It takes Sam half an hour to design a tower on

Triangle D E F is shown. The length of E F is 10, the length of D F is 7, and the length of D E is 12. What information relevant

Zarrin [17]

Answer:

34.98 square units.

Step-by-step explanation:

It is given that DEF is a triangle, EF=10, DF=7 and DE=12.

Information of sides of triangle is relevant to calculating area.

We should use Heron's formula.

According to Heron's formula, the area of triangle is

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where,

$s=\dfrac{a+b+c}{2}$

For triangle DEF, let a=10, b=7 and c=12.

Now,

$s=\dfrac{10+7+12}{2}=\dfrac{29}{2}=14.5$

Area of triangle is

$A=\sqrt{14.5(14.5-10)(14.5-7)(14.5-12)}$

$A=\sqrt{14.5(4.5)(7.5)(2.5)}$

$A=\sqrt{1223.4375}$

$A=34.977671$

$A\approx 34.98$

Therefore, the area of triangle DEF is 34.98 square units.

8 0

4 years ago

Read 2 more answers

I found the interval of convergence, but I am not sure how to do the second part, finding the sum of the series as a function of

antiseptic1488 [7]

The given series is geometric with common ratio $6^x - 9$ , which converges if $|6^x - 9|$ (i.e. the interval of convergence). We have the well-known result

$\displaystyle |r| < 1 \implies \sum_{n=0}^\infty ar^n = \frac{a}{1-r}$

If you're not familiar with that result, it's easy to reproduce.

Let $S_N$ be the $N$ -th partial sum of the infinite series,

$\displaystyle S_N = \sum_{n=0}^N \left(6^x - 9\right)^n = 1 + \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \cdots + \left(6^x - 9\right)^N$

Multiply both sides by the ratio.

$\left(6^x - 9\right) S_N = \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \left(6^x - 9\right)^3 + \cdots + \left(6^x - 9\right)^{N+1}$

Subtract this from $S_N$ to eliminate all the powers of the ratio between 0 and $N+1$ .

$\left(1 - \left(6^x - 9\right)\right) S_N = 1 - \left(6^x - 9\right)^{N+1}$

Solve for $S_N$ .

$S_N = \dfrac{1 - \left(6^x - 9\right)^{N+1}}{10-6^x}$

Now as $N\to\infty$ , the exponential term converges to 0 and we're left with

$\displaystyle \sum_{n=0}^\infty \left(6^x-9\right)^n = \lim_{N\to\infty} S_N = \boxed{\frac1{10-6^x}}$

7 0

2 years ago

In finding the product of (x+2) (x+3) using the FOIL METHOD, what is the LAST step? *

klemol [59]

Answer:

Last step of FOIL: Multiply 2 from the first binomial with 3 from the second binomial.

simplify: a? should be 25x^(6)y^(6)

Step-by-step explanation

6 0

3 years ago

I need help with my final study guide

Citrus2011 [14]

21) Since all angles = 180,
180=66 + 79 + (43 + x)
Subtract (66 + 79) from both sides, you’d get
35= 43 + x
subtract 43 from both sides and x = -8

6 0

3 years ago

Sonia is buying presents for her 3 younger brothers she wants each boy to have 4 toys how many toys will she need to buy .

otez555 [7]

Answer:

12

Step-by-step explanation:

she has 3 brothers times 4 toys.

6 0

3 years ago

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