All categories

4 years ago

Prove algebraically that: (2n^2 +1)^2 -(2n+1)

Mathematics

1 answer:

givi [52]4 years ago

6 0

Hello from MrBillDoesMath

Answer:

See below

Discussion:

Note the Question incorrectly shows (2n^2 +1) ^ 2. It should be (2n + 1) ^2.

(2 n + 1) ^2 - (2n +1) =

4n^2 + 4n + 1 - 2n - 1 = ( -1 + 1 = 0)

4n^2 + 4n -2n + (1-1) =

4(X) = 2 (2X)

Key point. The end result of the evaluation is a multiple of 2 so the result is an even integer.

Thank you,

Mr. B

You might be interested in

I need help ASAP pls help me with this question on my no check in

Veronika [31]

Answer: The answer is C

8 0

3 years ago

WILL MARK BRAINLIEST!!! PLZ HELP! The following graph describes function 1, and the equation below it describes function 2. Dete

Assoli18 [71]

Answer:

Step-by-step explanation:

The maximum/minimum values is simply the y-value of the vertex. Since both of the functions have a negative leading coefficient, they will both have maximum values.

For Function 1, we can see that the vertex is at (4,1). Thus, it's maximum value is at y=1.

For Function 2, we need to work out the vertex. To do this we can use:

$x=\frac{-b}{2a} ,y=f(-b/2a)$

To find the vertex.

Function 2 is defined by:

$f(x)=-x^2+4x+1$

Therefore:

$a=-1, b=4, c=1$

$x=-(4)/2(-1)=-4/-2=2\\f(2)=-(2)^2+4(2)+1\\=-4+8+1\\=4+1=5$

Thus, the vertex of Function 2 is at (2,5). Therefore, the maximum value of Function 2 is y=5.

5 is greater than 1, so the maximum value of Function 2 is greater.

The answer is choice C.

6 0

3 years ago

Find the projection of the vector A = î - 2ġ + k on the vector B = 4 i - 4ſ + 7k. 15. Given the vectors A = 2 i +3 ſ +6k and B =

Gwar [14]

Answer:

Part 1)

Projection of vector A on vector B equals 19 units

Part 2)

Projection of vector B' on vector A' equals 35 units

Step-by-step explanation:

For 2 vectors A and B the projection of A on B is given by the vector dot product of vector A and B

Given

$\overrightarrow{v_{a}}=\widehat{i}-2\widehat{j}+\widehat{k}$

Similarly vector B is written as

$\overrightarrow{v_{b}}=4\widehat{i}-4\widehat{j}+7\widehat{k}$

Thus the vector dot product of the 2 vectors is obtained as

$\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=(\widehat{i}-2\widehat{j}+\widehat{k})\cdot (4\widehat{i}-4\widehat{j}+7\widehat{k})\\\\\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=1\cdot 4+2\cdot 4+1\cdot 7=19$

Part 2)

Given vector A' as

$\overrightarrow{v_{a'}}=2\widehat{i}+3\widehat{j}+6\widehat{k}$

Similarly vector B' is written as

$\overrightarrow{v_{b'}}=\widehat{i}+5\widehat{j}+3\widehat{k}$

Thus the vector dot product of the 2 vectors is obtained as

$\overrightarrow{v_{b'}}\cdot \overrightarrow{v_{a'}}=(\widehat{i}+5\widehat{j}+3\widehat{k})\cdot (2\widehat{i}+3\widehat{j}+6\widehat{k})\\\\\overrightarrow{v_{a'}}\cdot \overrightarrow{v_{b'}}=1\cdot 2+5\cdot 3+3\cdot 6=35$

7 0

4 years ago

For a science experiment Ella recorded the time, in seconds, to boil 650 grams of solution. Her results were 24.5, 23.2, 29.8, a

bagirrra123 [75]

Answer:

Mean of boiling times = 26.9 seconds

Step-by-step explanation:

Times ella recorded are given as;

24.5 seconds, 23.2 seconds, 29.8 seconds, and 30.1 seconds.

Now, we want to find the mean of these boiling times.

Formula for mean is;

Mean = sum of terms/number of terms

In this question,

number of terms = 4

Sum of terms = 24.5 + 23.2 + 29.8 + 30.1 = 107.6

Thus,

Mean = 107.6/4

Mean = 26.9 seconds

8 0

3 years ago

What is the product? (9 t minus 4)(negative 9 t minus 4) negative 81 t squared minus 16 negative 81 t squared + 16 negative 81 t

liraira [26]

The product is negative 81 t squared + 16 ⇒ 2nd answer

Step-by-step explanation:

The product of two binomials (ax + b)(cx + d), where a, b, c, and d are constant

Multiply (ax) by (cx) ⇒ 1st × 1st
Multiply (ax) by (d) and (b) by (cx) ⇒ ext-reams and nears
Add the two products ⇒ like terms
Multiply (b) by (d) ⇒ 2nd × 2nd

Let us find the product of (9 t - 4) and (-9 t - 4)

Multiply the 1st two terms

∵ (9 t)(-9 t) = -81 t²

Multiply the ext-reams

∵ (9 t)(-4) = -36 t

Multiply the nears

∵ (-4)(-9 t) = 36 t

Add the like terms

∵ -36 t + 36 t = 0

Multiply the 2nd two terms

∵ (-4)(-4) = 16

Write the answer

∴ (9 t - 4)(-9 t - 4) = -81 t² + 0 + 16

∴ (9 t - 4)(-9 t - 4) = -81 t² + 16

The product is -81 t² + 16

Learn more:

You can learn more about the product of algebraic expressions in brainly.com/question/1617787

#LearnwithBrainly

7 0

4 years ago

Read 2 more answers