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3 years ago

The expression (27y^-2)^1/3 / y^-2/3 can be simplified and written without negative exponents as

Mathematics

1 answer:

Phoenix [80]3 years ago

4 0

Answer:

Step-by-step explanation:

$\displaystyle\tt \frac{(27y^{-2})^{\frac{1}{3}}}{y^{-\frac{2}{3}}}=\frac{(3^3\cdot y^{-2})^{\frac{1}{3}}}{y^{-\frac{2}{3}}}=\frac{3\cdot y^{-\frac{2}{3}}}{y^{-\frac{2}{3}}}=3$

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Choices; a) 60degree b) 70degree c)80degree d)90degree

storchak [24]

Answer:

∠ PTQ = 70°

Step-by-step explanation:

The angles subtended by the radii and tangents to the circle , sum to 180°

∠ PTQ + 110° = 180° ( subtract 110° from both sides )

∠ PTQ = 70°

7 0

3 years ago

What is the nth term?

kumpel [21]

Let $a_k$ denote the kth term of the sequence. Then

$a_k=a_1+d(k-1)$

where d is the common difference between consecutive terms in the sequence and a₁ is the first term.

The sum of the first n terms is

$S_n=\displaystyle\sum_{k=1}^na_k=a_1+a_2+\cdots+a_{n-1}+a_n$

From the formula for $a_k$ , we get

$S_n=\displaystyle\sum_{k=1}^n(a_1+d(k-1))=a_1\sum_{k=1}^n1+d\sum_{k=1}^n(k-1)$

$S_n=\displaystyle na_1+d\sum_{k=0}^{n-1}k$

$S_n=na_1+\dfrac{d(n-1)n}2$

$S_n=\dfrac n2(2a_1-d+dn)$

So we have $d=-5$ , and $2a_1-d=16$ so that $a_1=\frac{11}2$ .

Then the nth term in the sequence is

$a_n=\dfrac{11}2-5(n-1)=\boxed{\dfrac{21-10n}2}$

7 0

3 years ago

A botanist was measuring how tall her plant grew. After two weeks it had grown 12.93 inches.The second week alone it had grown 3

Korolek [52]

Answer:

9.5 inches

Step-by-step explanation:

The relationship is presumed to be ...

(first week's growth) + (second week's growth) = (growth in two weeks)

(first week's growth) + 3.43 inches = 12.93 inches . . . . . fill in the numbers

Subtract 3.43 from both sides of the equation:

first week's growth = 12.93 inches - 3.43 inches

first week's growth = 9.50 inches

The plant grew 9.50 inches in the first week.

6 0

3 years ago

What is 2 times 2/6?

Aloiza [94]

Hi there!

I can see why you've posted a question like this here - For adding, subtracting, multiplying, or dividing fractions by whole numbers can be difficult to come out with a precise answer, so let me make it look easier for you!

So, the steps are:

Smush the 2 (whole number) and the 2 (the numerator of the fraction) together on top so its (2)(2) over 6. I can show you what I mean, if you'd like.

$\frac{(2)(2)}{6}$ This is what it should look like.

Now, what is 2 times 2? You can use a calculator for this part.

$2 *2 = 4$

Now, we can get to the last part, my favorite one!

Simplify $\frac{4}{6}$ down to $\frac{2}{3}$ .

How did we do it? EASY!

See what number does evenly into both numerators and denominators. In this case, 2 goes into 4 twice, and 2 goes into 6 three times, so we're left with our beautiful answer $\frac{2}{3}$ .

That wasn't so bad, was it? You can use this as a guide for figuring out math problems like these, in case you're stuck again. But just in case, message me if you need anymore help! :D

4 0

3 years ago

Read 2 more answers

What happens to the area of a circle when the radius is tripled?

patriot [66]

The circle would triple because the radius is equal to its area

6 0

3 years ago

Read 2 more answers