The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex].
Procedure - Determination of the root of radical functionIn this question we need to find the root of the radical function [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex], which must be simplified by algebraic means.
First, we need to elevate each side of the expression by third power:
[tex]\left(\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n+\sqrt{n^{2}+8}} \right)^{3} = 512[/tex]
[tex]2\cdot n + 3\cdot \sqrt[3]{(n+\sqrt{n^{2}+8})^{2}\cdot (n-\sqrt{n^{2}+8})} + 3\cdot \sqrt[3]{(n-\sqrt{n^{2}+8})^{2}\cdot (n+\sqrt{n^{2}+8})} = 512[/tex]
[tex]2\cdot n -6\cdot (\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n-\sqrt{n^{2}+8}}) = 512[/tex]
[tex]2\cdot n - 6\cdot (8) = 512[/tex]
[tex]n = 280[/tex]
The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex]. [tex]\blacksquare[/tex]
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pls help meeeeeeeeeee
Step-by-step explanation:
VW to WY have the ratio 3/2.
VX to XZ must have the same ratio.
and VX > VW.
so,
30 and 20 is possible, as 30/20 = 3/2.
3 and 2 is not possible, because 6 > 3.
27 and 18 is possible, as 27/18 = 3/2.
13.2 and 8.8 is possible, 13.2/8.8 = 3/2.
8.7 and 5.7 is not possible, as 8.7/5.7 is not 3/2.
8.7/3 = 2.9
but 2.9×2 = 5.8 and not 5.7.
which integer represents 8°c below 0?immersive reader (1 point)
Answer: -8
Step-by-step explanation: negative numbers are below zero in this case its 8 below zero which the keyword is below which means less than negative integers are less than zero so its -8
Someone help me please
Answer:
Step-by-step explanation:
any minus temperature is < 7oC
0 is < 7oC
1 ... 6 is < 7oC
the weight of a chimpanzee ,y in pounds x months after birth is modeled by the equation y=1.5x+8. Which represents the equation when solved for x?
Answer:
Step-by-step explanation:
The temperature at 7:00 a.m, was 12 C, and by 7:00 p.m, it had dropped
to -10°C. Which expression represents the change in temperature:
(A 12 + (-10)
(B 12 - 10
(C -10 + 12
(D -10 - 12
Answer: D -10 - 12
Step-by-step explanation:
Temperature change is (Final T) - (Initial T)
(Final T) = -10C
(Initial T) = 12
(Final T) - (Initial T) = -10C - 12C
Temp Change - 22C
Help me please
H please
Answer:
pi
Step-by-step explanation:
I need these answers in 5 MINUTES PLZ HELP
Answer: 1. w=-30%
2. c=361
Step-by-step explanation: 1. 15+15=30 2. a looks the same size as c so c is 361 or same as a
PLEASE HELP QUESTION IN PIC.
Answer:
Perimeter= 40
Area= 120.7
Step-by-step explanation:
Reflect parallelogram EFGH with E(-4,5), F(3,6), G(2,3) and H(-5,2) in the x-axis. what are the coordinates of F?
Select the correct answer.
If a = 0.3 and b =0.5, what is the value of a+b?
A.8/10
B.8/9
C.80/99
D.88/100
Answer:
B
Step-by-step explanation:
The winner of the local triathlon swam 0.5 miles, biked 15 miles and ran 2.5 miles. He finished the race in 54 minutes. For the entire triathlon, what was his average speed in miles per hour?
Answer:
15 or 15.546
Step-by-step explanation:
you add all the numbers then divide by 54
Based on the information given, the speed is 20 miles per hour.
From the information given, the winner of the local triathlon swam 0.5 miles, biked 15 miles and ran 2.5 miles and he finished the race in 54 minutes.
Note that 54 minutes = 0.9 hour.
The speed will be:
= (0.5 + 15 + 2.5) / 0.9
= 18/0.9
= 20 miles per hour.
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It is a Saturday morning, and Jeremy has discovered he has a leak coming from the water heater in his attic. Since plumbers charge extra to come out on weekends, Jeremy is planning to use buckets to catch the dripping water. He places a bucket under the drip and steps outside to walk the dog. In 20 min, the bucket is 1/8 of the way full. What is the rate at which the water is leaking per hour? and what is the longest time he can be away from the house before the bucket will overflow?
Step-by-step explanation:
You start by asking yourself or as I call it crossmultiply
if 20 min the bucket is 1/8 full what about 8/8 or a whole
20×8/8×1/8
=160 min or 2.6 hrs
Answer:
[tex]2\frac{1}{2} hours[/tex]
Step-by-step explanation:
What is the rate at which the water is leaking per hour?
rate: [tex]\frac{1}{5} buckets = \frac{1}{5}/ \frac{1}{2} buckets/ hr\\ ----\\\frac{1}{2} hour = \frac{2}{5} buckets/ hr[/tex]
Write an equation that represents the relationship between the number of buckets filled, , in hours.
[tex]y=\frac{2}{5}x[/tex]
What is the longest that Jeremy can be away from the house before the bucket will overflow?
[tex]\frac{5}{2}[/tex] or [tex]2\frac{1}{2} hours[/tex]
A solid object where the radius of bse is 7cm and height is 12cm
Answer:
A cylinder with a base radius of 7cm and a height of 12 cm.
Step-by-step explanation:
A solid object =7cm
height=12cm
Now,
we know that l = b×g
=12×7
= 84
−
3
x
+
y
=
−3x+y=
−
3
−3
−
6
x
+
2
y
=
−6x+2y=
−
3
−3
Answer: -3x+4
Step-by-step explanation:
combine like terms.
3x+ -6x=-3
-3+-3+2= -4
-3x + -4
if a car travels for 3 hours its average speed is 75km/h work out the total distance the car travels
Answer:
225 km
Step-by-step explanation:
75 · 3 = 225
Answer:
225 km
Step-by-step explanation:
Distance = Speed × Time
Distance = 75km/h × 3
Distance = 225km
The recipe for 4 people says I need 300g of sugar. I am making for 10 people. How much sugar do I need in g?
Answer:
750g
Step-by-step explanation:
300 divided by 4, for amount of sugar per person
you'll get 75
then multiply 75 by 10 for 10 people
you get 750g
d20) A department store buys 200 shirts at
of $2,400 and sells them at a selling price of $20
each. Find the percent markup.
Pls answer now I need it pls
What is the slope of a line perpendicular to the line whose equation is x-y=6x−y=6. Fully simplify your answer.
I forgot how to do this lol
A bookstore sells 2 books for $22.50 which table represents the relationship between number of books and the total price
Answer:
Can you show what are the tables?-
..............................
Answer:
A rational number is a number that doesn't terminate or repeat
a non rational number is a number that terminates or repeats
so she basicelly got mixed up
Hope This Helps!!!
what will be the total surface area of a cylinder if
h = 22cm
and
r = 3cm
TSA = ?
Please give me the answer plssss??
Answer:
total surface area of a cylinder is 471 cm²
A car is 200 inches long the truck is 50% longer than the car how long is the truck
Answer:
300
Step-by-step explanation:
This question is pretty simple.
First, we just have to find 50% of 200.
So 50% is also 1/2.
1/2 of 200 is just 100. The question says that the truck is 50% LONGER than the car.
So 50% longer is 100 and 100+200(the length of the car) is 300.
The answer.
Don’t answer just for points please~ I need help and I’m struggling lol
Answer: 50
Step-by-step explanation:
5x + 55 = 2x + 100
5x = 2x + 45
3x = 45
x = 15
y equals angle 2
180 = 5(15) + 55 + y
180 = 75 + 55 + y
180 = 130 + y
50 = y
angle is 50
We know that:
=> m∠2 + 5x + 55 = 180°=> 5x + 55 = 2x + 100Because of 180° angle formula.
First, let's solve for x. Then we will solve m∠2.
=> 5x + 55 = 2x + 100=> 5x - 2x = 100 - 55=> 3x = 45=> x = 15Since we have found x, it is time to find m∠2.
=> 5(15) + 55 + m∠2 = 180=> 75 + 55 + m∠2 = 180=> 130 + m∠2 = 180=> m∠2 = 180 - 130=> m∠2 = 50Conclusion:Therefore, the measure of m∠2 is 50°
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Which triangles could not be similar to triangle ABC ? triangle a b c with right angle b. side a b is 12 cm. side b c is 5 cm. side a c is 13 cm. Select each correct answer. Right triangle D E F with right angle at E. D E is 8 centimeters. D F is 10 centimeters. E F is 6 centimeters. Right triangle J K L with right angle at K. J K is 36 centimeters. J L is 39 centimeters. K L is 25 centimeters. Right triangle M N O with right angle at N. M N is 35 centimeters. M O is 37 centimeters. N O is 12 centimeters. Right triangle G H I with right angle at H. G H is 6 centimeters. G I is 6.5 centimeters. H I is 2.5 centimeters.
Answer:
triangle JKL
Step-by-step explanation:
This is because the lengths of each side JKL is a factor to ABC
respectively .
AB=12,JK=36
AC=13,JL=39
BC=5,KL=25
I hope you understand
What is the equation of the line in standard form?
(2,2)
Step-by-step explanation:
You have to add them together and minus the negatives
A cylindrical, wooden table top has a density of 0.42 g cm 3 and a mass of 0.25 kg.
The table top has a depth of 6 cm.
Find the radius of the table top, rounded to 1 dp.
The radius of the table top, rounded to 1 dp is 5.6 cm
From the question,
We are to determine the radius of the table top
First, we will determine the volume of the cylindrical wooden table
From the given information
Density = 0.42 g/cm³
Mass = 0.25 kg = 250 g
Using the formula
[tex]Volume = \frac{Mass}{Density}[/tex]
∴ [tex]Volume = \frac{250}{0.42}[/tex]
Volume = 595.238 cm³
Now, for the radius of the table top
Using the formula for volume of a cylinder
[tex]V = \pi r^{2}h[/tex]
Where V is the volume
r is the radius
and h is the height or depth
From the given information
h = 6cm
Putting the parameters into the formula
[tex]595.238 = \pi r^{2} \times 6[/tex]
∴ [tex]r^{2} = \frac{595.238}{6\pi }[/tex]
[tex]r^{2} =31.57835667[/tex]
[tex]r =\sqrt{31.57835667}[/tex]
r = 5.6 cm
Hence, the radius of the table top, rounded to 1 dp is 5.6 cm
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A car is traveling at a steady speed. It travels 2 1/2 miles in 3 1/3 minutes. How far will it travel in 21 minute? In 1 hour?
PT.2 OF MY HW IT IS UNIT RATE PLEASE HELP!
Answer:
Car 1
Step-by-step explanation:
Answer: Car 1
Step-by-step explanation:
Notice that the speed of each car is the slope of the line that represents its average speed.
Since the graph of the speed of Car 1 passes through (0,0) and (4,256), we get that its slope is:
256/4 = 64
Therefore the average speed of Car 1 is 64 mi/h.
Now, since the equation that represents the average speed of Car 2 is in slope-intercept form, we get that its slope is 55.
Therefore the average speed of Car 2 is 55 mi/h.
Answer: Car 1.
Simplify the expression. Write your answer as a power.
4.5^5/4.5^3
The simplified expression is