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2 years ago

12

he length of the base of an isosceles triangle is x. The length of a leg is 4xminus2. The perimeter of the triangle is 50. Find

x.

1 answer:

Effectus [21]2 years ago

8 0

Answer:

10.4

Step-by-step explanation:

x+4x-2=50

5x-2=50

5x=52

x=52/5 or 10.4

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Find the sum of the first 25 terms in this geometric series:<br> 8 + 6 + 4.5...

Ksivusya [100]

Step-by-step explanation:

Given the geometric sequence

8 + 6 + 4.5...

A geometric sequence has a constant ratio and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=\frac{3}{4}$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=8$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=8\left(\frac{3}{4}\right)^{n-1}$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}$

$=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}$

$=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$

$=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32$

$=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}$

$=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}$ ∵ $\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}$

$=32\cdot \frac{4^{25}-3^{25}}{4^{25}}$

$=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}$

$=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}$ ∵ $\mathrm{Factor}\:32:\ 2^5$ , $\mathrm{Factor}\:4^{25}:\ 2^{50}$

so

$=\frac{4^{25}-3^{25}}{2^{45}}$ ∵ $\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}$

$=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}$

$=32-\frac{3^{25}}{2^{45}}$ ∵ $\frac{4^{25}}{2^{45}}=32$

$=32-0.024$ ∵ $\frac{3^{25}}{2^{45}}=0.024$

$=31.98$

Therefore, the sum of the first 25 terms in this geometric series: 31.98

3 0

3 years ago

If f is a continuous function such that the integral from 1 to 4 of f of x, dx equals 10, evaluate the integral from 2 to 8 of 2

IgorLugansk [536]

Answer: 10

Step-by-step explanation:

Since integral from 1 to 4 of f(x) =10

To evaluate integral from 2 to 8 of 2 times f(2x), using substitution method

Let U = 2x, dU = 2dx, dx = dU/2

Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.

Since this limit are the same as the limit for the question,

Therefore, F(4) - F(1) = F(8) - F(2) = 10

Substituting dx=dU/2

Gives,

Integral from 2 to 8 of 2 times f(2x)= (1/2)(2)(F(8)-F(2)) = 10

6 0

2 years ago

Round 35.45 to the nearest whole number

AVprozaik [17]

35.45 rounded to the nearest whole number would be 35.

5 0

2 years ago

Read 2 more answers

The nth term of a sequence is 60-8n. Find the largest number in this sequence.

natka813 [3]

Answer:

52

Step-by-step explanation:

1st term is =60-8=52

a2=60-16=44

a3=60-24=36

a4=60-32=28

a5=60-40=20

a6=60-48=12

....

sI the terms are 52,44,36,28, 20,12,4,-4,-12....

so the largest term is 52

6 0

2 years ago

Look at the model below which are true

OLga [1]

3(2+x)

open the parenthesis

= 6 + 3x

3(2+x) = 6 + 3x

Hence the statement of equality is true

H is the correct option

6 0

9 months ago