The area of the cylinder is a function of its height (h) and radius, ([tex]\mathbf{4\sqrt 3}[/tex])
The exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]
The given parameters are:
[tex]\mathbf{Area =56\pi\sqrt 6}[/tex]
[tex]\mathbf{r=4\sqrt 3}[/tex]
The surface area of a cylinder is calculated as:
[tex]\mathbf{Area = 2\pi rh + 2\pi r^2}[/tex]
Substitute values for Area
[tex]\mathbf{56\pi\sqrt 6= 2\pi rh + 2\pi r^2}[/tex]
Divide through by pi
[tex]\mathbf{56\sqrt 6= 2 rh + 2r^2}[/tex]
Substitute value for r
[tex]\mathbf{56\sqrt 6= 2 (4\sqrt 3)h + 2(4\sqrt 3)^2}[/tex]
[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 2\times 48}[/tex]
[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 96}[/tex]
Collect like terms
[tex]\mathbf{8h\sqrt 3 = 56\sqrt 6- 96}[/tex]
Make h the subject
[tex]\mathbf{h = \frac{56\sqrt 6}{8\sqrt 3}- \frac{96}{8\sqrt 3}}[/tex]
[tex]\mathbf{h = 7\sqrt 2- \frac{12}{\sqrt 3}}[/tex]
Rationalize
[tex]\mathbf{h = 7\sqrt 2- \frac{12\sqrt 3}{3}}[/tex]
[tex]\mathbf{h = 7\sqrt 2- 4\sqrt 3}[/tex]
Hence, the exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]
Read more about surface areas t:
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Consider the rational function:
f(3) = 22-53-6
22 +31-10
Which values are restrictions on the domain of f(x)?
theres also an answer option of x=5 but it wouldnt fit in the picture
2&3
Step-by-step explanation:
You have to factorise the second equation and you have to solve it. so you have x²-2x-3x+6
x(x-2)-3(x-2)
(x-2)(x-3)=0
Then you have to find x for each equation.
x-2=0
x=2
x-3=0
x=3
So the restricions are 2&3.
How do I Graph 2y=-8
A loan used for buying a home is called a mortgage. The Fortunato family is borrowing $430,000 to buy a home. They are taking out a 30-year mortgage at a rate of 3.55%. a. Compute the monthly payment to the nearest cent. fill in the blank 1 b. Find the total of all of the monthly payments for 30 years. fill in the blank 2 c. What is the total interest? fill in the blank 3 d. Which is greater, the interest or the original cost of the home?
Using compound interest, it is found that:
a) The monthly payments are of $3,401.49.
b) The total of all monthly payments for 30 years is of $1,224,536.
c) The total interest is of $794,536.
d) The total interest is greater.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For the parameters, we have that:
The Fortunato family is borrowing $430,000 to buy a home, hence P = 430000.30-year mortgage, hence t = 30.Rate of 3.55%, hence r = 0.0355.Yearly compounding, hence n = 1.For practicality, first we are going to solve item b.
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(30) = 430000\left(1 + \frac{0.0355}{1}\right)^{30}[/tex]
[tex]A(30) = 1224536[/tex]
The total of all monthly payments for 30 years is of $1,224,536.
Item a:
$1,224,536 is paid in 30 x 12 = 360 months, hence:
1224536/360 = $3,401.49.
The monthly payments are of $3,401.49.
Item c:
The interest is the total subtracted from the principal, hence:
1224536 - 430000 = $794,536.
The total interest is of $794,536.
Item d:
Loan of $430,000, interest of $794,536, hence the total interest is greater.
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4. Which values are solutions of
2x – 1= 7? Select all that apply.
A) X=-4
(B) x = -3
C=3
D= 4
Answer:
D. x = 4
Step-by-step explanation:
2x – 1= 7
add 1 to both sides:
2x=8
divide both sides by 2:
x=4
One solution.
please help with this algebra ii question
Answer:
Second Choice
Step-by-step explanation:
The vertex form can be expressed as:
[tex] \displaystyle \large{f(x) = a {(x - h)}^{2} + k}[/tex]
We know that the vertex is (h,k) which we are given (-3,-1). Substitute h = -3 and k = -1 in:
[tex] \displaystyle \large{f(x) = a {(x - ( - 3))}^{2} - 1} \\ \displaystyle \large{f(x) = a {(x + 3)}^{2} - 1}[/tex]
Now we know that the parabola passes through (-2,1). Substitute x = -2 and f(x) = 1 then solve for a.
[tex] \displaystyle \large{1= a {( - 2 + 3)}^{2} - 1} \\ \displaystyle \large{1= a {(1)}^{2} - 1} \\ \displaystyle \large{1= a - 1} \\ \displaystyle \large{1 + 1= a } \\ \displaystyle \large{2 = a}[/tex]
Therefore a = 2.
Hence:-
[tex] \displaystyle \large{f(x) = 2{(x + 3)}^{2} - 1}[/tex]
What is an equation of the linethat passes through the points (3,-8) and (1,-2)
Answer:
y=3x+1
Step-by-step explanation:
m= [tex]\frac{-2-(-8)}{1-3} =\frac{-6}{2}[/tex] or -3
-8= -3(3) + b
-8= -9 + b
+9 +9
1=b
Then put in slope intercept form:
y= 3x+1
Hope this helps! :)
Round the number 245,382 to the nearest given place value.
13. hundred
14. ten-thousand
16. ten
15. thousand
The value of each digit in a number is known as the place value. The number 245,382 to the nearest hundred place value is 245,400.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
The given number 245,382 can be rounded off to the nearest given place values as,
A.) hundred
The hundred is the third place in any number from the right end since the second value is 8 which is close to 10, therefore, the hundred place value will be rounded off to the next number.
245,400
B.) ten-thousand
The ten-thousand is the fifth place in any number from the right end since the fourth value is 5 followed by 382 which is more close to 50,000 than 40,000 , therefore, the ten-thousand place value will be rounded off to the next number.
250,000
C.) ten
The ten is the second place in any number from the right end since the first value is 2 which is close to 0, therefore, the ten place value will be the same while the first place will become zero.
245,380
D.) thousand
The thousand is the fourth place in any number from the right end since the third value is 3 which is close to 0, therefore, the thousand place value will be the same while the third place and the ahead will become zero.
245,000
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--- point (MC) 8 9 What is the value of m in the equation? 239 - 7 = m - 2
Answer:
m=234
Step-by-step explanation:
239-7=232
The equation now looks like this:
232=m-2
Add 2 on both sides:
m=234
Hope this helps!
is -5.25 greater than -3
Answer:
False -5.25 is < (less than) -3
Step-by-step explanation:
Hey can someone help please hurry it’s important
[tex]\large\underline{\sf{Solution-}}[/tex]
Given info:
6885 ÷ 46
Here, we have given divisor (43) & dividend (6885). And in problem they asked to find quotient & remainder.
Let's solve!!
[tex] \sf{46 \overline{\bigg)68885 \bigg(}149← \red{Quotient}} \\ \sf \underline{ 46 \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf{228 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf{ \underline{ - 184 \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \sf0445 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \underline{ \sf - 414 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf{031 \red{←Remainder}} \\ [/tex]
[tex] \therefore \: \sf{Quotient = 149 \: and \: Remainder \: = 31} \\ [/tex]
[tex] \sf{Now,} \\ [/tex]
[tex] \sf{Divisor \times Quotient + Remainder } \\ [/tex]
[tex] \sf = 46 \times 149 + 31 \\ [/tex]
[tex] \sf = 6854 + 31 \\ [/tex]
[tex] \sf{ = 6885} \\ [/tex]
[tex] \sf = \red{ Dividend}. \\ [/tex]
how do I determine what a function is for a line graph
Answer: Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Step-by-step explanation:
please be super quick 3 minutessssss
Answer:
im pretty sure its B
Step-by-step explanation:
I THINK SOOO AHH
What percent of the hours were billed by Jon, Roy, or Dean?
Write your answer using a percent
sign (%).
Answer:
10%
Step-by-step explanation:
please tell me if im right or wrong
Please help. I will give brainly. Thank you
Answer:
1.
a = 1.96
( 1.4 x 1.4)
b= 3750
c= 1/48
2.
a= 2?
dont take my word on that but here.( An arithmetic sequence is any list of numbers that differ, from one to the next, by a constant amount. For example, the list of even numbers, 0,2,4,6,8… is an arithmetic sequence, because the difference from one number in the list to the next is always 2.[1] If you know you are working with an arithmetic sequence, you may be asked to find the very next term from a given list. You may also be asked to fill in a gap where a term is missing. Finally, you might want to know, for example, the 100th term, without actually writing out all 100 terms. A few simple steps can help you do any of these.
b= 3
c= 16-4a
( IM NOT SO CONFIDENT ABOUT 2)
3.
a= 17
b= ( 2squared - 1)
Step-by-step explanation:
Answer:
thank you for the points bozzo
Circle each input value. Underline each output value. 1. {(1, 1), (2, 3), (3,5)} 2. {(6,2), (5, 3), (4,8)}
Answer:
The first numbers in the sets are input and the second numbers are outputs.
1. {(1, 1), (2, 3), (3,5)}
Input = 1, 2, 3Output = 1, 3, 52. {(6,2), (5, 3), (4,8)}
Input = 6, 5, 4Output = 2, 3, 8i am just completely lost at this point so pls just answer properly
Answer:
$80
Step-by-step explanation:
192÷12=16
16•5=80
Answer:
Elena puts in $80 into her savings account
Step-by-step explanation:
You need to multiply 5/12 and 192. Think of "5/12 x 192" as "5/12 of 192." If you don't know how to multiply a fraction with a whole number, you can convert the fraction to a decimal. Hope this helps!
what is the total surface area of the prism in square inches
Answer:
Surface area of a square prism = 4 × (s × h) = 4sh, where, s is the length of the side of the square and h is the height of the square prism.
Fatima drove 100 miles in 4 hours. What is the constant of proportionality for 100 miles in 4 hours and 200 miles in 8 hours? Please answer ASAP.
Answer:
25
Step-by-step explanation:
4 hours goes into 100 miles 25 times.
HELP!
A group of activists wants to raise money for a good cause, so they decide to sponsor a bicycle race. It receives $60 per cyclist entry and $15,000 in donations, but it must spend $18 per entry to cover the cost of the race.
Write and solve an inequality to determine the number of cyclists the group needs to raise at least $57,000.
9514 1404 393
Answer:
60x +15000 ≥ 18x + 57000≥ 1000 cyclistsStep-by-step explanation:
We want ...
revenue ≥ cost + desired profit
60x +15000 ≥ 18x + 57000 . . . . . . an inequalty
42x ≥ 42000 . . . . . . . . . . . . . . . . subtract 18x+15000
x ≥ 1000 . . . . . . . . . . . . . . . . . . divide by 42
The group needs at least 1000 cyclists to raise at least $57,000.
what is the LCD of 3/5, 1/10, 1/2
Identify the angles that each have a measure of 60\degree
Answer:
parrelel
Step-by-step explanation:
Is this relation a function? Justify your answer.
Answer:
Yes
Step-by-step explanation:
(I can only read the graph).
Since for each dot, a vertical line drawn through it only intersects that dot, we conclude that the relation is a function.
Look at the graph below.
What is the slope of the line?
OA. 5
OB. -5
oc. 1
OD. -
Help or don’t eiether way you’re amazing
Answer:
267 (please double check this!!!)
Step-by-step explanation:
Separate the block into sections that you can find the volume for easily and figure out the measurements for each
the two smaller blocks on top will be symmetrical
the bottom area is 5 high and 3 deep and you get the length by adding 4+5+4 because that's the length of the whole thing
so 13*3*5 = 195
The two smaller blocks is just adding a *2 once you figure out the one
it's 3 deep still and 4 wide, if you subtract the total height from the height given of the bottom part you get 3
3*4*3 = 36
you have another one of those blocks so it'd be 36*2
then you add them both 72+195 = 267
A truck can be rented from Company A for $80 a day plus $0.40 per mile. Company B charges $40 a day plus $0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same. At nothing miles, the rental costs are the same from either company
Heyyy help maybe????????????
Complete the following.Write the answers in your journal
I learned filtering of solid and liquid mixtures can be saperated with the use of____ or____ as a medium in which_______material in the medium
Sieving is a method in which ________of ________sizes are separated from a mixture on the basis of the _____
Answer:
1.FILTER WATER 2.FILTER CLOTH
3.LIQUIDS
4.INSOLUBLE
5.DIFFERENCE
c. The double shadedregion represents
of the whole.
Step-by-step explanation:
please the information needed is up the paper. you took a picture of no. 2 instead of no. 1
Dùng kí hiệu toán học để viết mệnh đề sau:
Định nghĩa : tam giác ABC gọi là tam giác cân nếu có hai góc bằng nhau
Answer:
g vs lhnkdeugyvsvjxbd shall
the ratio 4:2 is equivalent to 2
To make pastry for an apple pie, you need 4 oz flour and 2 oz fat. The ratio of flour to fat is
4 : 2 .
But this ratio can be simplified in the same way that two fractions can be simplified. We just
cancel by a common factor. So
4 : 2 = 2 : 1 .