3 years ago

Evaluate (101.5)²-(100.5)²

Mathematics

1 answer:

makvit [3.9K]3 years ago

8 0

You can exploit the difference-of-squares identity,

a² - b² = (a - b) (a + b)

Then

101.5² - 100.5² = (101.5 - 100.5) * (101.5 + 100.5)

101.5² - 100.5² = 1 * 202

101.5² - 100.5² = 202

You might be interested in

Find the trigonometric integral. (Use C for the constant of integration.)

Olin [163]

Suppose we let $u=\sin\theta+\cos\theta$ , so that $\mathrm du=(\cos\theta-\sin\theta)\,\mathrm d\theta$ .

Also, recall the double angle identity for cosine:

$\cos(2\theta)=\cos^2\theta-\sin^2\theta=(\cos\theta-\sin\theta)(\cos\theta+\sin\theta)$

So, we can rewrite and compute the integral using the substitution, as

$\displaystyle\int\cos(2\theta)(\sin\theta+\cos\theta)^3\,\mathrm d\theta$

$=\displaystyle\int u\cdot u^3\,\mathrm du$

$=\displaystyle\int u^4\,\mathrm du$

$=\dfrac{u^5}5+C$

$=\boxed{\dfrac{(\cos\theta+\sin\theta)^5}5+C}$

4 0

3 years ago

The street signs in a subdivision are in the shape of

4vir4ik [10]

72 I think it is I believe

5 0

3 years ago

It’s system of equations but it needs to be solved in substitution if you can answer I’ll give five stars

Aloiza [94]

2x - 3(x-1) = -1
2x -3x + 3 = -1
-1x + 3 = -1
-1x = -4
x = 4

y = 4 - 1
y = 3

8 0

3 years ago

Read 2 more answers

In a survey of nursing students pursuing a master's degree, 75 percent stated that they expect to be promoted to a higher positi

Schach [20]

I believe the answer is C:)

5 0

3 years ago

The pentagons ABCDE and JKLMN are similar find the length x of JK

never [62]

The second shape is double the first so you would do AB = 2 and then times by 2 as its double and you will get 4
answer = 4

3 0

2 years ago

Read 2 more answers

Evaluate (101.5)²-(100.5)²​

Evaluate (101.5)²-(100.5)²