[tex]\large\underline{\sf{Solution-}}[/tex]
We need to solve,
[tex]\dfrac{\sqrt{112}-\sqrt{80}}{\sqrt{20}-\sqrt{28}}[/tex]
We can write the above mentioned expression as,
[tex]\sf\longmapsto\dfrac{\sqrt{2\times2\times2\times2\times7}-\sqrt{2\times2\times2\times5}}{\sqrt{2\times2\times5}-\sqrt{2\times2\times7}}[/tex]
So,
[tex]\sf\longmapsto\dfrac{\sqrt{4\times4\times7}-\sqrt{4\times4\times5}}{\sqrt{2^2\times5}-\sqrt{2^2\times7}}[/tex]
So,
[tex]\sf\longmapsto\dfrac{\sqrt{4^2\times7}-\sqrt{4^2\times5}}{\sqrt{2^2\times5}-\sqrt{2^2\times7}}[/tex]
Hence,
[tex]\sf\longmapsto\dfrac{4\sqrt{7}-4\sqrt{5}}{2\sqrt{5}-2\sqrt{7}}[/tex]
Taking common in respective terms,
[tex]\sf\longmapsto\dfrac{4(\sqrt{7}-\sqrt{5})}{2(\sqrt{5}-\sqrt{7})}[/tex]
On cancelling 4 with 2,
[tex]\sf\longmapsto\dfrac{4\!\!\!/^{\:2}(\sqrt{7}-\sqrt{5})}{2\!\!\!/(\sqrt{5}-\sqrt{7})}[/tex]
[tex]\sf\longmapsto\dfrac{2(\sqrt{7}-\sqrt{5})}{(\sqrt{5}-\sqrt{7})}[/tex]
Taking (-) common,
[tex]\sf\longmapsto\dfrac{-2(\sqrt{5}-\sqrt{7})}{(\sqrt{5}-\sqrt{7})}[/tex]
So, (√5 - √7) gets cut,
Hence,
[tex]\longmapsto\bf\dfrac{\sqrt{112}-\sqrt{80}}{\sqrt{20}-\sqrt{28}}=-2[/tex]
A container manufacturing company was contracted to design and manufacture cylindrical cans for fruit juice. The volume of each can needs to be 0.946 liters. In order to minimize production costs, the company wishes to design cans that require the smallest amount of material possible. (This means that you need to design a can with volume=.946 liters and the smallest possible surface area. Explain the relationship between the surface area and the amount of material.)
The volume of the cylinder is the amount of fruit juice it can contain.
The relationship between the volume and the surface area is:
[tex]\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}[/tex]
The given parameter is:
[tex]\mathbf{V = 0.946}[/tex]
The volume of a cylinder is calculated as:
[tex]\mathbf{V = \pi r^2 h}[/tex]
Make h the subject
[tex]\mathbf{h = \frac{V}{ \pi r^2}}[/tex]
The surface area (A) of a cylinder is:
[tex]\mathbf{A = \pi r^2 + \pi rh}[/tex]
Substitute [tex]\mathbf{h = \frac{V}{ \pi r^2}}[/tex]
[tex]\mathbf{A = \pi r^2 + \pi r \times \frac{V}{\pi r^2}}[/tex]
[tex]\mathbf{A = \pi r^2 + \frac{V}{r}}[/tex]
Differentiate
[tex]\mathbf{A' = 2\pi r - Vr^{-2}}[/tex]
Set to 0
[tex]\mathbf{2\pi r - Vr^{-2} = 0}[/tex]
Rewrite as:
[tex]\mathbf{ 2\pi r = Vr^{-2}}[/tex]
Multiply through by r^2
[tex]\mathbf{ 2\pi r^3 = V}[/tex]
Solve for r
[tex]\mathbf{r = \sqrt[3]{\frac{V}{2\pi}}}[/tex]
[tex]\mathbf{A = \pi r^2 + \frac{0.946}{r}}[/tex]
So, we have:
[tex]\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}[/tex]
Hence, the relationship between the volume and the surface area is:
[tex]\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}[/tex]
Read more about surface areas and volumes at:
https://brainly.com/question/3628550
Doug entered a canoe race. He rowed 3 ½ miles in ½ hour. What is his average speed in miles per hour
Answer:
7 miles per hour
Step-by-step explanation:
3.5 times 2.
What is the slope of this line?
Step-by-step explanation:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Answer:
slope = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, 5) and (x₂, y₂ ) = (3, 2) ← points on graph
m = [tex]\frac{2-5}{3-7}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]
Shannon swam 100 meters in 56.24 seconds. Rick swam 100 meters
in 59.48 seconds. Rick took how many seconds longer to swim
100 meters than Shannon?
I’m kinda in a rush anyone mind helping?
Answer:
find the difference between the two times by subtracting them;
59.48-56.24= 3.24 seconds
Step-by-step explanation:
let (3x+24) represent the measure of a right angle. what are the possible values of x?
Answer:
x=22
Step-by-step explanation:
because 3x+24=90
3x=90-24
3x=66
x=22
brainlist please
write the equation for the slope intercept form
Answer:
y=2/3x-1
Step-by-step explanation:
jada has $20 to spend on games and rides at a carnival. Games cost $1 each and rides are $2 each.
which equation represents the relationship between the number of games, x , and the number of rides, y,
that Jada could do if she spends all her money?
A: x + y =20
B: 22 + 4 = 20
C: 0+2y=20
Answer:
I believe its A
Step-by-step explanation:
Hope it helps
QUWX is a field in the shape of a Trapezium whose parallel sides are 121m and 56m and the non parallel sides are 82m and34m. find the cost of ploughing the field at Rs 14.89 per square kilometre.(help with this one)
Answer:
hence the total cost to plough the trapezium field
is Rs. 893500.50
Step-by-step explanation:
the required answer may be wrong .... but this is the way to do it....
hope this helped you...☺️
comment if any confusion
Where on the coordinate plane is the point (-85, 52) located?
Right answer but i am not conform
x = - 85
y = 52
\frac { 3 ^ { p + 1 } - 3 ^ { p } } { 2 \times 3 ^ { p } } = 1
Answer:
Given equation:
[tex](3^{p+1} - 3^p) /(2 *3^p) = 1[/tex]Solving for p:
[tex]3^{p+1} - 3^p = 2 *3^p[/tex][tex]3*3^p - 3^p = 2 *3^p[/tex][tex]2 *3^p =2 *3^p[/tex]p - any real number
We can state the initial expression is correct for any value of p.
Answer:
True for all p
Step-by-step explanation:
Given equation:
[tex]\dfrac{3^{p+1}-3^{p}}{2 \times 3^{p}}=1[/tex]
Multiply both sides by [tex]2 \times 3^p[/tex]:
[tex]\implies 3^{p+1}-3^p=2 \times 3^p[/tex]
Add [tex]3^p[/tex] to both sides:
[tex]\implies 3^{p+1}-3^p+3^p=2 \times 3^p+3^p[/tex]
[tex]\implies 3^{p+1}=3 \times 3^p[/tex]
Rewrite 3 as 3¹:
[tex]\implies 3^{p+1}=3^1 \times 3^p[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 3^{p+1}=3^{1+p}[/tex]
[tex]\implies 3^{p+1}=3^{p+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies p+1=p+1[/tex]
Subtract 1 from both sides:
[tex]\implies p+1-1=p+1-1[/tex]
[tex]\implies p=p[/tex]
Therefore as both sides are equal, true for all p.
138 cups of flour used in 46 dozen brownies. a
Answer:
whats the question?
Function 1 is defined by following table what function has greater y- intercept?
Answer:
They both have the same y intercept
Step-by-step explanation:
(1,0)(0,3)
(0,3)(1,-1)
In a certain Algebra 2 class of 29 students, 8 of them play basketball and 16 of them play baseball. There are 11 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Answer:
18/29
Step-by-step explanation:
The probability that a student chosen randomly from the class plays basketball or baseball is 18/29
How to determine the probability?The given parameters are:
Students = 29Basketball = 8Baseball = 16Neither = 11The number of students that play basketball or baseball is:
Basketball or Baseball = Students - Neither
This gives
Basketball or Baseball = 29 - 11
Basketball or Baseball = 18
The probabilty is then calculated as:
P = Basketball or Baseball/Students
This gives
P = 18/29
Hence, the probability that a student chosen randomly from the class plays basketball or baseball is 18/29
Read more about probability at:
https://brainly.com/question/251701
LAM 1 Mod 6 Question 4b-s2.
Answer:
there is one line of symmetry if you look closely at the shape
Is the triangle isosceles, equilateral, or
neither?
70°
55°
55°
A. isosceles
B. equilateral
C. neither
Answer:
It is isosceles triangle because its base angles are equal .
plz mark me brainest
Answer: A. isosceles
Step-by-step explanation:
an isosceles triangle is a triangle that has two sides of equal length.
You can read about isosceles triangle more : https://en.wikipedia.org/wiki/Isosceles_triangle
please give me a brainliest answer
A blank 2-column table with 3 rows. Column 1 is labeled Column A and Column 2 is labeled Column B. A blank graph has label B on the x-axis and label A on the y-axis. Weather data is collected to analyze wind speed according to temperature. Identify the variables as either input or output to label the table and graph. Column A = Column B = Label A = Label B =
A= temperature column B= wind speed. Label A= wind speed label B= Temperature
Hellur, I need help with geometry homework....
Answer:
24
Step-by-step explanation:
all 3 corners of any triangle adds to 180
the big triangle gives you 94 and 41 which equals 135. even though there's a line cutting off the last corner it still counts towards the 180 of the big triangle
180 - 135 = 45
now you know 2 corners of the smaller triangle
111+45 = 156
156+x= 180
x= 24
The force (F) needed to cause the acceleration (a) of an object of mass, m, is given by the equation, F=ma where m is the object’s mass. If a 12-Newton force causes the object to accelerate to 3 m/s2, what is that object’s mass? The unit for this mass is kg.
From Newton’s Second Law of Motion, the force needed to accelerate a moving object of mass m at acceleration a is given by ;
F = ma
In this case, m = 5kg, a = 6m/s^2 and we want to find F
F = 5 x 6
F = 30N
Therefore, a force of 30N is needed to accelerate a 5kg object at 6m/s^2.
When negative five is subtracted from a number the result is 10.
Find the number.
O 15
O -5
O -15
O 5
.............................
Answer:
D. 5
Step-by-step explanation:
Ok, so the number is represented by n.
n-(-5)=10.
Negative Times Negative makes Positive. The equation is now:
n+5=10
Subtract 5 from both sides.
n=5
Graph: y+2= -3/4 (x + 4)
Click or tap the graph to plot a point.
The y-intercept of the line is (0, -5) and plot the coordinate points (0, -5) and (4, -8) on the graph.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given equation is y+2= -3/4 (x+4).
Graph the line using the slope and y-intercept, or two points.
Slope: -3/4
y-intercept: (0, -5)
Plot the coordinate points (0, -5) and (4, -8)
Hence, plot the coordinate points (0, -5) and (4, -8) on the graph.
To learn more about the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ7
-6/1 x - 3/5 divided by -0.25
Answer:
-14.4
Step-by-step explanation:
-6x(-0.6)x(-4)= -14.4
[tex] - \frac{6(5 - 2x)}{5x} [/tex]
i hope its help
What is 4 plus 3 plus 6 plus 10
Answer:
23
Step-by-step explanation:
4+3+6+10
4+3 = 7
7 + 6 = 13
13 + 10 = 23
This is super easy, no offense
what is the explicit rule for the geometric sequence 1/64, 1/16, 1/4, 1
Answer:
[tex]\frac{1}{\sqrt[n]{64}}[/tex]
Step-by-step explanation:
[tex]\frac{1}{\sqrt[1]{64}} =\frac{1}{64}[/tex]
[tex]\frac{1}{\sqrt[2]{64}} =\frac{1}{16}[/tex]
[tex]\frac{1}{\sqrt[3]{64}} =\frac{1}{4}[/tex]
[tex]\frac{1}{\sqrt[4]{64}} =\frac{1}{1}[/tex]
Write the equation of the line through
(4, 4) and (2, 2) in point-slope form.
Answer:
y-4=1x-4
Step-by-step explanation:
put in format : y2-y1=m(x2-x1)
y-4 = 1(x-4)
distribute
y-4=1x-4
Find the average rate of change of the function from X1 to X2.
Function
f(x) = -7x + 16
x-Values
X1 = 0, X2 = 3
Answer:
75-82, in Exercises 75-82, find the average rate of change of the function from x1 to x2. function f(x) = 3x +8 x-values x1=0, x2=3
estimate 1.75 * 12.5
Answer:
21.875, round as needed.
Step-by-step explanation:
1.75 * 12.5
21.875
You can also round to:
21.88
21.9
22
Just depends on what your teacher is asking
can somebody please help me with this, also show work so that way i can copy because this is due tmr and i have no clue how to do this at all, thank you so much! (also its 8th grade math)
Solve the system of equations by the substitution method. x+4y=6 y=3−x
Answer:
x = 2, y = 1
Step-by-step explanation:
x + 4y = 6 and y = 3 - x have to be rearranged: x + 4y = 6 and x + y = 3
You subtract the equations to eliminate one of the variables (x) so that the other can be found
Complete the following statement. Write your answer as a decimal or whole number. % of $600 = $120
Answer: 20%
Step-by-step explanation: 600*0.20 = 120
Please help I don’t get the question
Answer:
I need this in essay form......
Phaeton, who has just discovered that is he is the son of the sun god, pays a visit to his father and makes a special request. In this passage consider how the author uses literary elements such as plot and language to reinforce the theme of the dangers of pride.