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3 years ago

What is the area of a triangle expressed as a monomial

Mathematics

2 answers:

Jobisdone [24]3 years ago

8 0

Answer:

$28x^2$

Step-by-step explanation:

$area \:o f \: \triangle = \frac{1}{2} \times 8x \times 7x \\ = 4x \times 7x \\ = 28 {x}^{2}$

zmey [24]3 years ago

6 0

Triangle area =1/2 x high x base
=1/2 X 7x X 8x= 1/2 X 56x
28x

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Please help! 20 points!!!

KonstantinChe [14]

Answer:

SOLUTION STEPS

+−6

Multiply 6 and 8 to get 48.

48+5

−

6×3+1

Add 48 and 5 to get 53.

−

6×3+1

Multiply 6 and 3 to get 18.

−

18+1

Add 18 and 1 to get 19.

−

Least common multiple of 8 and 3 is 24. Convert

and

to fractions with denominator 24.

159

−

152

Since

159

and

152

have the same denominator, subtract them by subtracting their numerators.

159−152

Subtract 152 from 159 to get 7.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

100 pounds of chocolate is packaged into boxes each containing 1^1/4 pounds of chocolate. Each box is then sold for $1.75. What

sertanlavr [38]

Answer:

$140

Step-by-step explanation:

Total Amount of chocolate = 100 Pounds

Amount of chocolate in one box = 1 1/4 Pounds = 5/4 Pounds

Number of boxes = 100/(5/4) = 80 boxes

Cost of one box = $1.75

Total selling price = 80×1.75 = 140

The total selling price for all the boxes of chocolate is $140

8 0

2 years ago

Read 2 more answers

Which soap deal has the lowest price per ounce?

aleksklad [387]

It is D. look how it skipped oz

6 0

3 years ago

Read 2 more answers

Juan scored 26 points in the first half of the basketball game, and he scored n points in the second half of the game. Write an

astraxan [27]

$Points_{total}=26+n$
$Points_{total}=26+18$
$Points_{total}=44$

7 0

3 years ago

Let f(x) = [infinity] xn n2 n = 1. find the intervals of convergence for f. (enter your answers using interval notation. ) find

inna [77]

Best guess for the function is

$\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}$

By the ratio test, the series converges for

$\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1$

When $x=1$ , $f(x)$ is a convergent $p$ -series.

When $x=-1$ , $f(x)$ is a convergent alternating series.

So, the interval of convergence for $f(x)$ is the closed interval $\boxed{-1 \le x \le 1}$ .

The derivative of $f$ is the series

$\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n$

which also converges for $|x|$ by the ratio test:

$\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1$

When $x=1$ , $f'(x)$ becomes the divergent harmonic series.

When $x=-1$ , $f'(x)$ is a convergent alternating series.

The interval of convergence for $f'(x)$ is then the closed-open interval $\boxed{-1 \le x < 1}$ .

Differentiating $f$ once more gives the series

$\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)$

The first series is geometric and converges for $|x|$ , endpoints not included.

The second series is $f'(x)$ , which we know converges for $-1\le x$ .

Putting these intervals together, we see that $f''(x)$ converges only on the open interval $\boxed{-1 < x < 1}$ .

6 0

2 years ago