Look at the table. Make a conjecture about the sum of the first 20 positive even numbers.
Answers
Answer:
Hence, the conjecture for the sum of first 20 positive integer is:
20×21=420
Step-by-step explanation:
The table is given as:
2 = 2 =1.2
2+4 = 6 = 2.3
2+4+6 = 12 = 3.4
2+4+6+8 = 20 = 4.5
2+4+6+8+10 = 30 = 5.6
Hence, we see the pattern as:
2+4+6+....+2n= n(n+1)
which is the sum of first n even positive integers.
Hence, we are asked to find the sum of first 20 positive even numbers that is we are asked to find the sum when n=20.
i.e. the sum of:
2+4+6+8+..........+40=20(20+1)
2+4+6+8+........+40=20×21=420.
Hence, the conjecture for the sum of first 20 positive integer is:
20×21=420
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Answers
The sum of a number and two is doubled: 2(N+2)
Six less than 3 times the number : 3N-6
The result is : =
Let's put it all together.
The answer is d)10.
Check your answer.
The sum of a number and two is doubled: 2(10+2)=24
Six less than 3 times the number : 3(10)-6=24
Good answer.
Final answer:
To solve the problem, create the equation 2(x + 2) = 3x - 6. Simplify the equation and solve for x to find the number.
Explanation:
To solve this problem, we can create an equation based on the given information. Let's call the number we're trying to find 'x'. The sum of the number and two can be written as (x + 2). Doubling this expression gives us 2(x + 2). 'Six less than three times the number' can be written as 3x - 6. So, we have the equation 2(x + 2) = 3x - 6. Solving this equation will give us the value of the number 'x'.
Expanding the equation, we get 2x + 4 = 3x - 6. Simplifying it further, we can subtract 2x from both sides to get 4 = x - 6. Adding 6 to both sides gives us 10 = x. Therefore, the number we're looking for is 10.
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Thinking further,
V(R,h)=f(R) for h=3R
V=πR²*3R/2=πR^3
dV/dt=45
but dV/dt=dV/dR* dR/dt==>45=3πR²*dR/dt
==>dR/dt=45/(3πR² )
If R=4 then dR/dt=15/(π*16)=0.2984155...≈0.298
Without any certainty!!!
Final answer:
The rate of increase of the radius when the radius of the cone is 4 cm is approximately 0.299 cm/s. This was calculated by using the derivative of the volume of a cone with respect to its radius, with the height of the cone always being three times the radius.
Explanation:
The subject of this question relates to the rate of change in the context of the volume and radius of a cone. The volume of a right circular cone is given by the formula V = 1/3πr²h. Given that the height is always three times the radius, we can substitute h = 3r into the formula, which gives V = 1/3πr³ * 3 = πr³.
The rate of change of the volume with respect to time (dV/dt) is given as 45 cm³/s. We can set up an equation using the derivative of the volume with respect to the radius and the relation dV/dt = (dV/dr)(dr/dt). Calculating the derivative of the volume with respect to the radius, we find that dV/dr = 3πr². Substituting the provided values into our relation gives us 45 = 3π(4)²*dr/dt. Solving for dr/dt, we find the rate of change of the radius to be approximately 0.299 cm/s to 3 significant figures.
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Answers
Answer:
7m-3
Step-by-step explanation:
first, distribute
m+3m+3m-3
then, combine all like terms
m+6m-3
7m-3
i hope this helps! have a nice day!
Answers
The first one is always what is given.
Then work through the rest.
See the attached picture:
Answer:
This one is actually in order already.
First box to A.
Second box to B
Third box to C.
Fourth box to D.
Fifth box to E.
Step-by-step explanation:
You always start with the given. So the first box goes to A.
The second box goes with B. When angle is bisected it is cut into two congruent halves. That means that left part of the angle of A has an equal measurement to that of the right part of the angle of A. So Angle BAD is congruent to Angle CAD.
Those base angles are B and C even though it isn't written there.
x (related) x is the reflexive property. This is what you have here where the related part is the congruence and the element being talking about is AD on both sides. So The third box goes with the reflexive option. The third box goes with C.
So you have by the given that AB and AC are congruent; those are the left and right leg of the big triangle.
You also have that Angle's BAD and CAD are congruent (those are the angles at the top in the two different triangles. You also have that they share the side right after.
So you are given 2 corresponding sides are congruent and the angle right between them in each is congruent.
We have enough information to prove the triangles are congruent by SAS. This fourth box should be matched with D.
Lastly, since the triangles are already congruent by SAS, then the other remaining corresponding sides are congruent and the other remaining corresponding angles are congruent. So Angle B and Angle C are congruent due to corresponding parts of congruent triangles are congruent. Last box is to be matched with E.
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50/20=2.5
both carpenters are working at the same speed rate as 2.5=2.5