Answer:
The capacity of the container is 2546.78 cm³.
Step-by-step explanation:
The volume of the frustum of a cone is:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
The information provided is:
r = 16/2 = 8 cm
R = 24/2 = 12 cm
h = 8 cm
Compute the capacity of the container as follows:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
[tex]=\frac{\pi\cdot8}{3}\cdot[(12)^{2}+(12\cdot 8)+(8)^{2}]\\\\=\frac{8\pi}{3}\times [144+96+64]\\\\=\frac{8\pi}{3}\times304\\\\=2546.784445\\\\\approx 2546.78[/tex]
Thus, the capacity of the container is 2546.78 cm³.
calculate the amount and compound interest on rupees 4000 at the rate of 8% per annum compounded annually for 2 years
Step-by-step explanation:
To calculate the compound interest we use the formula
C = A - PWhere
A is the amount
P is the principal
C is the compound interest
To find the amount we use the formula
[tex]A = P(1 + \frac{r}{100} ) ^{n} [/tex]where P is the principal
r is the rate
n is the period
From the question
P = 4000 rupees
rate = 8%
n = 2 years
Substitute the values into the above formula
That's
[tex]A = 4000( 1 + \frac{8}{100} )^{2} [/tex][tex]A = 4000 ({1 + 0.08})^{2} [/tex][tex]A = 4000 ({1.08})^{2} [/tex]A = 4665.6
The amount is 4665.60 rupeesSince the amount is found we can now find the compound interest
C = 4665.60 - 4000
C = 665.6
The compound interest is 665.60 rupeesHope this helps you
URGENT PLZ HELP THANK YOU!
Answer:
[tex](-5)^{11}[/tex]
Step-by-step explanation:
We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].
b is 5, c is -6, and a is -5 so:
[tex]-5^{5-(-6)}\\-5^{11}[/tex]
Hope this helped!
56:31
Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each portion weighs 3 pounds. Which equation and solution shows the total amount of chopped vegetables she used in the mixture?
Answer:
The equation is (2+x) / 4 = 3
Total amount of chopped vegetables = 10 pounds
Step-by-step explanation:
Meat=2 pounds
Vegetables=x
Mixture= 2+x
She divides the mixture into 4 equal portions
(2+x)/4
Each portion weighs 3 pounds
(2+x)/4=3
Solve the equation
(2+x)/4=3
Cross product
(2+x) = 4 × 3
2+x=12
x=12-2
=10
x=10 pounds
Total amount of chopped vegetables = 10 pounds
convert 28km into cm
Answer:
28km to cm = 2,800,000cm
Step-by-step explanation:
In order to convert km to cm you have to times it by 100,000
So... 28 x 100,000 = 2,800,000
Hope this helps
Answer:2,800,000cm
Step-by-step explanation:
To convert a larger unit into a smaller unit, you must first check how much does the smaller unit need to make the larger unit. Then multiply the given larger unit to the amount of smaller unit that is equal to 1 of the larger unit.
Because: 100,000cm = 1km
So = 28km×100,000 =2,800,000cm
who is going to win the race?
Answer:
The correct answer is
Step-by-step explanation:
Red team is going to win the race as they have covered more area than other teams. I am a 100% sure of this answer.Hope this helps....Have a nice day!!!!Answer:
Red Team
Step-by-step explanation:
Given the trinomial, what is the value of the coefficient B in the factored form? 2x2 − 12xy − 32y2 = 2(x − 8y)(x + By) −4 −2 2 4
Answer:
B is related to the last term of trinomial
Last term on the left hand side of the equation = Last term on the right hand side of the equation.
The last term on the right hand side is gotten by multiplying all the terms on the right of the two expression.
-32y²= 2*-8y*By
-32y² = -16By² Compare both
32 = 16B
16B = 32
B = 32/16
B = 2.
Answer:
B = 2
Step-by-step explanation:
2x^2 − 12xy − 32y^2
Factor out a 2
2 ( x^2 -6xy -16y^2)
Factor inside the parentheses
What two numbers multiply to -16 and add to -6
-8 * 2 = -16
-8+2 = -6
2( x-8y) ( x+2y)
B = 2
Plz help me this is probably easy but im just not seeing it plz help me ASAP
Answer: is attatched to the photo I sent
Step-by-step explanation:
I admit, this is tricky, just remember to think about it as where the shapes are the most similar. I'm not exactly sure how to explain it, but where it reflects like a mirror is the "copy"
The example I'm thinking of attached too, but these over lap so its diffucult
Is the given equation a quadratic equation? Explain. x(x−6)=−5
The equation is not a quadratic equation because there is no x2-term.
The equation is a quadratic equation because there is an x2-term.
The equation is not a quadratic equation because the expression is not equal to zero.
The equation is not a quadratic equation because there is a term with degree higher than 2.
I think the answer is A but im not sure.
Answer:
The equation is a quadratic equation because there is an x2-term.
Step-by-step explanation:
x(x−6)=−5
Distribute
x^2 -6x = -5
The equation is a quadratic equation because there is an x^2-term.
Answer:
Your required answer is option A.
Step-by-step explanation:
Here,
The given equation is;
x(x-6)=-5
now,
while finding x.
either or,
x=-5 (x-6)=-5
x= 1 (shifting-6 in next side)
now, the value of x is -5,1.
so, it's a quadratic equation.
( in quadratic equation the variable always has two values after solution)
Hope it helps..
In the diagram of the right triangle shown find the value of c.
Answer:
Hey there!
20^2+25^2=c^2
400+625=c^2
1025=c^2
Square root 1025 is the correct answer, so option C.
Let me know if this helps :)
Answer: B
Step-by-step explanation:
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
last option
Step-by-step explanation:
Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷ x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.
Which equation has a constant of proportionality equal to 3? A. y= 8/5 x B. y= 1/3 x C. y= 1/4 x D. y= 18/6 x PLEASE HELP ME :c
Answer:
(D) [tex]y=\frac{18}{6}x[/tex]
Step-by-step explanation:
We will be able to know if an equation has a constant of proportionality of 3 if the constant which is being multiplied by x is equal to 3.
[tex]\frac{8}{5} =1.6[/tex] so no for A.
[tex]\frac{1}{3} = 0.\overline{33}[/tex] so no for B too.
[tex]\frac{1}{4} = 0.25[/tex] so no for C as well.
[tex]\frac{18}{6} = 3[/tex], so D works.
Hope this helped!
What Is the answer to it?
Answer:
2(x + 10)
Step-by-step explanation:
The sum of x and 10 is x + 10
The product of 2 and x + 10 means multiply them, thus
2 × (x + 10)
= 2(x + 10) ← parenthesis indicates x and 10 are added before being multiplied by 2
Need help pls will give you five stars
Answer:
[tex]\boxed{A. (1,1)}[/tex]
Step-by-step explanation:
Well since in,
[tex]f(x) = -3x^2 + 6x - 2[/tex]
the 3x^2is negative that means the parabola has a maximum not a minimum meaning we can take out choices,
B and D.
To find the maximum let’s graph the given equation,
Look at the image below.
By looking at the image we can tell that the maximum is at (1,1).
So the answer is choice A (1,1)
Help please on this question. I’d appreciate it if you answered.
Ok so the letters overwrap all of the alphabets and the other terms are in.
Answer:
see below
Step-by-step explanation:
Consonants and vowels do not overlap
There are no consonants that are vowels and no vowels that are consonants
That means the circles will never touch
The pH of 0.0001 M solution of Ca(OH)2 is
Step-by-step explanation:
Since Ca(OH)2 is Basic, we need to find pOH:
pOH = - log [OH-]
pOH = - log(0.0001)
pOH = - ( - 4)
pOH = 4
Since, pH + pOH = 14
Therefore,
pH of 0.0001M sol. of Ca(OH)2 = 10
Point E is on line segment DF. Given DE
EF.
6 and DF =9, determine the length EF
Answer:
3Step-by-step explanation:
IF point E lies on the line segment DF, this means that all the points DEF are collinear and DE+EF = DF.
Given parameter
DE = 6
DF = 9
Required
EF
Substituting the given parameter into the expression above to get the required will be;
DE+EF = DF.
EF = DF-DE
EF = 9-6
EF = 3
Hence the length of EF is equivalent to 3
Porfavor, necesito ayuda con estos ejercicios.
Lo siento, no hablo español pero utilicé Google Translate .
HAHAHAHAHA
Graham uses a hot water bottle on an injury to his back he incurred playing basketball. He fills the bottle with water that is 100°F. After 25 minutes, Graham finds that the bottle has cooled and stops using it. What is the domain and range?
Answer:
Domain= time
Range= temperature
Step-by-step explanation:
Initially hot water cools down over time.
This can be expressed as a function of a temperature by a time. It takes 25 minutes for water to cooled down from 100°F to body temperature.
For any value of the time (from zero to 25 minutes), the temperature has certain value (from 100°F to body temperature). As time value increases, temperature value decreases accordingly.
In this example, time is the domain and temperature is the range.
convert American $553 in Nepal rupees
Answer:
65,994.52 Nepalese Rupee
Step-by-step explanation:
using conversion rate 1 usd = 119.74 nepalese rupee
553*119.74
10q-30q is equivalent to
Answer:
please mark my answer brainliest
Step-by-step explanation:
10q (1-3)
Line a and t are parallel. What is the value of x?
7x - 48
5x
pls help me
Answer:
x = 24
Step-by-step explanation:
We know that lines s and t are parallel. Then by definition, the two labelled angles, which are same-side angles, are congruent and equal in measure.
Then, we set the expressions equal to each other:
7x - 48 = 5x
Subtract 5x from both sides:
7x - 5x - 48 = 0
2x - 48 = 0
Add 48 to both sides:
2x = 48
Divide by 2:
x = 48/2 = 24
Thus, x = 24.
~ an aesthetics lover
What is another way to write 100,203 in other forms
Answer:
You can write in
Step-by-step explanation:
Lakhs
First write 100,203.
Put ones,tens,hundreds,thousands,ten thousands and lakh on top of each number from the extreme left.
This is how you can write 100,203 in another way. You can't write in any other way than this one.
Hope this helps....
Have a nice day!!!!
A 10 gram sample of a substance that’s used to detect explosives has a k-value of 0.1356.Find the substances half life in days.Round your answer to the nearest tenth.
Answer:
t ≈ 5.1 days
Step-by-step explanation:
A 10 gram sample of a substance thats used to detect explosives has a k-value of 0.1356. Find the substances half-life in days. round your answer to the nearest tenth. N=N₀ e^-kt N₀= initial mass (at time t = 0) N = mass at time t k= a positive constant that depends on the substance itself and on the units used to measure time t=time in days
The initial condition is that, at time t = 0, the amount of substance contains originally 10 grams
Find the value of N₀
N=N₀ e^-kt
We substitute:
10 = N₀ {e^(-0.1356)*0}
10 = N₀ (e^0)
10=N₀(1)
10=N₀
N₀ = 10
When the substance is in half-life
That is, half of the original substance (5 grams)
Find t
N=N₀ e^-kt
5 = 10 e^(-0.1356*t)
0.5 = e^(-0.1356*t)
Bring down t by multiplying natural log on both sides
ln(0.5) = -0.1356*t
Divide both sides by -0.1356
t = -(ln(0.5) / 0.1356
t ≈ 5.11 days
To the nearest tenth
t ≈ 5.1 days
Answer:
5.1 days in Plato
Step-by-step explanation:
suppose you are mixing red and blue paint in a bucket. do you think the final color of the mixed paint will be the same whether you add the blue or the red paint first?relate your answer to a property of real numbers
Answer:
It does not matter which color you add first because either way you will end up with the same color, purple. We can relate this to the commutative property of addition because blue + red = red + blue.
Pls mark it Brainliest!!!
Expand the following using the Binomial Theorem and Pascal’s triangle. Show your work. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5
Answer:
The answer is below
Step-by-step explanation:
Expansion using pascal triangle:
a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ =
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
Expansion using binomial where [tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]
a) (x + 2)⁶ = C(6,0)[x⁶2⁰] + C(6,1)[(x⁵)(2)¹] + C(6,2)[(x⁴)(2²)] + C(6,3)[(x³)(2³)] + C(6,4)[(x²)(2⁴)] + C(6,5)[(x)(2⁵)] + C(6,6)[(2⁶)]
= x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = C(4,0)[x⁴] + C(4,1)[(x³)(-4)] + C(4,2)[(x²)(-4)²] + C(4,3)[(x)(-4)³] + C(4,4)[(x⁰)(-4)⁴]
= x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = C(5,0)[(2x)⁵] + C(5,1)[(2x)⁴(3)] + C(5,2)[(2x)³(3)²] + C(5,3)[(2x)²(3)³] + C(5,4)[(2x)(3)⁴] + C(5,5)[(2x)⁰(3)⁵]
= (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = C(4,0){(2x)⁴(-3y)⁰} + C(4,1)[(2x)³(-3y)] + C(4,2)[(2x)²(-3y)²] + C(4,3)[(2x)(-3y)³] + C(4,4)[(2x)⁰(-3y)⁴]
= 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
In the expansion of (3a + 4b)⁸, the only possible variable terms are a⁵b³, b⁸, a⁴b⁴, a⁸, ab⁷ because for each of them, the sum of there powers is eight. If the sum of the powers is not 8 then it is not correct.
For a²b³, the sum of the power is 5, for ab⁸ the sum of power is 9 and for a⁶b⁵ the sum of the power is 11 therefore thy are not correct.
As per the question expand the bimonoidal theorem and the pascal triangle. Showing the (x+2)6 (x-4)4 (2x+3)5 (2x-3y)4.
Expansion using pascal triangle:a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶) = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4) =x⁴-16x³+96x²-256x+256c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴ = 16x⁴- 96x³ + 216x² - 216x + 81.Learn more about the use the binomial theorem.
brainly.com/question/11995132.
Arc length practice
Answer:
[tex]\large\boxed{s = 4\pi}[/tex]
Step-by-step explanation:
The arc length is determined by the formula [tex]s=r\theta[/tex], where s is the arc length, r is the radius, and [tex]\theta[/tex] is the value of the central angle (in radian formatting).
By substituting the values for the radius and the central angle, you can solve for the arc length.
[tex]\text{The radius is half of the diameter -} \: \boxed{\frac{4}{2}=2}[/tex].
The central angle is converted to radian form by multiplying the angle in degrees by the fraction of π/180 - 360° * π/180 = 360π/180 = 2π.
Now, substitute the values and solve for s.
s = (2)(2π)
[tex]\large\boxed{s = 4\pi}[/tex]
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What are all the possible lengths TP$? Enter the possible values, separated by commas.
====================================================
Explanation:
A drawing may be helpful to see what's going on. Check out the diagram below. This is one way of drawing out the two triangles. The locations of the points don't really matter, and neither does the the orientation of how you rotate things. What does matter is we have the right points connected to form the segments mentioned.
----------
For now, focus on triangle TIP only. In order to have this be isosceles, we must make TP = 5 or TP = 7.
If TP = 5, then it's the same length as TI.
If TP = 7, then it's the same length as PI.
In either case, we have exactly two sides the same length (the other side different) which is what it means for a triangle to be isosceles.
----------
Let's consider triangle TOP. For it to be isosceles, we must have two sides the same length. We already locked in TP to be either 5 or 7 in the previous section above. So there's no way that TP could be 11 units long to match up with PO = 11.
If TP = 5, then OT must also be 5 units long so that triangle TOP is isosceles.
If TP = 7, then OT = 7 for similar reasoning.
Either way, TP only has two choices on what it could be.
----------
In short, we basically just write the first two values given to us to get the two triangles to be isosceles. We can't use TP = 11 as it would make triangle TIP to be scalene (all sides are different lengths).
Answer:
So we all cheat AOPS huh
Step-by-step explanation:
What is the difference between {2,3} and {{2,3}}
[tex]\{2,3\}[/tex] is a set containing two elements - numbers 2 and 3
[tex]\{\{2,3\}\}[/tex] is a set containing one element - a set [tex]\{2,3\}[/tex]
ABC is an eqilateral triangle with sides 10cm find the length of the prependicular from A to BC
All sides are equal in an equilateral triangle and the perpendicular bisects the side too.
so BC will be bisected and the segments be 5 each.
you can use Pythagoras theorem to find the altitude length, hypotenuse will be one side of the triangle.
[tex] 5^2+h^2=10^2[/tex]
$h^2=100-25=75$
$h=\sqrt{75}=5\sqrt3$
(x^2-4x)^2+7x^2-28x+12=0
Answer:
[tex]x^4-9x^2-28x=-12[/tex]
Step-by-step explanation:
[tex](x^2-4x)^2+7x^2-28x+12=0[/tex]
[tex](x^4-16x^2)+7x^2-28x=-12[/tex]
[tex]x^4-9x^2-28x=-12[/tex]
