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]
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(01.02 MC)The number line shows the distance in meters of two jellyfish, A and B, from a predator located at point X:
Write an expression using subtraction to find the distance between the two jellyfish. (5 points)
Show your work and solve for the distance using additive inverses. (5 points)
hello again!
you can calculate the distance between A and B by subtracting
distance = B-A=0.5m-(-1.5)m=2m
Zahin has 4/6
kg of rice. She divides it into 5 equal portions to cook for dinner. How much rice, in kilograms, does she use to cook one portion for dinner?
fraction word problem
Answer:
2/15 or 0.13
Step-by-step explanation:
first you multiply 2/3 and 1/5 which gets you 2/15
Reniel is 13 years old. He is two years younger than his brother, Gelo. If Gelo is five times older than their sister, how old is their sister?
Helppppppppppppppppppppppppppppppppppp
Answer:
The answer would be 7 I hope this helps! : )
Answer:
it's 2
Step-by-step explanation:
if we solve 3×2×1/3
then we will get 2 .
The location of the
circumcenter of TrIangle ABC is:
A. Point D
B. Point E
C. Point F
Answer:
it'd be F
Step-by-step explanation:
just did it on my acellus
The location of the circumcenter of triangle ABC is at ''Point D.''
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
The triangle ABC is shown in figure.
Now,
We know that;
The circumcenter of the triangle is the point at which the distance between the vertices with the circumcenter is equal to each other.
In figure ABC;
⇒ AD = BD = CD
So, The circumcenter of triangle ABC is at point D.
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Write True or False for each statement.
(a) A square is a special rectangle.
true or false?
(b) The diagonals of a rhombus are equal in length.
true or false?
(c) A kite has both pairs of opposite angles equal.
true or false?
Answer:
A) true
B) true
C) true
hope that helps :)
-8+r>-8
please show work
Hello there!
-8+r>-8
Move all the numbers to the right:
r>-8+8
r>0
Hope it helps!
~Just a joyful teen
[tex]GraceRosalia[/tex]
Show your solution follow the steps need an answer, please need an answer, please.
Step-by-step explanation:
21. x² - 4x - 5 > 0
→ (x - 5) (x - 1) > 0
{x - 5 > 0
{x + 1 > 0
{x - 5 < 0
{x + 1 < 0
{x > 5
{x > -1
{x < 5
{x < -1
= x < -1 or x > 5
therefore, option A is correct
22). 4p² - 1 ≤ 0
(2p - 1) (2p + 1) ≤ 0
{2p - 1 ≤ 0
{2p + 1 ≥ 0
{2p - 1 ≥ 0
{2p + 1 ≤ 0
{p ≤ 1/2
{p ≥ -1/2
{p ≥ 1/2
{p ≤ -1/2
1/2 ≤ p ≤ 1/2
{p ≥ 1/2
{p ≤ -1/2
-1/2 ≤ p ≤ 1/2
therefore, option A is correct.
23). y < 3x² + 3x - 6
3x² + 3x - 6 = 0
3x² + 6x - 3x - 6 = 0
3x(x +2) - 3(x +2) = 0
(x +2) (3) (-3) = 0
x = -2, 1
this is the correct ans. but their is no option similar to it.
25. x and y are root of
m² - 11m + 18 = 0
hence, x + y = 11
xy = 18
2xy = 36
now, x² + y²
= (x +y)² - 2xy
= (11)² - 36
= 121 - 36
= 85
therefore, option A is correct.
26. x² - 2x - 120
(x -1)² - 1 - 1² = 0
(x -1)² = 1 + 1²
x - 1² = 2
x - 1 = ±√2
1 ± √2
therefore, option A is correct.
hope this answer helps you dear..take care!
Answer:
Step-by-step explanation:
21) x² - 4x - 5 > 0
x² - x + 5x - 5 > 0
x(x - 1) + 5(x - 1) > 0
(x - 1) (x + 5) > 0
x - 1 >0 or x + 5 > 0
x > 1 or x > - 5 Ans: D
22) 4p² ≤ 1
p² ≤ 1/4
p ≤ 1/2 or p ≥ -1/2
-1/2 ≥ p ≤ 1/2
23)y < 3x² + 3x - 6
(1 , -7)
x = 1 and y = -7
-7 < 3*1 + 3*1 - 6
-7 < 3 + 3 - 6
-7 < 0
(1 , -7) satisfies the equation.
Option b
24) 5x² - 7x = 0
a = 5 ; b = -7 ;c = 0
Discriminant = b² - 4ac = 49 - 0 = 0
[tex]x = \dfrac{-b+\sqrt{D}}{2a} \ ; \ \dfrac{-b-\sqrt{D}}{2a}\\\\x = \dfrac{7+\sqrt{49}}{10} ; \dfrac{7-\sqrt{49}}{10}\\\\x = \dfrac{7+7}{10};\dfrac{7-7}{10}\\\\x =\dfrac{14}{10} ; 0\\\\x = \dfrac{7}{5}; 0[/tex]
x = 0 ; x = 7/5 Option a)
25) m² - 11 m + 18 = 0
m² - 2m - 9m + (-9)*(-2) = 0
m(m - 2) - 9(m - 2) = 0
(m - 2)(m - 9) = 0
m = 2 , 9
x = 2 and y =9
x² + y² = 2² + 9² = 4 + 81 = 85 Option a)
26) x² - 2x - 1 = 0
Add the constant 1 to both sides
x² - 2x = 1
Divide the coefficient of x by 2. 2/2 = 1. Now add this 1 to both sides of the equation.
x² - 2x + 1 = 1+1
x² - 2x + 1 = 2
(x - 1)² = 2
Take square root
x - 1 = ±√2
x = 1 ± √2 Option a)
Claire's suitcase weighs 15 pounds less than her older sisters.
Together the suitcases weigh 109 pounds. How many pounds does
Claire's older sister's suitcase weigh?
bro i read it wrong that's my bad hold on ill get the right one rq
A city has a population of 280,000 people. Suppose that each year the population grows by 4.75% . What will the population be after 7 years ? Use the calculator provided and round your answer to the nearest whole number.
Write an equation in slope intercept form that goes through the point (5,-7) and is PARALLEL to the line y=-3x+8
Answer:
there is no line parallel to y = -3x + 8 that goes through (5, -7). this point falls on this line
Step-by-step explanation:
[tex]y = - 3x + 8[/tex]
[tex] - 7 = - 3(5) + b \\ - 7 = - 15 + b \\ b = 8[/tex]
The answer is
[tex]y = - 3x + 8[/tex]
3. Simplify the expression (x3 - 5x2 + 7x - 12) = (x – 4) using long division. Show your work.
Answer:
Answer:
x^2-x+3
Step-by-step explanation:
(x^3-5x^2+7x-12)÷(x-4)
x^3−5x^2+7x−12
Factors of 12,
1,2,3,4,6,12
Substitute 4 into x. Since the result is 0, x-4 is a factor..
4^3−5×4^2+7×4−12=0
x-4
x^2 -x 3
x-4 | x^3 -5x^2 7x -12
x^3 -4x
-x^2 7x -12
-x^2 4x
3x -12
3x -12
x^2−x+3
(x^2−x+3)(x−4)
x−4
(x^2−x+3)
Answer = x^2-x+3
Hopes this helps
Please Help!!!!!!!!!!!
what is the ninth term of the arithmetic sequence a(n)=14 + 2(n-1)?
A. 21
B. 23
C. 30
D. 32
Answer:
C= 30
Step-by-step explanation:
Please help with question got stuck
Answer:
y=4x
Step-by-step explanation:
Y=6x+13 x-intercept and y-intercept
Answer:
y int (0, 13)
x int (-13/6,0)
just make the x = 0 and solve to get y
same with the x make y =0 and solve
Plsssss Help i have no idea how to do this
Answer:
500
Step-by-step explanation:
1. given w(x)=4x
a. graph r(x)=4 x w(x). then complete the table of corresponding points on r (x). How do you graph this?
Answer:
Step-by-step explanation:
a). When graph w(x) is transformed to r(x) = 4 × w(x), graph of w(x) is vertically stretched by a scale factor of 4.
Table for the corresponding points will be,
x w(x) r(x)
0 0 0×4 = 0
15 60 60×4 = 240
30 120 120×4 = 480
45 180 180×4 = 720
b). As discussed in part (a), graph of w(x) will be vertically stretched by a scale factor of 4 to produce the graph of r(x).
c). Since, w(x) = 4x
and r(x) = 4[w(x)]
r(x) = 4(4x) = 16x
r(x) = 16x
4%*57+(7654*34562)-68+1-213=?
Step-by-step explanation:
264537270.28
ok..... oddly..
please help me if you can. Sorry if it’s blurry
Step-by-step explanation:
oh, come on, just multiplication.
7.5×10⁴ years is 7.5×10000 =75000 years.
0.005 inches per year for 75000 years means
0.005 × 75000 = 5 × 75 = 375 inches.
Brianna works for a large fast food chain recording and publishing training videos for employees. Which job title would Brianna MOST likely have?
Answer:
Multimedia Specialist
Step-by-step explanation:
Had a question like this before
or security reasons, a company will enclose a rectangular area of 11,200 m2 in the rear of its plant. One side will be bounded by the building and the other three sides by fencing. If the bounding side of the building is 150 m long and 300 m of fencing will be used, what will be the dimensions of the rectangular area?
The dimensions of the rectangle are 150 m and 75 m respectively.
Let x be the length of the rectangular area and y be the width of the rectangular area.
Its area A = xy
Given that its area is 11,000 m², xy = 11000 m² (1)
Also, since the bounding side of the building is 150 m long and the fencing is 300 m, the perimeter of the rectangular area is P = 150 m + 300 m = 450 m.
Also, the perimeter of the rectangular area is P = 2(x + y)
Since P = 450 m
2(x + y) = 450 m
x + y = 225 m (2)
Since the bounding side of the building represents one dimension of the rectangle, x = 150 m.
Substituting x into (2), we get the other dimension
x + y = 225
150 + y = 225
y = 225 m - 150 m
y = 75 m
So, the dimensions of the rectangle are 150 m and 75 m respectively.
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Help with Algebra 2, forgot how to do it
Answer:
[tex]f(x) = 3 \: \: \: \: for \: \: \: \: - 6 < x < 1 \\ f(x) = - x \: \: \: \: for \: \: \: \: 1 < x < 6[/tex]
PLEASE HELP I NEED TO DO THIS RIGHT
Answer:
C maybe i dunno but gl
Answer:
A
Step-by-step explanation:
Given a function f(x) where the first derivative with respect to x evaluated in two equals
f'(2)=1/2
The slope of the tangent line is
mt=1/2
Therefore, the slope of the normal line is
mn=-1/(1/2)
mn=-2
Evaluating the given point in the general form
y-y1=m(x-x1)
y-(-1)=-2(x-2)
y+1=-2x+4
y=-2x+3
Multiply. Enter the product in simplest form.
7
9
×
4
7
=
Aria's height is 3 inches less than her brother's height. Her brother's height is unknown.
Which expression shows Aria's height? Use x for her brother's height.
Aria's height is 3 inches less than her brother's height. Her brother's height is unknown.
Which expression shows Aria's height? Use x for her brother's height.
A.x/3
B.3x
C.x + 3
D.x – 3
Balto” is a 6 year old 35 kg intact husky mix. He presents through the ER after likely being HBC (hit by car) with anisocoria and nystagmus, both signs of head trauma. The doctor instructs you to give 1 g/kg mannitol IV to decrease intracranial pressure. Mannitol is a 20 % solution. How many grams will “Balto” receive? How many mgs? How many mls?
If we give 1 g/kg of mannitol, it then follows that Balto needs to receive 35g of mannitol.
What is percent concentration?Percent is one of the ways of expression the concentration of a solute in a solvent. In this case, the concentration of the mannitol is 20%. This implies that there are 20 g of mannitol in 100 g of solution.
Thus, If we give 1 g/kg of mannitol, it then follows that Balto needs to receive 35g of mannitol.
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Hello, please be honest, is this correct?
Answer:
Yes that is correct you got keep up good work
Estimate the difference by rounding each number to the nearest whole
367.2-294.8
A. 72
B.72.4
C.73
D.80
Answer:
A. 72
Step-by-step explanation:
367.2 -> 367
294.8 -> 295
367
- 295
____
072
if you weren't estimating you would get B because you wouldn't round the numbers.
since the question says to round and then estimate, the answer should be A.
Label the figure.
20,24,114,702
A student in a foreign language program learns 15 new words each week. Which graph best represents the relationship between x, the number of weeks the student has been in the program and y, the total number of new words the student has learned
Linear equations are represented by straight line.
The required graph is graph (a).
The given parameters are:
[tex]\mathbf{Rate =15}[/tex]
Let x represents the number of weeks, and y represents the number of words in week x.
So, we have:
[tex]\mathbf{y = Rate \times x}[/tex]
Substitute 15 for Rate
[tex]\mathbf{y = 15\times x}[/tex]
[tex]\mathbf{y = 15x}[/tex]
The above equation means that:
[tex]\mathbf{(x,y) = (0,0)(1,15),(2,30)....}[/tex]
The graph that represents the above ordered pair is graph (a).
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Answer:
im lost
Step-by-step explanation:
;;..