The tank is full of water and all of the water is to be pumped over the top of the tank is 643,094.07 ft-lbs .
Consider a slice shown at a height of v and suppose that the slice has a thickness of Δv. The volume of the slice is then π( 3 )^2 Δv = 9π Δv which is the area of the disk of radius 3 times the thickness of the slice.
= 62.4 ( 9 π Δ v ) = 561.6 π Δ v
Δ W = ( 561.6 π Δ v ) ( 27 − v ) = 561.6 π ( 27 − v ) Δ v ft-lbs
Work = [tex]\int\limits^{27}_0[/tex]561.6 π ( 27 − v ) d v
= 561.6 π ( 27 v − 1 / 2 v^2 ) | 27_ 0
= 561.6 π ( 27 ∗ 27 − 1 / 2 ( 27 )^2
= 1,023,516 π / 5
= 643,094.07 ft-lbs
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The table below shows the linear relationship between
the distance in feet below sea level and the time in
seconds traveled by a submarine.
What is the rate of change low of the distance in the feet below sea level with respect to time that the box submarine traveled?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below
[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{545})\qquad (\stackrel{x_2}{44}~,~\stackrel{y_2}{864}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{864}-\stackrel{y1}{545}}}{\underset{run} {\underset{x_2}{44}-\underset{x_1}{15}}} \implies \cfrac{ 319 }{ 29 } \implies \text{\LARGE 11}[/tex]
Hence, the slope of the line is [tex]m=11[/tex].
What is the slope of line?
The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]can be easily determined by finding the difference between the coordinates of the points.
As we know that,
The slope has several names
(1) average rate of change
(2)rate of change
(3)delta[tex]Y[/tex] over delta[tex]X[/tex]
(4)Δ[tex]y[/tex]over Δ[tex]x[/tex]
(5)rise over run
(6)gradient
(7)constant of proportionality
So, the same cat wearing the different costumes to get the slope of the straight line, the two points are
[tex](x_1,y_1)=(15,545)\\(x_2,y_2)=(44,864)[/tex]
[tex]m=\frac{864-545}{44-15}\\\\m=\frac{319}{29}\\\\m=11[/tex]
Hence, the slope of the line is [tex]m=11[/tex].
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Write the equation of the line in point-slope form. (hint the y intercept is (0, -5)
show work
the area of the triangle formed by the x and y intercepts of the parabola y=0.5(x-3)(x+k) is equal to 1.5 square units. find all possible values of k.
The possible values of k are -0.56, -3.56, -2 and -1.
Find all possible values of k ?We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)
Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k
So, the y-intercept is (0,-1.5k).
Thus, the height of the triangle becomes |-1.5k| = 1.5k
Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.
As, area of a triangle = 1/2 * (base )* (height )
Substituting the values, we get,
1.5=1/2 *(3+k)*(1.5k)
i.e.3= 4.5 k + 1.5k ²
i.e. k = -0.56 and k = -3.56
or
1.5=1/2* (-3-k )*(1.5k)
i.e.
3 = -4.5 k - 1.5²
i.e. k = -2 and k = -1.
Thus, the possible values of k are -0.56, -3.56, -2 and -1.
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Determine the value for j in the equation 17 over 20 equals j plus 11 over 20. 3 over 20 6 over 20 6 over 40 28 over 40
FLVS MATH MIDDLE
On solving the provided question, we get the following linear equation as the , that is j = 6/20.
What is a linear equation?A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
How do you identify a linear equation?A mathematical equation is said to be linear if it has the formula y=mx+b, where m denotes the slope and b the y-intercept.
Why is it called linear equation?An algebraic equation is said to be linear if each term has an exponent of 1, and if the equation is graphed, it always produces a straight line. This is the basis for its designation as a "linear equation."
the linear equation:
[tex]17/20 = j + 11/20\\ 17/20 - 11/20 = j + 11/20 - 11/20\\ (17 - 11)/20 = j\\ 6/20 = j[/tex]
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Which of these conditions might be true if polygons abcd and klmn are similar?
In the given situation, where polygons ABCD and KLMN are similar, the TRUE statement will be (A) "while the lengths of the matching sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."
What do we mean by polygons?A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry.
A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.
A polygonal circuit's segments are referred to as its edges or sides.
So, provided that polygons ABCD and KLMN are identical, the correct condition can be "while the lengths of the corresponding sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."
Therefore, in the given situation, where polygons ABCD and KLMN are similar, the TRUE statement will be (A) "while the lengths of the matching sides of ABCD and KLMN are equal, ABCD's sides are only half as long as KLMN's."
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Complete question:
Which of these conditions might be true if polygons ABCD and KLMN are similar?
A. The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of the corresponding sides of ABCD are half those of KLMN.
B. The measures of corresponding angles of ABCD and KLMN are in the ratio 1 : 2, but the lengths of corresponding sides of ABCD and KLMN are not proportional.
C. The lengths of the corresponding sides of ABCD and KLMN are equal, but the measures of corresponding angles of ABCD and KLMN are not equal.
D. The lengths of the corresponding sides of ABCD and KLMN are proportional, but the measures of corresponding angles of ABCD and KLMN are not equal.
E. The measures of corresponding angles of ABCD and KLMN are not proportional, but the lengths of corresponding sides of ABCD and KLMN are proportional.
5. Find the sum of the first ten terms of each arithmetic series. (2 marks each = 4 marks)
a. 2+8+14+...
b. 45 +39 +33 +...
i dont now when i can help but this is my answer
Victoria needs to order some new supplies for the restaurant where she works. The restaurant needs at least 673 glasses. There are currently 368 glasses. If each set on sale contains 10 glasses, write and solve an inequality which can be used to determine xx, the number of sets of glasses victoria could buy for the restaurant to have enough glasses.
Number of glasses Victoria need to buy for restaurant are at least 31 from the inequality given by 10x + 368 ≥ 673.
As given in the question,
Number of glasses required in the restaurant at least 673.
Number of glasses currently available in the restaurant = 368
Number of glasses in each set used to sale = 10
Let 'x' represent the number of sets of the glasses Victoria need to buy.
Required inequality is given by :
10x + 368 ≥ 673
⇒ 10x + 368 - 368 ≥ 673 - 368
⇒ 10x ≥ 305
⇒ x ≥ 30.5
Number of sets bought by Victoria = At least 31
Therefore, from the inequality 10x + 368 ≥ 673 the number of sets of glasses bought by Victoria is equal to at least 31.
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Calculate the average rate of change for the T chart below
Please help calculate for the first 3 weeks, first 4 weeks and the overall average rate of change for brainliest
Answer:
Designate the remaining pair of coordinates as "set 2." Using the previous coordinates (3, 4) and (1, 2), the coordinate pair (1, 2) becomes "set 2" and will be your x2 and y2 values in the formula. Therefore, x1 is 3, y1 is 4, x2 is 1 and y2 is 2. Now that you have your values, you can plug them into the formula.
who walks at a faster rate : somone who walks 60 feet in 10 seconds or someone who walks 42 feet in 6 seconds
Answer:
I think someone who walks 60 feet in 10 seconds. Let me know if I'm wrong.
Step-by-step explanation:
10/60=.16667
6/42=0.1428
The length of a rectangle of fixed area varies inversely as the width. If the
length of the rectangle is 6 feet when the width is 12 feet, find the length of the
rectangle when the width is 4 feet
Answer:
the length of the
rectangle when the width is 4 feet is 8
What is the next term in the following sequence: 0, 5, 11, 18, … 24 26 23 25
Answer: i think the next number should be 26
Step-by-step explanation:
Sandpiper Company ha 25,000 hare of cumulative preferred 1% tock, $150 par and 50,000 hare of $5 par common tock. The following amount were ditributed a dividend:
20Y1 $75,000
20Y2 15,000
20Y3 112,500
Determine the dividend per hare for preferred and common tock for each year. Round all anwer to two decimal place
$22500 is interest rate of common tock for each year.
What is an explanation of the interest rate?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off.
Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.
Amount distributed as dividends = $15000
Total Preferred dividend to be paid = $37500
But Total Preferred dividend paid/avaiable = $15000
dividend per share(P.S) = $0.60 **(15000 / 25000shares)
Since the preferred stock cumulative dividend to be paid in Next year due to less payment in current year would be = $22500 or $0.90 per share
Remaining dividend = 0
Equity dividend per share = 0
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A feather blew out of a bird nest 10 feet in the air. It drifted to the ground at a constant rate of 2 feet per second.
Write an equation that shows the relationship between the elevation of the feather, y, and the number of seconds it has been falling, x.
the equation of the function is y=-2x+10
John recieved a $3,000 loan. If he payed $450 in interet in 2 year. What i the imple interet rate on the loan
Using the interest rate formula, we know that the simple interest rate on the loan is 5.75%.
What is the simple interest rate?Simple interest is calculated by multiplying the principal by the time, interest rate, and time period.
"Simple Interest = Principal x Interest Rate x Time" is the written formula.
The simplest method for computing interest.
So, the interest rate on the loan is:
Formula to be used: I = p*r*t
Where I am the interest, p is the principal amount, r stand for rates and t stands for time.
I = p*r*t
3450 = 3000*2*r
3450/6000 = r
r = 0.575%
That is a 5.75% interest rate
Therefore, using the interest rate formula, we know that the simple interest rate on the loan is of 5.75%.
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Over a four month period the price of an ounce of gold steadily increased from
$1000 to $1400. What was the monthly multiplier? What was the monthly
percent increase?
Answer:
%10
Step-by-step explanation:
If the gold steadily increased $400 over a four-month period, we need to figure out how much the gold increased each month.
400 ÷ 4 = 100
Now that we figured out that the gold steadily increased $100 every month, we now need to figure out what percent it grew.
1000 ÷ 100 = 10
The price grew %10 every month.
What is the domain of this table?
A is the answer
Domain is all x-values and Range is y-values.
Hope this helps!!:)
- 4.5N = 135
What is N?
Answer:
n=-30
Step-by-step explanation:
-4.5n=135
n=135/-4.5
n=-30
Provide the missing statement and reasons for the following proof:
The two column proof showing that AB ≅ CD and AD ≅ BC are congruent by CPCTC is as detailed below.
How to solve two column proof?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
The two column proof that shows AB ≅ CD and AD ≅ BC is as follows;
Statement 1; Parallelogram ABCD with diagonal AC
Reason 1: Given
Statement 2; AB ║ CD and AD ║ BC
Reason 2; Definition of Parallelogram
Statement 3; ∠1 ≅ ∠2 and ∠3 ≅ ∠4
Reason 3; Definition of angle bisector
Statement 4; AC ≅ AC
Reason 4; Reflexive Property of congruence
Statement 5; ΔABC ≅ ΔCDA
Reason 5; ASA Congruency postulate
Statement 6; AB ≅ CD and AD ≅ BC
Reason 6; CPCTC
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Choose Yes or No to tell if the fraction
3
5
will make each equation true.
7
20
+
□
=
19
20
Choose...
□
+
3
10
=
3
15
Choose...
1
2
+
2
3
=
□
Choose...
1
10
+
1
2
=
□
Choose...
Answer:
1. Yes
2. No
3. No
4. Yes
Step-by-step explanation:
To find out whether or not 3/5 will make each equation true, simply input 3/5 in the missing slots and solve to see if they equal to the value intended.
Please help me with this!
Answer:
The regualar hippo massed 4.45 times as much as the pygmy hippo. (Not sure what I should round to)
Step-by-step explanation:
First, convert each of the fractions to a whole number. To do this get the whole number to the left of the fraction multiply it by the denominator and add the numerator. Once you have found both masses. Get the mass of the regular hippo and divide by the pygmy hippos mass.
Reguar Hippo Mass Calcualtion:
24*2=48
48+1=49kg
Pygmy Hippo Mass Calcualtion:
5*2=10
10+1-11kg
Final Calcuation:
49/11=4.45kg
Answer: 4.45 times as much
Let me know if this helped!
What is the best estimate of 49.13 ÷ 0.58?
A. 80
B. 40
C. 25
D. 50
Answer:
D. 50
Step-by-step explanation:
number to 49.13
Answer:
A
Step-by-step explanation:
The sales tax rate in a city is 7.11%. How much sales tax is charged on a purchase of 2 telephones at $ 48.67 each? What is the total price?
PLS I NEED HELP
well, both telephones cost 48.67 * 2 = 97.34, now let's get the tax and add it to it
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.11\% of 97.34}}{\left( \cfrac{7.11}{100} \right)97.34} ~~ \approx ~~ 6.92~\hfill \underset{total~price}{\stackrel{97.34~~ + ~~6.92}{\approx \text{\LARGE 104.26}}}[/tex]
100 points + brainlist if correct and well explained:
What are the vertex and range of y = |3x + 6| − 4?
(−2, −4); −∞ < y < ∞
(−2, −4); −4 ≤ y < ∞
(0, −4); −∞ < y < ∞
(0, −4); −4 ≤ y < ∞
The vertex of y = |3x + 6| − 4 is (-2, -4) and the range of y = |3x + 6| − 4 is −4 ≤ y < ∞.
What is meant by vertex?A parabola's vertex is the location at which it crosses its axis of symmetry. The vertex will be the lowest point on the graph, or the point at the base of the "U"-shape, if the coefficient of the x2 term is positive.
The point is called the vertex (h, k). As we are all aware, a parabola's conventional equation is y = ax2 + bx + c. The bottom of the U-shaped curve is where the vertex is located if the coefficient x2 is positive, and the top of the curve is where the vertex is located if it is negative.
Given,
y = |3x + 6| − 4
The vertex of y = |3x + 6| − 4 is,
We have to find the absolute values zeroes,
3x+6=0
x= -2
To find the value of y, substitute x value in the above,
y= -4
(x, y)=(-2, -4)
Therefore, the vertex of y = |3x + 6| − 4 is (-2, -4)
And now,
The range of y = |3x + 6| − 4 is,
It can be defined by f(x)≥k
k= -4
f(x)≥ -4
Therefore, the range of y = |3x + 6| − 4 is −4 ≤ y < ∞.
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Answer:
(−2, −4); −4 ≤ y < ∞
Step-by-step explanation:
Find k so that Kx^2+12x+9 is the square of a binomial
k = 4 will make the polynomial a perfect square of a binomial.
What is perfect square binomial?A trinomial that factors into a perfect square binomial yields the square of a binomial. For instance, because it factors to (x + y)2, the trinomial x2 + 2xy + y2 is a perfect square binomial.
How perfect square formula looks like?The perfect square formula looks like:
[tex]ax^{2} +2abx+b^{2} =(ax+b)^{2} \\ax^{2} -2abx+b^{2} =(ax-b)^{2}[/tex]
Given polynomial is,
kx² +12x + 9
We have to find the value of 'k' for which the given polynomial is a square of a binomial.
To find this we will use the formula,
(a +b)² = a² +2ab + b²
kx² + 12x + 9 = kx² + 2(6x) + 3²
= kx² + 2(3)(2x) + 3²
By comparing this with the formula of (a + b)²,
b = 3
a = 2x
(2x)²+2(2x)(3) + 3² = (2x + 3)²
4x² + 12x + 9 = (2x + 3)²
Therefore, k = 4 will make the polynomial a perfect square of a binomial.
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k = 4 will make the polynomial a perfect square of a binomial.
What is perfect square binomial?
A trinomial that factors into a perfect square binomial yields the square of a binomial. For instance, because it factors to (x + y)2, the trinomial x2 + 2xy + y2 is a perfect square binomial.
How perfect square formula looks like?
The perfect square formula looks like:
Given polynomial is,
kx² +12x + 9
We have to find the value of 'k' for which the given polynomial is a square of a binomial.
To find this we will use the formula,
(a +b)² = a² +2ab + b²
kx² + 12x + 9 = kx² + 2(6x) + 3²
= kx² + 2(3)(2x) + 3²
By comparing this with the formula of (a + b)²,
b = 3
a = 2x
(2x)²+2(2x)(3) + 3² = (2x + 3)²
4x² + 12x + 9 = (2x + 3)²
Therefore, k = 4 will make the polynomial a perfect square of a binomial.
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Estimate −74.41- 55.816 by first rounding each number to the nearest whole number.
PLEASE HELP!!!
Answer: -130.
Step-by-step explanation: To round −74.41 to the nearest whole number, we look at the tens place, which is the digit 4 in the number −74.41. Since 4 is less than 5, we round down to the previous whole number, which is −74.
To round 55.816 to the nearest whole number, we look at the tens place, which is the digit 8 in the number 55.816. Since 8 is greater than or equal to 5, we round up to the next whole number, which is 56.
Now that we have rounded both numbers to the nearest whole number, we can easily subtract them to get an approximate answer:
-74 - 56 = -130
Therefore, an approximate solution to −74.41- 55.816 is -130.
What is the Median? The student council sells candy bars to raise money for a dance.
Use the bar graph shown to answer the questions below.
A bar graph titled Candy Bars Sold. The vertical axis shows Number of Candy Bars with values ranging from 0 to 100. The horizontal axis shows Student Council Members with names as Dave, Jenny, John, Sarah, Alex. Points are (Dave, 90), (Jenny, 50), (John, 60), (Sarah, 70), and (Alex, 50).
What is the mode for this data set?
Mode =
50
candy bars
What is the median for this data set?
Median =
candy bars
What is the mean for this data set?
Mean =
64
candy bars
Answer:
50
Step-by-step explanation:
ezpz
Find an equation of the line that goes through the points (-3,-11) and (8,55). Write your answer in the form
y=mx+b.
y =
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{55}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{55}-\stackrel{y1}{(-11)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{55 +11}{8 +3} \implies \cfrac{ 66 }{ 11 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 6 ( x +3) \\\\\\ y+11=6x+18\implies {\Large \begin{array}{llll} y=6x+7 \end{array}}[/tex]
rewrite the equation x^2+26x+164.5=0 in the form (x-p)^2=q
We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:
(x + 13)^2 = 4.5
How to rewrite the quadratic equation?Here we want to rewrite the quadratic equation:
x^2 + 26x + 164.5 = 0
To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:
(a + b) = a^2 + 2ab + b^2
We can rewrite the given quadratic as:
x^2 + 26x + 164.5 = 0
x^2 + 2*13*x + 164.5 = 0
The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:
x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0
x^2 + 2*13*x + 169 - 4.5 = 0
(x + 13)^2 = 4.5
That is the equation we wanted to get.
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How many negative factors and positive factors do you need to guarantee a negative product with 4 factors? With 5? Is there more than one possibility for any of these? Is there a pattern?
The number of negative and positive factors needed to guarantee a negative product with four factors with factors is 10 and there is a pastern
What are factors of a number?You should understand that the factors of a number is a number which can divide a number without a reminder
The factors must have a constant difference
Taking 1 as a factor for instance
1+5=5
Taking the number 20 for instance
The factors of 20 are
20=1,2,4,5,10,20
-1*20=-20
.1*-20=-20
-2*10=-20 and 2*-10=20
-4*5=-20 and 4*-5=20
The order is that the subsequent terms must be gotten by a difference of 1 and a divisor of 5
Therefore the number of factors is gotten by allocating by after the other a negative sign to the numbers
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Anais goes to the store to get granola bars 1 pack of 100 granola bars is $8.67.
Another pack of granola bars is 50 granola bars for $5.48. Which is the better buy?
The better option is to buy the Granola bar.
What is a unit value?
When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities.
To determine which is the better buy, you need to compare the price per granola bar for each option. To do this, you can divide the price of each pack by the number of granola bars it contains.
For the first pack of 100 granola bars, the price per granola bar is $8.67 / 100 granola bars = $0.09 per granola bar.
For the second pack of 50 granola bars, the price per granola bar is $5.48 / 50 granola bars = $0.11 per granola bar.
Since the price per granola bar is lower for the first pack, it is the better buy. You would save money by purchasing the first pack of 100 granola bars instead of the second pack of 50 granola bars.
Hence, the better option is to buy the Granola bar.
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