Answer: [tex]11250\pi \\[/tex] cm^3
Step-by-step explanation:
This could be solved with integral calculus or simple arithmetic.
If you need to show the work in calculus, let me know, otherwise, here's the easiest way to reach the answer:
Volume of a solid is equal to the area of its 2D projection multiplied by its height, assuming that it's uniform throughout its entire height. Fortunately, a cylinder is uniform throughout its height.
What is a cylinder's 2D projection? A circle!
Area of a circle = [tex]\pi r^{2}[/tex]
r = 15
Area = 225pi cm^2
Now, we multiply the area of the 2D projection by the height of the cylinder.
225pi * 50 = 11250pi cm^3
What is the distance between A(5,-2) and B(-2,4)?
Answer:
[tex]\sqrt{85}[/tex]
Step-by-step explanation:
Let's use the distance formula to solve for the distance between the two given points!
d = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex]
Now, we input the points:
(5-(-2) + (-2-4)
(which will equal...)
(7) + (-6)
Now we input the solutions we got here to the distance formula:
[tex]d =\sqrt{(7)^2 + (-6)^2[/tex]
(we simplify....)
[tex]7^2 = 49\\(-6)^2 = 36[/tex]
input these solutions into the distance formula again...
[tex]\sqrt{49 + 36} = \sqrt{85}[/tex]
85 is not a number that can be square rooted properly, nor does it have any perfect squares available to divide equally.
Therefore, we conclude that the distance between A(5, -2) and B(-2,4) is [tex]\sqrt{85}[/tex].
What are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x² + x - 12?
Answer:
All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.
help meeeeeeeeeeeeeeeeeeeeeee
What is the the measure and length of arc MC
As given by the question
There are given that the measuring circle.
Now,
From the given circle, the length of the MN is 28 units, because the half of the length of the MN is 14. So just multiply by 2 into half of the given value.
Hence, the length of MN is 28 units.
Now,
For the measure of MN:
The measurement of the angle MN is 74 degrees.
Hence, a measure of arc MN is 74 degrees. and the length of segment MN is 28 units.
which statement is true and why? & why not the others?
For this problem, we have three circles with different radii. We need to determine which circles are similar and point out the reason for our statement.
Every circle has the same shape, the only thing that sets them apart is the radii. Since we can represent the relationship between the radii as fractions, then all circles are similar. Due to this, the only correct option is the second one. "Circle 1 is similar to both circle 2 and circle 3".
Dave jogs 8 feet per second. Give each rate in miles per hour.
Answer:
Step-by-step explanation:
first find seconds in an hour
60(seconds in a minute) *60(minutes in an hour) = 3600 seconds in an hour
then multiply 8 by 3600 to see how many feet per hour
28,800
we need miles so there are 5280 feet in a mile
28800/5280 is 5.45454545 or 5.455 miles per hour
Give the point-slope form of the equation of the line that is perpendicular to y= -4x/5+10 and contains P(5,6)
You have to write the equation of a line perpendicular to
[tex]y=-\frac{4}{5}x+10[/tex]That crosses the point (5, 6)
A caracteristic of a line permendicular to another one is that its slope pf the perpendicular line is the negative inverse of the slope of the first line.
So for example if you have two lines:
1_ y=mx+b
and
2_ y=nx+c
And both lines are perpendicular, the slope of the second one will be the negative inverse of the slope of the first one, that is:
[tex]n=-\frac{1}{m}[/tex]The slope of the given line is m=-4/5
The negative inverse is
[tex]-(\frac{1}{-\frac{4}{5}})=-(-\frac{5}{4})=\frac{5}{4}[/tex]Now that you know the slope of the perpendicular line, use it along with the given point (5, 6)
in the slope-point formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{5}{4}(x-5) \end{gathered}[/tex]I’m not firmiliar with the sun or difference of cubes (HW assignment)
Given:
[tex]125r^3-216[/tex]Find-: Factor using the formula of the sum or difference of cube.
Sol:
Factoring sum and differences of cubs is:
[tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ x^3+y^3=(x+y)(x^2+y^2-xy) \end{gathered}[/tex]Apply for the given information.
[tex]\begin{gathered} =125r^3-216 \\ \\ =(5r)^3-(6)^3 \end{gathered}[/tex][tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ (5r)^3-(6)^3=(5r-6)((5r)^2+(6)^2+(5r)(6)) \\ \\ =(5r-6)(25r^2+36+30r) \end{gathered}[/tex]I need answers to 6a and 6b. This is for my homework :,)
The system of equations has 3 cases
1. y = ax + b, y = ax + c
Since the coefficient of x and y are the same, and the y-intercepts are different, then
The two lines are parallel
2. y = ax + b, y = dx + c
Since the 2 lines have different coefficients of x, then
The two lines are intersected
3. y = ax + b, y = ax + b
Since the two lines have equal coefficients of x and equal y-intercepted, then
The two lines are coincide (same line)
6. a)
Since the system of equations is
[tex]\begin{gathered} y=2x+3 \\ y=12x-2 \end{gathered}[/tex]The coefficients of x not equal
Then from case 2 above
The two lines are intersected
6.b
Since the system of equations is
[tex]\begin{gathered} y=13x+2 \\ y=13x-2 \end{gathered}[/tex]The coefficients of x are equal
The y-interceptes not equal
Then from case 1 above
The two lines are parallel
Solve triangle EFG with the given parts.f = 17.78, F = 27.3°, G = 102.1°
STEP - BY - STEP EXPLANATION
What to find?
g, E and e
Given:
Step 1
Find the measure of side g using the sine ratio.
[tex]\begin{gathered} \frac{sinF}{f}=\frac{sinG}{g} \\ \\ \frac{sin27.3}{17.78}=\frac{sin102.1}{g} \\ \\ gsin27.3=17.78sin102.1 \\ \\ g=\frac{17.78sin102.1}{sin27.3} \\ \\ g\approx37.9 \end{gathered}[/tex]Step 2
Find angle E.
[tex]E+F+G=180(sum\text{ of interior angle in a triangle\rparen}[/tex][tex]\begin{gathered} E+27.3+102.1=180 \\ \\ E=180-102.1-27.3 \\ \\ E=50.6° \end{gathered}[/tex]Step 3
Find side e using the sine ratio.
[tex]\begin{gathered} \frac{sinE}{e}=\frac{sinF}{f} \\ \\ \frac{sin50.6}{e}=\frac{sin27.3}{17.78} \\ \\ esin27.3=17.78sin50.6 \\ \\ e=\frac{17.78sin50.6}{sin27.3} \\ \\ e\approx29.96 \end{gathered}[/tex]ANSWER
g=37.9
E=50.6°
e = 29.96
Solve these: state whether there is no solution, one solution specify it , or infinitely many Solutions.
Step 1:
Write the two systems of equations
y = 3x = 2
3x = y - 3
Step 2:
Substitute y from the first equation into the second equation
[tex]\begin{gathered} 3x\text{ = y - 3} \\ 3x\text{ = 3x + 2 - 3} \\ 3x\text{ - 3x = 2 - 3} \\ 0\text{ = 2 - 3} \\ 2\text{ = 3} \end{gathered}[/tex]Final answer
NO SOLUTION
If the area of the rectangle is 4836 square feet find the length of the rectangle
Solution
- Let the length of the rectangle be x
- Let the width of the rectangle be y.
- Thus, we can interpret the lines of the question as follows:
[tex]\begin{gathered} \text{ The length is 30 less than 6 times the width can be written as} \\ x=6y-30\text{ (Equation 1)} \\ \\ \text{The area of the rectangle is 4836. This is written as:} \\ xy=4836\text{ (Equation 2)} \end{gathered}[/tex]- Now, let us solve these two equations simultaneously.
- We shall proceed by solving the system of equations graphically.
- Wherever the graphs of Equation 1 and Equation 2 intersect represents the solution to the system of equations
- The plot of the equations is given below
- Observe that the graphs cross at two points. The first point is positive and the other, negative.
- Since we cannot have negative lengths (x) or width (y), we can discard the negative coordinates.
- Thus, the length (x) and width (y) are given below:
[tex]\begin{gathered} \text{length(x)}=156 \\ \text{width(y)}=31 \end{gathered}[/tex]Final Answer
The length of the rectangle is 156 feet
Convert 253 inches to yards using dimensional analysis.
As given by the question
There are given that the 253 inches
Now,
To convert the inches to yards, multiply the value in inches by the conversion factor 0.0277777787.
So,
[tex]253\times0.0277777787=7.0277778.[/tex]Hence, the value of the given inches is 7.0278 yards.
Describe where the function has a hole and how you found your answer.
Step 1:
Write the function
[tex]f(x)\text{ = }\frac{x^2+\text{ 7x + 10}}{x^2\text{ + 9x + 20}}\text{ }[/tex]Step 2:
Factorize both the numerator and the denominator.
[tex]\begin{gathered} f(x)\text{ = }\frac{x^2\text{ + 2x + 5x + 10}}{x^2\text{ + 4x + 5x + 20}} \\ f(x)\text{ = }\frac{x(x\text{ + 2) + 5(x + 2)}}{x(x\text{ + 4) + 5 (x + 4)}} \\ f(x)\text{ = }\frac{(x\text{ + 5)(x +2)}}{(x\text{ + 5)(x + 4)}} \end{gathered}[/tex]Step 3:
A hole is a common factor between the numerator and the denominator.
Hole: x + 5 = 0
x = -5
Final answer
Hole is -5
we need to seat 200 people. A table holds 8 people How Many tables do we need ?
Kyah, this is the solution to the exercise:
People = 200
Capacity of each table = 8 people
In consequence, we need:
Number of tables = People/Capacity of each table
Replacing by the values we know:
Number of tables = 200/8
Number of tables = 25
Use the Pythagorean Theorem to find x, in simplest radical form. 20
The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where }c\text{ is the hypotenuse, and }a\text{ and }b\text{ are the other two sides of a right triangle.} \end{gathered}[/tex]Given: c = 20, a = 8, and b = x. Find x.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8)^2+(x)^2=(20)^2 \\ 8^2+x^2=20^2^{} \\ 64+x^2=400 \\ x^2=400-64 \\ x^2=336 \\ \sqrt{x^2}=\sqrt[]{336} \\ x=\sqrt[]{16\cdot21} \\ x=4\sqrt{21}\text{ (final answer)} \end{gathered}[/tex]1 ptsQuestion 7Mike reads 5 pages an hour. The independent variable is time. What is the dependentvariable?O the number of pagesthe number of hoursO the number of books
We are given that Mike reads 5 pages an hour. This is the quotient of pages with respect to time. In this case, the time is the independent variable and the number of pages is the dependent variable since the number of pages depends on the time interval that is considered.
Dylan invested $93,000 in an account paying an interest rate of 3% compoundedquarterly. Assuming no deposits or withdrawals are made, how much money, to thenearest cent, would be in the account after 17 years?
The formula to calculate compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
[tex]\begin{gathered} A=\text{ final amount} \\ P=\text{ initial amount (principal)} \\ r=\text{ interest rate} \\ n=\text{ number of times interest applied per time period} \\ t=\text{ number of time period elapsed} \end{gathered}[/tex]The following parameters are given in the question:
[tex]\begin{gathered} P=93000 \\ r=\frac{3}{100}=0.03 \\ n=4(quarterly) \\ t=17\text{ years} \end{gathered}[/tex]We can substitute these values into the formula to calculate the final amount as follows:
[tex]A=93000(1+\frac{0.03}{4})^{4\times17}[/tex]Solving, we get:
[tex]\begin{gathered} A=93000\times1.0075^{68} \\ A=154,577.64 \end{gathered}[/tex]The amount after 17 years is $154,577.64
What is the name of the decimal number?7.1seventy-one seven and one hundredthsseven and one tenth seventeen
Answer:
seven and one-tenth.
Explanation:
To name decimal number, we first name the values before the decimal point, in this case, seven
Then, we add an and that corresponds to the decimal point
Finally, we say the number after the decimal point and the place of this number, in this case, one-tenth.
Therefore, the name of the decimal number 7.1 is:
seven and one-tenth.
estimate the product by rounding to the nearest ten: 28×51×76
To estimate each number by rounding it to the nearest ten, we will look at the unit digit,
If it is less than 5, then we replace it by 0 and keep the ten-digit as it
If it is 5 or more, then we will replace it by 0 and add the ten-digit by 1
Let us do that with every number
28, the unit digit is 8 which is greater than 5, then replace it by 0 and add 2 by 1
28 rounded to 30
51, the unit digit is 1 which is less than 5, then replace it by 0
51 rounded to 50
76, the unit digit is 6 which is greater than 5, then replace it by 0 and add 7 by 1
76 rounded to 80
Now let us multiply them
[tex]28\times51\times76=30\times50\times80=120,000[/tex]The product of the given numbers is 120,000
Mr. Hanes places the names of four of his students, Joe, Sofia, Hayden, and Bonita, on slips of paper. From these, he intends to randomly select two students to represent his class at the robotics convention. He draws the name of the first student, sets it aside, then draws the name of the second student. Whats the probability he draws he draws Sofia then joe?
Given:
Total student = 4
Joe, Sofia, Hayden, and Bonita.
Find-:
Probability he draws Sofia then Joe.
Explanation-:
Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The formula of probability:
[tex]P(A)=\frac{\text{ Number of favorable outcomes to A}}{\text{ Total number of possible outcomes}}[/tex]For Sofia.
Total number of possible outcomes = 4
Favorable outcomes for Sofia = 1
So probability for Sofia :
[tex]P(S)=\frac{1}{4}[/tex]After the first student set it aside.
For Joe.
Total number of possible outcomes = 3
A favorable outcome for Joe = 1
So probability for Joe.
[tex]P(J)=\frac{1}{3}[/tex]So probability for Sofia then joe is:
[tex]\begin{gathered} P=\frac{1}{4}\times\frac{1}{3} \\ \\ P=\frac{1}{12} \end{gathered}[/tex]
Given m//n find the value of x and y (5x+1)° (6x-10)° (y°)
To find the value of x, use the vertical angle theorem.
Vertical angles are congruent.
Thus we have:
6x - 10 = 5x + 1
Solve for x.
6x - 10 = 5x + 1
Add 10 to both sides:
6x - 10 + 10 = 5x + 1 + 10
6x = 5x + 11
Subtract 5x from both sides:
6x - 5x = 5x - 5x + 11
x = 11
To find the value of y, use corresponding angles thoerem.
When two parallel lines are crossed by a transversal, the angles in matching corners are correponding angles.
Corresponding angles are congruent.
Thus, we have:
y = 6x - 10
Substitiute x for 11:
y = 6(11) - 10
y = 66 - 10
y = 56°
ANSWER:
x = 11, y = 56°
Just give me the answer please, my device is at 10%
Solve for x
We can use sine
[tex]\begin{gathered} \sin 48^0=\frac{x}{17} \\ \text{Cross multiply} \\ x=17\times\sin 48^0 \\ x\text{ =17}\times0.7431448 \\ x=12.6\text{ } \end{gathered}[/tex]9km 87 m equals
option A = 9.087km
option B= 90.87km
option c = 0.9087km
option D= 908.7km
option e= none of these
please don't give wrong answer
rectangle rstw has diagonals RT and SW that intersect at Z. If RZ= 5x+8 and SW= 11x-3 find the value of x.
Answer:
19
Explanation:
We know that the diagonals of a rectangle are always equal, therefore RT = SW.
So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;
[tex]\begin{gathered} 2(5x+8)=11x-3 \\ 10x+16=11x-3 \\ 16+3=11x-10x \\ 19=x \\ \therefore x=19 \end{gathered}[/tex]Mr. McFall uses 2% cups of peanuts for every 1/2 cup of chocolate chips in a mixture. Enter the number of cups of peanuts for every 1 cup of chocolate chips. Remember to reduce.
To solve this problem I'll use proportions.
2 1/8 cups ------------------------ 1/2 cup of chocolate.
x ----------------------- 1 cup od chocolate chips
x = (1*2 1/8) / 1/2
x = 17/8 / 2
x = 4 % cups of peanuts
Learn with an example v Sharon has a red ribbon and an indigo ribbon. The red ribbon is 6 1/4 inches long. The indigo ribbon is 6 1/4 inches longer than the red ribbon. How long is the indigo ribbon?
Let R be the length of the red ribon and let I be the length of the indigo ribbon. We have that the red ribbon is 6 1/4 inches long, then:
[tex]R=6\frac{1}{4}=\frac{25}{4}[/tex]Then, the indigo ribbon is 6 1/4 inches longer than the red ribbon. Then we have:
[tex]I=R+6\frac{1}{4}[/tex]therefore:
[tex]I=\frac{25}{4}+\frac{25}{4}=\frac{50}{4}=\frac{25}{2}=12\frac{1}{2}[/tex]finally, we have that the indigo ribbon is 12 1/2 inches long
help meeeeeeeeee pleaseee !!!!!
The values of the composition of the functions are:
(f o g)(x) = -x³ - x + 1
(g o f)(x) = -x³ - x - 1
How to Determine the Composition of a Function?To find the value of the composition of a given function, the inner function is first evaluated, then the output of the inner function is then replaced into the outer function and simplified.
Given the functions:
f(x) = x³ + x + 1g(x) = -x(f o g)(x) = f(g(x))
Substitute -x for x into the function f(x) = x³ + x + 1:
f(g(x) = (-x)³ + (-x) + 1
f(g(x) = -x³ - x + 1
(g o f)(x) = g(f(x))
Substitute x³ + x + 1 for x into the function g(x) = -x:
g(f(x)) = -(x³ + x + 1)
g(f(x)) = -x³ - x - 1
Learn more about composition of function on:
https://brainly.com/question/10687170
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please try to answer quickly my brainly app keeps crashing
From the figure, the radius of the sphere is:
[tex]r=1\text{ in}[/tex]The volume of the sphere is given by the formula:
[tex]V=\frac{4}{3}\pi r³[/tex]Using the value of the radius:
[tex]\begin{gathered} V=\frac{4}{3}\pi(1)³ \\ \\ \therefore V=\frac{4\pi}{3}\text{ in^^b3} \end{gathered}[/tex]Approximating to the nearest cubic inch:
[tex]\therefore V\approx4\text{ in^^b3}[/tex]ther
The half life of titanium - 44 , a radioactive isotope, is 63 years. If a substance starts out with 1000 kg of titanium- 44( round all the answers to the nearest hundredth of a kilogram or year) A) how much titanium- 44 will remain after 441 years ? B) how long will it be before there is only 1 kg of titanium- 44 ?
a)
Every 63 years, the amount of titanium halves.
441 years later means how many halving?
441/63 = 7 halving
We start off with 1000 and do 7 halving to get the amount of Titanium-44 after 441 years.
[tex]\begin{gathered} 1000(\frac{1}{2})^7 \\ =7.8125 \end{gathered}[/tex]after 441 years, the amount of titanium remaining would be 7.8125 kg
b)
Let's find the point where the remaining titanium would be 1 kg.
That would be:
[tex]1=1000(\frac{1}{2})^t[/tex]t is the time we are looking for. We can solve this using Ln(natural log):
[tex]\begin{gathered} 1=1000(\frac{1}{2})^t \\ 0.001=\frac{1}{2}^t \\ ln(0.001)=\ln (\frac{1}{2}^t) \\ \\ t=\frac{\ln (0.001)}{\ln (\frac{1}{2})} \\ t=9.965 \end{gathered}[/tex]There is basically 9.965 halving. That would make the years approximately:
9.965 * 63 (half life) = 627.795 years (approx)