,
2+2y=8
2y=6
y=3
(x,y) = (0,3)
Now, substitute y=0 then find value of y as,
x+2(0)=8
x=8
(x,y) = (8,0)
It is given that P = x+3y
(x,y) = (0,3) then P= 0+3x3
P=9
The maximum valu P=9 and vertiex (0,3)
(x,y) = (8,0) then P=8+0= 8
The mininmum val
a rectangular Garden has a length of 10 m and a width of 8 meters fill in the Box to show the perimeter and the area of the garden
Explanation
Step 1
Area,To find the area of a rectangle, multiply its height by its width
then
[tex]\text{Area}_{rec\tan gle}=length\cdot width[/tex]Let
length=10 m
width=8 m
replace,
[tex]\begin{gathered} \text{Area}_{rec\tan gle}=length\cdot width \\ \text{Area}_{rec\tan gle}=10\text{ m }\cdot\text{ 8 m} \\ \text{Area}_{rec\tan gle}=80m^2 \end{gathered}[/tex]Step 2
find the perimeter:
Perimeter is the distance around the outside of a shape,so for the garden the perimeter is
[tex]\text{Perimeter}_{rec\tan gle}=2(length+width)[/tex]replace,
[tex]\begin{gathered} \text{Perimeter}_{\text{garden}}=2(10m+8m) \\ \text{Perimeter}_{\text{garden}}=2(18\text{ m)} \\ \text{Perimeter}_{\text{garden}}=36\text{ m} \end{gathered}[/tex]I hope this helps you
The measures of the angles of a triangle are shown in the figure below. Solve for x. (2x+6)° 42°
A triangle is a shape that has a total angle of 180°.
How to solve the triangle?It's important to note that a triangle is a shape that has three sides and the total sum is equal to 180°.
In this case, we have 2x + 6 and 42°. The other angle isn't given and this can't be solved further
The sides will have been illustrated as:
= a + b + c = 180
The expression given will then be allocated for each side to solve it further.
Note that an overview was given as the information is incomplete.
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oblem 9If 8 x 17 = 136, then 17 isI % of 136if 44 x 8 = 352, then 44 is% of 352
Let 'x' represents the missing number
a) x % of 136 = 17
[tex]\begin{gathered} \text{where, }x\text{ \% =}\frac{\text{x}}{100} \\ \frac{x}{100}of136=17 \\ \frac{x}{100}\times136=17 \\ \frac{136x}{100}=17 \\ 1.36x=17 \end{gathered}[/tex]Divide both sides by 1.36
[tex]\begin{gathered} \frac{1.36x}{1.36}=\frac{17}{1.36} \\ x=\frac{25}{2}=12.5 \\ \therefore x=12.5 \end{gathered}[/tex]Hence, 17 is 12.5% of 136.
b) x% of 352 = 44
[tex]\begin{gathered} \text{where, x\%=}\frac{\text{x}}{100} \\ \frac{x}{100}\times352=44 \\ \frac{352x}{100}=44 \\ 3.52x=44 \end{gathered}[/tex]Divide both sides by 3.52
[tex]\begin{gathered} \frac{3.52x}{3.52}=\frac{44}{3.52} \\ x=12.5 \\ \therefore x=12.5 \end{gathered}[/tex]Hence, 44 is 12.5% of 352.
Fred takes out a mortgage for $60,000 at 7% for 20 years. What are his monttpayment, the total amount paid, and the cost of the mortgage?
We will have the following:
First, we determine the monthly rate:
[tex]r_m=\frac{0.07}{12}=\frac{7}{1200}[/tex]Now, we determine the monthly payment:
[tex]\begin{gathered} A=P\frac{(1+r_m)^n}{(1+r_m)^n-1} \\ \\ \Rightarrow A=60000\frac{(1+(7/1200))^{^{240}}}{(1+(7/1200))^{240}-1}\Rightarrow A\approx465.18 \end{gathered}[/tex]So, the monthly payment will be approximately $465.18.
The total amount paid will be:
[tex]\begin{gathered} X=A\ast n\ast t \\ \\ \Rightarrow X=(465.18)(12)(20)\Rightarrow X\approx111643.2 \end{gathered}[/tex]So, the total payment will be approximately $111 643.2.
The cost of the mortgage is:
[tex]c=111643.2-60000\Rightarrow c\approx51643.2[/tex]So, the cost of the mortgage is approximately $51 643.2.
help video S-(x – 6)² +7 for 2 2 +3 x = 3 for Find f(3)
Explanation:
This is a function defined by parts. When x is not 3, the function has the equation on top, but when x is 3, the function has one value: 2.
Answer:
f(3) = 2
coupon A 45% off of a $73 jacket coupon B $30 rebate on a $73 Jacket
To be able to determine which among the coupon gives a lower price, let's determine what is 45% of $73 so that we could compare it with the $30 rebate. The highest amount among the two coupons will give you a lower price.
Let's determinte the 45% of 73:
[tex]\text{73 x }\frac{45\text{\%}}{100\text{\%}}\text{ }\rightarrow\text{ 73 x 0.45}[/tex][tex]\text{ = \$32.85}[/tex]Coupon A gives you $32.85 dollar off of a $73 Jacket.
Coupon A will give you a lower price compared to Coupon B. The price of the jacket will be $2.85 lesser than using Coupon B.
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The transformation of the map is given as; translation of 1 unit to the right and rotated 180 degree counterclockwise about origin.
What is termed as the translation?In geometry, translation refers to a function which moves an object a specified distance. The element is not otherwise altered. It is not rotated, mirrored, or resized.Each point of the element must be relocated within the same direction and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and the element after the translation is referred to as the image.For the given question;
The graph of the triangle is given,
The triangle is first translated to the 1 unit to its right such that vertex of the triangles lies on the y -axis.
Now, the triangle is rotated about origin in counter clock wise direction about 180 degrees.
Thus, the final image is shown by red triangle.
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Suppose that a regression line for some data transformed with logarithmspredicts that when x equals 4, log(y) will equal 2.671. What does theregression line predict y will equal when x equals 4?
Explanation:
The information that we have is that when the value of x is 4
[tex]x=4[/tex]The logarithm of y is 2.671
[tex]log(y)=2.671[/tex]The question is:
What does the regression line predict y will equal when x =4?
That means we need to solve for y in
[tex]log(y)=2.671[/tex]To find the predicted y-value.
To solve for y, we make 10 the base of the two sides of the equation as shown in the following expression:
[tex]10^{log(y)}=10^{2.671}[/tex]Due to the properties of logarithms, on the left side, we will be left only with 'y'
[tex]y=10^{2.671}[/tex]And finally, solving the operations on the right-hand side, the result is:
[tex]y=468.813[/tex]Answer:
[tex]y=468.813[/tex]Issac says that T' will be located at (4,20)Isabella says that T' will be located at (4,12(who is correct and why?
In the given triangle :
The coordinate of T is ( 2, 10 )
Triangle TUV will be dilated by a scale factor of 2
Thus, multiply the coordinates of TUV by 2
T' = 2 x T
T' = 2 x ( 2, 10 )
T' = ( 2x2, 2x10)
T' = ( 4, 20 )
So, T' will be located at ( 4, 20 )
Issac says that T' will be located at (4,20)
Answer : Issac says that T' will be located at (4,20)
The state of California charges homeowners approximately $1,200 per year in property taxes for every $100,000 a person's home is worth. If Mr. Cohen's home in Studio City, CA is worth $1,600,000, how much does he have to pay in property taxes per year? Set up a pair of equivalent ratios and then use your knowledge of cross products to solve. You may use calculator.
We have the next information
1,200 ----- 100,000
x ----- 1,600,000
x is the missing quantity
x can be calculated in this way
[tex]x=\frac{1,600,000\cdot1200}{100,000}=19200[/tex]Mr. Cohen has to pay per year $19,200 taxes per year
Which of the equations or inequalities below are true?O A. 7-26O B. 7-224O C. 7-23 5O D. 7 - 2 = -5
Given,
The equation orr inequalities are,
[tex]\begin{gathered} A)7-2\ge6 \\ B)7-2\ne4 \\ C)7-2\leq5 \\ D)7-2=-5 \end{gathered}[/tex]A) In the expression,
7 - 2 = 5
Hence, 7-2 =6 is incorrect.
B) In the expression,
7 - 2 = 5,
Hence,
[tex]7-2\ne4[/tex]Option B is correct.
C) In the expression,
7 - 2 = 5
7 - 2 < 5 is incorrect
Hence, 7 - 2 =< 5 is incorrect.
D)In the expression,
7 - 2 = 5
Hence, 7 - 2 =< -5 is incorrect.
Hence, option B is correct.
Please help me this is so confusing .which of the following, names a ray in the drawing?
From the given figure, let's select the rays given in the option.
A ray can be said to be a straight line which starts from a point and goes to infinity at the other end.
From the given figure, the rays are:
• NK
,• NJ
,• NL
,• NM
Therefore, from the list the, the ray is NK.
ANSWER:
NK
I don't understand this. Proving and applying ASA and Salad congruence
Given two triangles, we can say that they are congruent by the SAS postulate (Side Angle Side) if both triangles have two congruent sides and the angle that they form is also congruent
In this case, we have that triangle IHG and DFE have already two congruent sides, then, to make them congruent, the angle that they each form (angle IHG and angle DEF) must be congruent so we can use the SAS postulate
In the diagram below, if the measure of < C = 45 °, and side AB = 6.8, then side BC = _____.
Solution
Since
[tex]\begin{gathered} \tan45=\frac{6.8}{BC} \\ \\ \Rightarrow BC=\frac{6.8}{\tan45}=6.8\text{ since}\tan45=1 \end{gathered}[/tex]The correct option is A.
leon wrote an expression that is equivalent to (30+6)÷12 witch expression could be the one leon wrote
ANSWER
(3 · 3 · 2 · 2) ÷ (3 · 2 · 2)
EXPLANATION
The given expression is also equivalent to 36 ÷ 12 - because 30 + 6 = 36.
In the equivalent expression we have:
[tex]\begin{gathered} 3\cdot3\cdot2\cdot2=36 \\ 3\cdot2\cdot2=12 \end{gathered}[/tex]Therefore it's 36 ÷ 12 too
simplify 12 times y to the 6th power times z to the 4th power divided by 6 times y times z to the 6th power
The simplified expression of the given expression is 2y^5 z^{-2}
What is expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.
Given expression, [tex]\frac{12y^6 z^4}{6 yz^6}[/tex]
Simplifying and we get
[tex]\frac{12y^6 z^4}{6 yz^6}\\=2y^{6-1} z^{4-6}\\=2y^5 z^{-2}[/tex]
Therefore, the simplified expression of the given expression is 2y^5 z^{-2}
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Given AFGH ~ ALMN, which must be true? Select all that apply.A.FGLMFHLNB. FH ~ LNC.mZFmZLmZGmZMD. GHMNE. mZH ^mZN
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 32o. From a point 2,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 35o. How tall (in feet) is the mountain? Round to two decimal places.
___________
To calculate the angle of elevation, just measure the angle formed by the line of sight and the level plain. The elevation of the peak is 10406.58 feet at its highest point.
This is further explained below.
What is the height of the mountain?Where
<A=30
AB=2000
<A B C=180-33
<A B C=147
<B C A=180-<A-<A B C
< B C A=180-30-147
<BCA=3
To begin, the side length BC may be calculated by using the following formula:
[tex]\frac{B C}{\sin A}=\frac{A B}{\sin C}[/tex]
So, we have:
B C=sin A *(A B/sin C)
B C=sin (30) *2000/sin (3)
B C=19107.3
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Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) 9 + 4 + (-1) + ... + (-536)
SOLUTION
The terms below make an A.P. Now we are told to find the sum of the AP.
Sum of an AP is given by
[tex]S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack}[/tex]Where S = sum of the AP, a = first term = 9, d = -5, n= ?
So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"
[tex]\begin{gathered} \text{From T}_{n\text{ }}=\text{ a +(n-1)d where T}_{n\text{ }}=\text{ -536} \\ -536\text{ = 9+(n-1)-5} \\ -536\text{ = 9-5n+5} \\ -536\text{ = 14-5n} \\ -5n\text{ = -536-14} \\ -5n\text{ = -550} \\ n\text{ = 110} \end{gathered}[/tex]Now let's find the sum
[tex]\begin{gathered} S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack} \\ S\text{ = }\frac{110}{2}\lbrack2\times9\text{ + (110-1)-5\rbrack} \\ S\text{ = 55\lbrack{}18+(119)-5\rbrack} \\ S\text{ = 55\lbrack{}18 - 595\rbrack} \\ S\text{ = 55}\times-577 \\ S\text{ = -31735} \end{gathered}[/tex]Therefore, the sum = -31735
what is the slope of a line parallel to the line whose equation is 18 x - 3 y equals -45
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
Let's solve for "y" from the equation of the line given in the exercise, in order to express it in Slope-Intercept form:
[tex]\begin{gathered} 18x-3y=-45 \\ -3y=-18x-45 \\ y=\frac{-18x-45}{-3} \\ y=6x+15 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m=6 \\ b=15 \end{gathered}[/tex]By definition, the slopes of parallel lines are equal. Therefore, the slope of the line parallel to line given in the exercise, is:
[tex]m=6[/tex]3.
How much greater is the surface area of the rectangular prism than the surface area of the cube?
6 cm
(1 point)
3 cm
2 cm
O 36 cm²
O 33 cm²
O 18 cm²
O 45 cm²
3 cm
The dimensions of the rectangular prism of 6 cm by 3 cm by 2 cm and the dimension of the cube of 3 cm gives the amount the surface area of the prism is greater than the cube as 18 cm²
What is a rectangular prism?A rectangular prism is a six faced solid hexahedron.
The given dimension of the rectangular prism are:
Length = 6 cm
Height = 3 cm
Width = 2 cm
The side length of the cube = 3cm
The surface area of the rectangular prism is therefore:
[tex]A_p[/tex] = 6 × 3 × 2 + 6 × 2 × 2 + 3 × 2 × 2 = 72
The surface area of the rectangular prism is 72 cm²
The surface area of the cube: [tex]A_c[/tex] = 6 × 3² = 54
The surface area of the cube, [tex]A_c[/tex] = 54 cm²
The amount by which area of the rectangular prism is greater than the area of the cube is therefore: [tex]A_p[/tex] - [tex]A_c[/tex] = 72 cm² - 54 cm² = 18 cm²
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1. P(video games and kid is 10 to 12 years old)2. P(basketball/kid is 13 to 15 years old)3. P(kid is 13 to 15 years old/basketball)4. P(darts/kid is 10 to 15 years old)5. P(basketball and darts)6. P(basketball and kid is 13 to 18 years old)Answer the following problems about two way frequency tables make sure to reduce your fraction.
1. P(video games and kid is 10 to 12 years old)
[tex]\begin{gathered} P(video\text{ games and kid i 10 to 12 years old)} \\ =\text{ }\frac{number\text{ of kids 10 - 12 years old playing video games}}{total\text{ number of students}} \\ =\text{ }\frac{17}{143} \end{gathered}[/tex]Therefore,
The P(video games and kid is 10 to 12 years old) = 17/143
2. P(basketball/kid is 13 to 15 years old)
[tex]\begin{gathered} P\mleft(basketball/kid\text{ is 13 to 15 years old}\mright)\text{ } \\ =\text{ }\frac{number\text{ of kids 13 - 15 years old playing basketball}}{number\text{ of kids of age 13 to 15 years old}} \\ =\text{ }\frac{14}{45} \end{gathered}[/tex]P(basketball/kid is 13 to 15 years old) = 14/45
3. P(kid is 13 to 15 years old/basketball)
[tex]\begin{gathered} P(\text{kid is 13 to 15 years old / basket ball)} \\ =\text{ }\frac{number\text{ of kids aged 13 to 15 years old }}{number\text{ of kids playing basketball}} \\ =\text{ }\frac{14}{54} \\ =\text{ }\frac{7}{27} \end{gathered}[/tex]P(kid is 13 to 15 years old/basketball) = 7/27
4. P(darts/kid is 10 to 15 years old)
[tex]\begin{gathered} P(\text{darts / kid is 10 to 15 years old)} \\ =\text{ }\frac{number\text{ of kids age 10 to 15 playing darts}}{\text{number of kids age 10 to 15}} \\ =\text{ }\frac{kids\text{ age 10 to 12 + age 13 to 15 playing darts}}{\text{kids age 10 to 12 + age 13 to 15}} \\ =\text{ }\frac{12\text{ + 15}}{34\text{ + 45}} \\ =\text{ }\frac{27}{79} \end{gathered}[/tex]P(darts/kid is 10 to 15 years old) = 27/79
5. P(basketball and darts)
[tex]\begin{gathered} P(basketball\text{ and darts)} \\ \sin ce\text{ there are no kids playing basketball and darts at the } \\ \text{same time} \\ \text{then,} \\ P(basketball\text{ and darts) = 0} \end{gathered}[/tex]P(basketball and darts) = 0
6. P(basketball and kid is 13 to 18 years old)
[tex]\begin{gathered} P(\text{basketball and kid is 13 to 18 years old)} \\ =\text{ }\frac{number\text{ of kids 13 to 18 years playing basket}}{nu\text{mber of kid 13 to 18 years }} \\ =\text{ }\frac{\text{kids 13 to 15 years + 16 - 18 years playing basketball}}{\text{kids 13 to 15years + 16 to 18 years}} \\ =\text{ }\frac{14\text{ + 18}}{45\text{ + 35}} \\ =\text{ }\frac{32}{80} \\ =\frac{2}{5} \end{gathered}[/tex]P(basketball and kid is 13 to 18 years old) = 2/5
4(3c+3)-3c+1=3(3c+5)-2
The given equation is,
[tex]4(3c+3)-3c+1=3(3c+5)-2[/tex]The above equation can be simplified as follow,
[tex]undefined[/tex]Find the due date of a note dated October 24, 2018 for 2 months.
2 months after october 24th 2018 will be:
24th December 2018 which was a monday.
Add 3 days of grace period will give the due date to be 27th December 2018.
The Neckware association of America reported that 3% of ties sold in the United States are bow ties. If 4 customers who purchased a tie randomly selected,find the probability that at least 1 purchased a bow tie
Pr (people with bow ties) = 3% = 0.03
p = 0.03
Pr (people without bow tie) = 1 - 0.03 = 0.97
q = 0.97
n = 4 customers
[tex]Pr(at\text{ least 1 purchased a bow tie) = 1 - Pr(none purchased a bow tie)}[/tex]To find the probability that at least 1 purchased a bow tie, we will use a binomial probability formula:
[tex]p(x=^{}X)=^nC_xp^xq^{n\text{ - x}}[/tex][tex]\begin{gathered} \text{Pr(none purchased a bow tie) = p(x = 0)} \\ \text{p(x = 0) = }^4C_0\times p^0\times q^{4\text{ - }0} \\ \text{p(x = 0) = 1 }\times\text{ 1}\times q^4=(0.97)^4 \\ \text{p(x = 0) = }0.8853 \\ \\ \text{Pr(none purchased a bow tie) = }0.8853 \end{gathered}[/tex][tex]\begin{gathered} Pr(at\text{ least 1 purchased a bow tie) = 1 - 0.8853} \\ Pr(at\text{ least 1 purchased a bow tie) = 0.1147} \end{gathered}[/tex]Cut a 10-foot (ft.) long piece of wood into two pieces so that one piece is 2 ft longer than the other. Which of the following equations depicts the given situation?A. x/2 = 10B. x + 2 = 10C. 2x + 2 = 10D. None of the choices
Given:
Cut a 10-foot (ft.) long piece of wood into two pieces so that one piece is 2 ft longer than the other.
Required:
Which of the following equations depicts the given situation?
Explanation:
Let 10 feet long piece of wood cut into two pieces of length x(smaller piece) and
x+2 larger piece.
So, the equation will be
x + x + 2 =10
2x + 2=10
Answer:
Option C is correct.
Two right rectangular prisms are shown below. 2 inches 5 Inches 9 inches inches 7 NI inches inches Prism I Prism II If each prism is packed with small cubes of side length 1 inch, how many more cubes are in Prism Il than in Prism I? O 42 cubes О 210 cubes O 510 cubes O 720 cubes
The number of small cubes in the prism I can be determined as,
[tex]\begin{gathered} N_1=\frac{Volume\text{ of prism I}}{Volume\text{ of one small cube}} \\ =\frac{\frac{7}{4}\text{ in}\times\frac{5}{4}\text{ in}\times\frac{3}{2}\text{ in}}{\frac{1}{4}\text{ in}\times\frac{1}{4}\text{ in}\times\frac{1}{4}\text{ in}} \\ =210 \end{gathered}[/tex]The number of cubes in the prism II can be determined as,
[tex]\begin{gathered} N_2=\frac{2\text{ in}\times\frac{5}{2}\text{ in}\times\frac{9}{4}in}{\frac{1}{4}in\times\frac{1}{4}in\times\frac{1}{4}in} \\ N_2=720 \end{gathered}[/tex]The difference in the number of cubes is,
[tex]\begin{gathered} N_2-N_1=720-210 \\ =510 \end{gathered}[/tex]Thus, Prism II has 510 more cubes than Prism I.
Thus, option (c) is the correct solution.
Do 9 and 10 keep it 9th grade if you can Question 9-10
Given the formula for the volume of a cylinder:
[tex]V=\pi r^2h[/tex]You know that "r" is the radius of the cylinder and "h" is the height.
a. In order to solve the formula for "h", you can divide both sides of the formula by:
[tex]\pi r^2[/tex]As follows:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{V}{\pi r^2}[/tex]b. Having a cylindrical swimming pool, you know that:
[tex]\begin{gathered} r=12\text{ }ft \\ V=1810\text{ }ft^3 \end{gathered}[/tex]And, for this case:
[tex]\pi\approx3.14[/tex]Therefore, you can substitute values into the formula for the height of a cylinder found in Part "a" and evaluate:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{(3.14)(12\text{ }ft)^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{452.16\text{ }ft^2}[/tex][tex]h\approx4\text{ }ft[/tex]Hence, the answers are:
a.
[tex]h=\frac{V}{\pi r^2}[/tex]b.
[tex]h\approx4\text{ }ft[/tex]