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3 years ago

Find the diagonal of a square whose sides measure 3 square root 2

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

8 0

The Pythagorean theorem can be used to find the length of the diagonal (d) of a square.

d² = (3√2)² + (3√2)² = 18 + 18 = 36

d = √36 = 6

The measure of the diagonal is 6.

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Solve the inequality:3x+5>-10

Amanda [17]

3x>-10-5. 3x>-15. x>-15/3. x>-5.

7 0

3 years ago

Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

a. Recall that

$\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C$

For $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

$\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

We can shift the index to simplify the sum slightly.

$\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

$\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n$

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

$\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}$

4 0

3 years ago

Sammi has 2 1/3 feet of rope. If he cuts the rope into pieces that are each 1/2 foot long, there will be 1/3 foot of rope left o

Stells [14]

Answer:

Step-by-step explanation:

Sammi has 2 1/3 feet of rope.

To write this type of fraction = 2 + 1/3 - The integer 2 in the expression is the amount of feet of rope that was cut.

Thus to know the number of 1/2 foot pieces produced, let this number be x. Thus, we have 1/2 of x pieces = 2

x/2 = 2; x = 2x2 = 4.

Thus, Sanmi has 4 pieces of 1/2 foot long piece each of rope.

4 0

3 years ago

If x=-4 and y=6, then xy-3=

Anna11 [10]

Answer:

-12

Step-by-step explanation:

We start with the equation: $xy-3x$

Substitute the variables: $(-4)(6)-3(-4)$

Solve using order of operations (start with multiplication): $(-24)-(-12)$

And then addition/subtration: $(-24)-(-12)=-12$

3 0

3 years ago

What is 72 ounce in 2 steaks as a unit rate

Ilya [14]

The unit rate in this scenario is the number of ounces per steak/in one steak.

72 oz/2 steaks= 36 oz per steak

Final answer: 36 oz per steak

3 0

3 years ago