Here is a cuboid.
All measurements are in centimetres.
x is an integer.
The total volume of the cuboid is less than
900 cm^3
Show that x < 5.
Answers
Answer:
Look below
Step-by-step explanation:
-x*3x*2x=6x^3
-6x^3<900
-(cube root both sides)
-6x<9.654893846
-divide by 6
-x=1.609148974
And since 1.609148974 is less than 5, that means that X<5 is correct and hence proved
For given cuboid, x < 5
What is cuboid?"It is a three-dimensional geometric structure that has six rectangular faces, twelve edges and eight vertices."
Formula of the volume of the cuboid:V = l × w × h
where, l: length of the cuboid
w: width of the cuboid
h: height of the cuboid
For given example,
We have been given the total volume of the cuboid is less than 900 cm^3
⇒ V < 900 cm³
the length of the cuboid (l) = 3x
the width of the cuboid (w) = 2x
the height of the cuboid (h) = x
Using the formula of the volume of the cuboid,
⇒ V < 900
⇒ l × w × h < 900
⇒ (3x) × (2x) × (x) < 900
⇒ 6x³ < 900
⇒ x³ < 150
⇒ x < 5.3
⇒ x < 5
Therefore, for given cuboid, x < 5
Learn more about the volume of the cuboid here:
https://brainly.com/question/23118276
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Related Questions
The function h(t)=-16t^+144 represents the height, h(t), in feet of an object from the ground at t seconds after it is dropped. A realistic domain for this function is?
Answers
Answer:
[tex]0 \le t \le 3[/tex]
Step-by-step explanation:
Given
[tex]h(t) = -16t^2 + 144[/tex]
Required
Determine a reasonable domain
The domain is the possible values of t for which h(t) is true
Before the object is released, the value of t is:
[tex]t = 0[/tex]
Next, is to calculate the value of t after the ball reaches the ground.
At this point, h = 0.
So, we have:
[tex]h(t) = -16t^2 + 144[/tex]
[tex]0 = -16t^2 + 144[/tex]
[tex]16t^2 = 144[/tex]
Divide both sides by 16
[tex]t^2 = 9[/tex]
Take the positive square root of both sides
[tex]t = 3[/tex]
This means that the ball reaches the ground in 3 seconds.
So, the domain is:
[tex]0 \le t \le 3[/tex]
Please help! Giving 20 points!! I only need number 11
Answers
Triangle 1:
a=1/2(175)(280)
a=24,500km^2
Triangle 2:
a=1/2(790)(480)
a=189,600km^2
189,600km^2 + 24,500km^2 = 214,100km^2
Hope this helps!
calculate x. (geometry)
im in need of help, its due in like 14 minutes
Answers
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Isosceles triangles.
Since, the sides are equal, we can equate them, so we get as,
==> 16x + 13 = 24x -19
=> 24x -16x = 13+19
=> 8x = 32
x = 4
hence ==> x = 4.
One number is four more than a second number. Three times the first is 13 less than 2 times the second. Find the numbers
Answers
Answer:
11
Step-by-step explanation:
cuz i know lol
Given the function, where a, b, and c are positive numbers:
f(x) = (x - a)(x - b)2(x2 + c)
How many real roots does f(x) have, including multiple roots? |
How many imaginary roots does f(x) have?
Answers
Answer:
2 real roots and 1 imaginary roots
Step-by-step explanation:
f(x) = [tex](x-a)(x-b)^{2} (x^{2}+c)[/tex]
There are only 2 real roots and one imaginary roots.
Separate the equation into sections because the function is a multiplication with no outside sum or substraction:
Real Roots:
[tex](x-a)[/tex] = 0 when x = a
[tex](x-b)^{2}[/tex] = 0 when x = b
Imaginary roots:
[tex](x^{2}-c)[/tex] = 0 when x = [tex]\sqrt{-c}[/tex]
Is this statement true or false? A finance charge is what you pay to ship a purchase.
Answers
Answer:
false
Step-by-step explanation:
I took the test
Answer:
I think the answer is false
divide 80,000 by 100 please help
Answers
Answer:
800
Step-by-step explanation:
80000 / 100 is 800
Answer:
80,000/100= 800
....................
five people can finish painting a wall in 5 hours if only 2 people are available how many hours do they have to work to finish the same job
with solution please
and what type of proportion
thank you very much
Answers
Answer:
The number of hours required for 2 people to do the same job/work is 12.5 hours.step by step expanation:The number of hours required for 2 people to do the same job representedby x:
(5 people) (5 hours)x = ------------------------------ 2 people 25 hoursx = ------------------- 2x = 12.5 hoursHope it helpfullIn the figure below, mZ1 =(x+44) and mZ2=3xº.
Find the angle measures.
Answers
Answer:
where is the diagram? please provide the diagram.
What does inversely proportional mean
Answers
Answer:
dkdkkdjdkdkdkkskzksskisks
choose all of the statements that correctly compare the two functions shown (brainliest)
Answers
Answer:
it's B,C and D
Step-by-step explanation:
I had the USA testprep
hope this helps :)
Which expressions are equivalent to g + h + (j + k)? Check all that apply.
g + (h + j) + k
(g + h) + j k
(g + h) + j + k
g + (h j) + k
g h + j k
g (h + j) k
g + h (j + k)
Answers
Answer:
According to the associative property of equality: (a + b) + c = a + (b + c) we can see that the parenthesis do not mean anything when we are only doing addition.
So answers 1. and 3. are correct.
Step-by-step explanation:
Answer:
person above seems corect and he said a and c
A biologist estimates that the human body contains 90 pounds of water for every 100 pounds of body weight. At the rate estimate the number of pounds of water in a child who weighs 80 pounds
Answers
Answer:
72 lb
Step-by-step explanation:
Write and solve an equation of ratios:
80 pounds x
----------------- = ------------------
100 pounds 90 pounds
Cross multiplying, we get (100 pounds)x = 7200, or x = 72 pounds.
The 80 pound child's weight includes 72 pounds of water.
Which equation would help find the measure of ZM?
O x +52 + 78 = 180
O 52 + x = 180 + 78
O 180 + 52 = 78 + x
O 180 + x = 78 + 52
Answers
Answer:
[tex] \huge \boxed{ \boxed{ \sf x + 52 ^{o} + 7 {2}^{o} =18 {0}^{o} }}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:triangleequationPEMDASgiven:[tex]\angle V=52°[/tex][tex]\angle P=78°[/tex]to find:the equationtips and formulas:a triangle contains 180° let's solve:[tex]\text{since a triangle contains 180° the sum of the interior angles has to be 180°}[/tex]
[tex]\text{therefore the equation is}[/tex]
[tex] \mathfrak{x + {52}^{o} + {78}^{o} = 180 ^{0} }[/tex]
Explanation:
The sum of all 3 angles in a triangle is 180.
x + 78 + 52 = 180
x = 180 - 78 - 52
x = 50
Solve the equation: 2/3x+1/4=3
Answers
Answer:
x = 33/8
Step-by-step explanation:
2/3 x + 1/4 = 3
Subtract 1/4 from both sides.
2/3 x = 3 - 1/4
2/3 x = 12/4 - 1/4
2/3 x = 11/4
Multiply both sides by 3/2.
3/2 * 2/3 x = 3/2 * 11/4
x = 33/8
A fossilized leaf contains 8% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.
Answers
Answer:
Step-by-step explanation:
0.5^(t/5600) = 0.08
2^(-t/5600) = 0.08
-t/5600 = log₂0.08
t = -5600 log₂0.08 ≈ 20406 years
Can someone help me find the solution to these equations by using substitution
Answers
2) x=-2y
-2y-y = 9
-3y = 9
y = -3
x = -2(-3)
x = 6
(x,y) = (6,-3)
Fractions that are not equivalent to 1/5
Answers
Answer: 3/10
Step-by-step explanation:
1/5 isn’t equivalent to it
Answer:
Just random ones?
1/2, 1/3, 1/4, 1/6, 1/7
Step-by-step explanation:
Plz help will give brainliest for brainliest!!!!!!
Answers
Answer:
1
Step-by-step explanation:
The use of
Parenthesis(1+2)=3
Exponents- none
Multipy- 2 times the 3 is 6
Divide 6/6 is 1
Add- none
Subtract- none
Answer:
9
Step-by-step explanation:
you should have search it up :)
HAVE A GREAT DAY
I need a A in math can you help me with this answer
Answers
Answer: 13
Step-by-step explanation:
12^2+5^2=13^2
Find the slope of the line that passes through the points A (0, 2) and B (4, –1).
Use the formula (y2 - y1) / (x2 - x1)
Answers
Answer:
-3/4
Step-by-step explanation:
y2-y1/x2-x1 =
-1-2/4-0=
-3/4
calvin has a fever with 38.5 degrees celsius, after taking medicine it drops by 2 degrees celsius. write the temperature of calvin after taking medicine
Answers
Answer:
36.5 degrees Celsius
Step-by-step explanation:
38.5-2=36.5 degrees Celsius
Michael has read 1/2 of a book. Amelia has read 2/3 of the same book. Who has read more of the book?
Answers
Answer:
amelia
Step-by-step explanation:
Answer:
Step-by-step explanation:
To compare fractions, they need to have a common denominator.
The least common denominator of 1/2 and 2/3 is 6.
1/2 = 3/6
2/3 = 4/6
Now find the fraction with the larger numerator.
4/6 > 3/6, so 2/3 > 1/2
Need help. Whixh of these are functions?
Answers
Answer: C and D are functions.
Step-by-step explanation:
Let f be a differentiable function such that f(1)=π2 and f′(x)=3arctan(x2−3x+2). What is the value of f(3) ?
Answers
Answer:
2.899
Step-by-step explanation:
Given that:
[tex]f' (x) =3 tan ^{-1} (x^2 -3x +2)[/tex]
[tex]\text{applying integration on both sides with respect to x}[/tex]
[tex]\int \limits ^{3}_{1}} f'(x) \ dx = \int ^3_1 3tan ^{-1} (x^2 -3x+2) \ dx[/tex]
[tex]f(3)-f(1)= 3 \int ^3_1 3tan ^{-1} (x^2 -3x+2) \ dx[/tex]
[tex]f(3) = \dfrac{\pi}{2}+3\int^{3}_{1} tan^{-1} (x^2 -3x+2)dx ---(1)[/tex]
[tex]\text{consider } \ \ 3\int^{3}_{1} tan^{-1} (x^2 -3x+2)dx[/tex]
[tex]h = \dfrac{b-a}{n}[/tex]
[tex]where; n = 10 , a =1, b= 3[/tex]
[tex]h = \dfrac{3-1}{10}[/tex]
[tex]h = \dfrac{2}{10}[/tex]
[tex]h = 0.2[/tex]
[tex]\text{The value of x and corresponding } y = 3tan^{-1}(x^2-3x+2) \ are:[/tex]
x 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
y f(0) f(1.2) f(1.4) f(1.6) f(1.8) f(2.0) f(2.2) f(2.4) f(2.6) f(2.8) f(3)
By simpson's rule:
[tex]\int \limits ^3_1 \ 3 tan^{-1} (x^2-3x+2) dx \simeq \dfrac{h}{3}(y_o+y_{10}) +4(y_1+y_3+y_5+y_7+y_9)+2(y_2+y_4+y_6+y_8)][/tex]
[tex]=\dfrac{0.2}{3}\Big[(0+3.3214)+(-1.9039+2.8265+1.4133+6.1259+11.5657)+2(-1.4133-0.9519+1.4133+4.5899)\Big][/tex]
[tex]= 1.32804[/tex]
[tex]\text{From}; f(3) = \dfrac{\pi}{2}+1.32804 \\ \\ f(3) = 2.89883633 \\ \\ \mathbf{f(3) \simeq 2.899}[/tex]
Trapezoidal rule is used to evaluate the area of the curve by using various strips of equal width which is in the form of trapezoids. The value of [tex]f(3)[/tex] is 2.8989.
Given information
In the given problem [tex]f[/tex] is the function such that,
[tex]f(1)=\dfrac{\pi}{2} \\[/tex]
The differentiated function is,
[tex]f'(x)=3\tan^-(x^2-3x+2)[/tex]
Integrate the above equation with respect to the x,
[tex]\int\limits^3_1 {f'(x)} \, dx =\int\limits^3_1 {3\tan^-(x^2-3x+2)} \, dx\\f(3)-f(1) =\int\limits^3_1 {3\tan^-(x^2-3x+2)} \, dx\\f(3) =3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx +f(1)\\f(3) =3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx +\dfrac{\pi}{2}[/tex] .........1
Let the above equation is the equation number 1.
Let the integrated function,
[tex]y=3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx[/tex]
Solve the above equation using the trapezoidal rule.
Trapezoidal rule-Trapezoidal rule is used to evaluate the area of the curve by using various strips of equal width which is in the form of trapezoids.
In the given problem,
[tex]h=\dfrac{b-a}{n}[/tex]
Use this formula for the integrated function,
[tex]h=\dfrac{3-1}{10}\\h=0.2[/tex]
Use the Simpson formula to solve the above equation,
[tex]=3\int\limits^3_1 {\tan^-(x^2-3x+2)} \, dx[/tex]
[tex]=\dfrac{h}{3} (y_0+y_{10})+4(y_1+y_3+y_{5}+y_7+y_{9})+2(y_2+y_{4}+y_6+y_{8})[/tex]
Find the value of y by putting the values in the given formula. Thus,
[tex]=\dfrac{0.2}{3} (0+3.3214)+4(-1.9039+2.8266+1.4133+6.1259+11.5657)+2(-1.4133-0.9519+1.4133+4.5899)\\=1.32804[/tex]
Put this value in equation 1,
[tex]f(3) =1.30824 +\dfrac{\pi}{2}\\f(3)=2.8989[/tex]
Thus the value of [tex]f(3)[/tex] is 2.8989.
Learn more about the trapezoidal rule here;
https://brainly.com/question/15323877
Work out the area of the parallelogram.
9m
7m
10m
The diagram is not drawn to scale.
m2
Answers
Answer:
9m×7m:10m-2m paràllelogram
Answer:
A = 70 m²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
Here b = 10 and h = 7 , then
A = 10 × 7 = 70 m²
Each student in a group of 32 students was asked the following question.
"Do you have a desktop computer (D), a laptop (L) or a tablet (T )?"
Their answers showed that
Answers
Answer:
.shsnxbjsjJsjsiakzjxjisksjxjs
The value of a fifth stock, stock E, changed by 2 1/2 times as much as Stock D. What is the change in value in Stock E?
Answers
Answer: — Cramer: Tesla is the first non-traditional tech stock that could move the market ... The electric car maker has a 1.69% weighting in the index, the fifth largest. ... (S&P Dow Jones uses float-adjusted market value rather than the outright number.) ... For every $11.11 Tesla moves, the S&P 500 changes 1 point, ...
pls Brainliest
Jon is hitting baseballs. The height of the ball is given by h(t) = - 16t? + 5t + 5 where t is in
seconds. When will the baseball hit the ground?
Answers
Your equation is wrong. See below for correct equation.
The ball will hit the ground when h(t) is 0.
Here is the set up:
0 = -16t^2 + 5t + 5
Solve for t to find your answer.
simplify -2.2f + 0.8f - 15 - 3 please help
Answers
It would be -1.4f-18. I hope this helps!!
Answer:
Simplify the expression.
− 1.4 f − 18
Step-by-step explanation: