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2 years ago

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

2 answers:

6 0

$\bf \stackrel{A(n)=1+(n-1)(-5.7)}{ \begin{array}{ll} n\qquad \qquad &A(n)\\ \cline{1-2} 1&1+(1-1)(-5.7)\\ &1+0\\ &1\\\\ 4&1+(4-1)(-5.7)\\ &1+(3)(-5.7)\\ &1-17.1\\ &-16.1\\\\ 10&1+(10-1)(-5.7)\\ &1+(9)(-5.7)\\ &1-51.3\\ &-50.3 \end{array} }$

jasenka [17]2 years ago

4 0

1, - 16.1, - 50.3 ← third on list

To find the required terms, substitute n = 1, 4, 10 into the rule and evaluate

A(1) = 1 + (1 - 1)(- 5.7) = 1 + 0 = 1

A(4) = 1 + (4 - 1)(- 5.7 ) = 1 + (3 × - 5.7 ) = 1 - 17.1 = - 16.1

A(10) = 1 + (10 - 1 )(- 5.7) = 1 + (9 × - 5.7) = 1 - 51.3 = - 50.3

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Tasya [4]

Answer:

72 ft

Step-by-step explanation:

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2 years ago

Find the area of the region bounded by the given curves. y = 9x2 ln(x), y = 36 ln(x)

oee [108]

Alrighty
find where they intersect

9x²ln(x)=36ln(x)
divide both sides by 9
x²ln(x)=4ln(x)
$ln(x^{x^2})=ln(x^4)$
so
$x^{x^2}=x^4$
so x=1 and and 2 (x can't be 0 or -2 because ln(0) and ln(-2) don't exist)

so intersect at x=1 and x=2
which is on top?

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36ln(1.5)=36ln(1.5)
36ln(1.5) is on top
so

that will be
the area is
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2 years ago

Please help me! Thanks in advance

Studentka2010 [4]

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2 years ago

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SVETLANKA909090 [29]

Answer:

angle ABC = 30°

Step-by-step explanation:

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6 0

1 year ago

A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

3 0

2 years ago