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2 years ago

The area of a circle is 30.85cm2. Find the length of the radius rounded to 2 DP

Mathematics

1 answer:

Alex17521 [72]2 years ago

4 0

Answer: 3.13

Step-by-step explanation:

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Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783, which equation could be used to fi

stepladder [879]

(2x+1)=Jeremy´s age
(2x+3)=Sam´s age.
we suggest this equation:
(2x+1)(2x+3)=783
4x²+6x+2x+3=783
4x²+8x-780=0
x²+2x-195=0

We solve this quadratic equation:
x=[-2⁺₋√(4-4*1*(-195))]/2=(-2⁺₋28)/2

x₁=(-2-28)/2=-15 this solution is not valid.
x₂=(-2+28)/2=13

Jeremy´s age=2x+1=2*13+1=27
Sam´s age=2x+3=2*13+3=29

7 0

3 years ago

Factor the trinomial 5x^2-x-4

LenaWriter [7]

Answer:

Step-by-step explanation:

$5x^2-x-4\\\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(5x^2+4x\right)+\left(-5x-4\right)\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}5x^2+4x\mathrm{:\quad }x\left(5x+4\right)\\\mathrm{Factor\:out\:}-1\mathrm{\:from\:}-5x-4\mathrm{:\quad }-\left(5x+4\right)\\\\=x\left(5x+4\right)-\left(5x+4\right)\\\\\mathrm{Factor\:out\:common\:term\:}5x+4\\=\left(5x+4\right)\left(x-1\right)$

6 0

3 years ago

Read 2 more answers

a) What is an alternating series? An alternating series is a whose terms are__________ . (b) Under what conditions does an alter

andriy [413]

Answer:

a) An alternating series is a whose terms are alternately positive and negative

b) An alternating series $\sum_{n=1}^{\infty} a_n = \sum_{n=1}^{\infty} (-1)^{n-1} b_n$ where bn = |an|, converges if $0< b_{n+1} \leq b_n$ for all n, and $\lim_{n \to \infty} b_n =$ 0

c) The error involved in using the partial sum sn as an approximation to the total sum s is the remainder Rn = s − sn and the size of the error is bn + 1

Step-by-step explanation:

Part a

An Alternating series is an infinite series given on these three possible general forms given by:

$\sum_{n=0}^{\infty} (-1)^{n} b_n$

$\sum_{n=0}^{\infty} (-1)^{n+1} b_n$

$\sum_{n=0}^{\infty} (-1)^{n-1} b_n$

For all $a_n >0, \forall n$

The initial counter can be n=0 or n =1. Based on the pattern of the series the signs of the general terms alternately positive and negative.

Part b

An alternating series $\sum_{n=1}^{\infty} a_n = \sum_{n=1}^{\infty} (-1)^{n-1} b_n$ where bn = |an| converges if $0< b_{n+1} \leq b_n$ for all n and $\lim_{n \to \infty} b_n$ =0

Is necessary that limit when n tends to infinity for the nth term of bn converges to 0, because this is one of two conditions in order to an alternate series converges, the two conditions are given by the following theorem:

Theorem (Alternating series test)

If a sequence of positive terms {bn} is monotonically decreasing and

$\lim_{n \to \infty} b_n = 0$ , then the alternating series $\sum (-1)^{n-1} b_n$ converges if:

i) $0 \leq b_{n+1} \leq b_n \forall n$

ii) $\lim_{n \to \infty} b_n = 0$

then $\sum_{n=1}^{\infty}(-1)^{n-1} b_n$ converges

Proof

For this proof we just need to consider the sum for a subsequence of even partial sums. We will see that the subsequence is monotonically increasing. And by the monotonic sequence theorem the limit for this subsquence when we approach to infinity is a defined term, let's say, s. So then the we have a bound and then

$|s_n -s| < \epsilon$ for all n, and that implies that the series converges to a value, s.

And this complete the proof.

Part c

An important term is the partial sum of a series and that is defined as the sum of the first n terms in the series

By definition the Remainder of a Series is The difference between the nth partial sum and the sum of a series, on this form:

Rn = s - sn

Where $s_n$ represent the partial sum for the series and s the total for the sum.

Is important to notice that the size of the error is at most $b_{n+1}$ by the following theorem:

Theorem (Alternating series sum estimation)

If $\sum (-1)^{n-1} b_n$ is the sum of an alternating series that satisfies

i) $0 \leq b_{n+1} \leq b_n \forall n$

ii) $\lim_{n \to \infty} b_n = 0$

Then then $\mid s - s_n \mid \leq b_{n+1}$

Proof

In the proof of the alternating series test, and we analyze the subsequence, s we will notice that are monotonically decreasing. So then based on this the sequence of partial sums sn oscillates around s so that the sum s always lies between any two consecutive partial sums sn and sn+1.

$\mid{s -s_n} \mid \leq \mid{s_{n+1} -s_n}\mid = b_{n+1}$

And this complete the proof.

5 0

3 years ago

Which equation has no solution?

vitfil [10]

The second option

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8 0

2 years ago

You are remodeling your bedroom. You will paint all 4 walls and the door. There are no windows in the room. The floor is 9' by 1

Aleksandr [31]

Answer:

Part 1) The area of the 4 walls is $368\ ft^2$

Part 2) You will have to buy 2 gallons

Part 3) You will have to buy 3 gallons

Part 4) $\$75$

Part 5) The area of the floor is $126\ ft^2$

Part 6) $\$850.5$

Part 7) $\$1,008$

Part 8) $\$472.5$

Step-by-step explanation:

Part 1) What is the area of all 4 walls together?

we know that

The area of all 4 walls together is equal to the perimeter of the floor multiplied by the height of the wall (8 ft)

The perimeter of the floor is

$P=2(9+14)=46\ ft$

The area of the walls is

$46(8)=368\ ft^2$

Part 2) If a gallon of paint covers 350 sq. ft., How many gallons will you have to buy?

using proportion

$\frac{1}{350}\ \frac{gal}{ft^2}=\frac{x}{368}\ \frac{gal}{ft^2}\\\\x=368/350\\\\x=1.05\ gal$

Remember that you can't buy a fraction of gallon

You will have to buy 2 gallons

Part 3) How many gallons will it take to put on 2 coats of paint?

Now the area will be

$368(2)=736\ ft^2$

using proportion

$\frac{1}{350}\ \frac{gal}{ft^2}=\frac{x}{736}\ \frac{gal}{ft^2}\\\\x=736/350\\\\x=2.10\ gal$

Remember that you can't buy a fraction of gallon

You will have to buy 3 gallons

Part 4) If the paint costs $25 per gallon, and you are applying 2 coats of paint, how much will you spend on paint?

To find the cost multiply the number of gallons by $25 per gallon

$3(25)=\$75$

Part 5) What is the area of the floor?

The area of the floor (rectangle ) is equal to multiply the length of the floor by the width of the floor

$A=(9)(14)=126\ ft^2$

Part 6) What is the cost to redo the floor in oak?

To find the cost multiply the area of the floor by $6.75 per square foot

$126(6.75)=\$850.5$

Part 7) What is the cost to redo the floor in maple?

To find the cost multiply the area of the floor by $8.00 per square foot

$126(8.00)=\$1,008$

Part 8) What is the cost to redo the floor in carpet?

To find the cost multiply the area of the floor by $3.75 per square foot

$126(3.75)=\$472.5$

5 0

3 years ago