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3 years ago

Whats the constant of 18z-7(-3+2z)

Mathematics

1 answer:

cricket20 [7]3 years ago

3 0

Answer:

Step-by-step explanation:

18z -7(-3+2z)

-7*-3=21

they dont have variebles so they are your constants. You'd multiply them together to get the whole answer

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Prove that 1³+2³+....n³=n²(n+1)²/4. principle of mathematics induction

alex41 [277]

<h3>The Simplified Question:-</h3>

$\sf 1^3+2^3\dots n^3=\dfrac{n^2(n+1)^2}{2}$

$\\ \sf\longmapsto 1^3+2^3+\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2$

<h3>Solution:-</h3>

Let

$\\ \sf\longmapsto P(n)=1^3+2^3\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2$

For n=1

$\\ \sf\longmapsto P(1)=\left(\dfrac{1(1+1)}{2}\right)^2$

$\\ \sf\longmapsto P(1)=\left(\dfrac{1(2)}{2}\right)^2$

$\\ \sf\longmapsto P(1)=\left(\dfrac{2}{2}\right)^2$

$\\ \sf\longmapsto P(1)=(1)^2$

$\\ \bf\longmapsto P(1)=1=1^3$

Let k be any positive integer.

$\\ \sf\longmapsto P(k)= 1^3+2^3\dots k^3=\left(\dfrac{k(k+1)}{2}\right)^2$

We have to prove that p(k+1) is true.

consider

$\sf 1^3+2^3\dots k^3+(k+1)^3$

$\\ \sf\longmapsto \left(\dfrac{k(k+1)}{2}\right)^2+(k+1)^3$

$\\ \sf\longmapsto \dfrac{k^2(k+1)^2}{4}+(k+1)^3$

$\\ \sf\longmapsto \dfrac{k^2(k+1)^2+4(k+1)^3}{4}$

$\\ \sf\longmapsto \dfrac{k+1)^2\left\{k^2+4k+4\right\}}{4}$

$\\ \sf\longmapsto \dfrac{(k+1)^2(k+2)^2}{4}$

$\\ \sf\longmapsto \dfrac{(k+1)^2(k+1+1)^2}{4}$

$\\ \sf\longmapsto \left(\dfrac{(k+1)(k+1+1)}{2}\right)^2$

$\\ \sf\longmapsto (1^3+2^3+3^3\dots k^3)+(k+1)^3$

Thus P(k+1) is true whenever P(k) is true.

Hence by the Principal of mathematical induction statement P(n) is true for $\bf n\epsilon N.$

Note:-

We can solve without simplifying the Question .I did it for clear steps and understanding .

<h3>Learn More:-</h3>

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6 0

3 years ago

Read 2 more answers

last year 11,375 people participated in Macy's Thanksgiving day parade. The ratio of female to male participants was 4:3. How ma

FrozenT [24]

Answer:

there is 6500 females

there is 4875 males

and there is 1625 more females than males

8 0

3 years ago

Graph the following inequality and then select the correct graph below x + 2 > 1

posledela

Answer:

The graph is attached below.

Step-by-step explanation:

First, we want to isolate the "x" term from the equation. We do this by subtracting "2" from both sides.

This gives us x is greater than -1. So, we can graph:

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3 years ago

2. What is the 50th term in the sequence t(n) = 2 + 8n?

kap26 [50]

Answer:

402?

2+ 8(50)?

not sure

Step-by-step explanation:

if so mark the brainliest!

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3 years ago

The concentration of a saline solution is given by the function <img src="https://tex.z-dn.net/?f=C%28x%29%3D%5Cfrac%7B0.2%7D%7B

katrin2010 [14]

Answer:

We have to add 1.86 L of water to make the solution 7% saline.

Step-by-step explanation:

The concentration of a saline solution is given by

C(x) = $\frac{0.2}{1+x}$

where x represents the amount of water used to dilute the solution.

We have to find how much water must be added to obtain a solution that is 7% saline.

If we see the equation we notice that as we add the value of x, the concentration of the solution decreases.

Here C(x) = 0.07

0.07 = $\frac{0.2}{1+x}$

Rearranging,

1 + x = $\frac{0.2}{0.07}$

1 + x = 2.86

x = 1.86 L

We have to add 1.86 L of water to make the solution 7% saline.

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3 years ago