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3 years ago

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Carlson's wheelbarrow can hold 460 pounds. if he has 187 pounds of rocks in the wheelbarrow, what number of pounds, p, can he pu

t in the wheelbarrow without going over the weight limit?
PLEASE HELP ME!!!.

1 answer:

Rudik [331]3 years ago

8 0

Step-by-step explanation:

i think you just have to subtract 460-187 equals 273 so he can put 273 or something lower then that

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The sum of the first n terms of an arithmetic series is n/2(3n-5). If the second and fourth terms of the arithmetic series are t

sergiy2304 [10]

Let <em>a</em> be the first term in the arithmetic sequence. Since it's arithmetic, consecutive terms in the sequence differ by a constant <em>d</em>, so the sequence is

<em>a</em>, <em>a</em> + <em>d</em>, <em>a</em> + 2<em>d</em>, <em>a</em> + 3<em>d</em>, …

with the <em>n</em>-th term, <em>a</em> + (<em>n</em> - 1)<em>d</em>.

The sum of the first <em>n</em> terms of this sequence is given:

$a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n(3n-5)}2$

We can simplify the left side as

$\displaystyle \sum_{i=1}^n (a+(i-1)d) = (a-d)\sum_{i=1}^n1 + d\sum_{i=1}^ni = an+\dfrac{dn(n-1)}2$

so that

$an+\dfrac{dn(n-1)}2 = \dfrac{n(3n-5)}2$

or

$a+\dfrac{d(n-1)}2 = \dfrac{3n-5}2$

Let <em>b</em> be the first term in the geometric sequence. Consecutive terms in this sequence are scaled by a fixed factor <em>r</em>, so the sequence is

<em>b</em>, <em>br</em>, <em>br</em> ², <em>br</em> ³, …

with <em>n</em>-th term <em>br</em> ⁿ⁻¹.

The second arithmetic term is equal to the second geometric term, and the fourth arithmetic term is equal to the third geometric term, so

$\begin{cases}a+d = br \\\\ a+3d = br^2\end{cases}$

and it follows that

$\dfrac{br^2}{br} = r = \dfrac{a+3d}{a+d}$

From the earlier result, we then have

$n=7 \implies a+\dfrac{d(7-1)}2 = a+3d = \dfrac{3\cdot7-5}2 = 8$

and

$n=2 \implies a+\dfrac{d(2-1)}2 = a+d = \dfrac{3\cdot2-5}2 = \dfrac12$

so that

$r = \dfrac8{\frac12} = 16$

and since the second arithmetic and geometric terms are both 1/2, this means that

$br=16b=\dfrac12 \implies b = \dfrac1{32}$

The sum of the first 11 terms of the geometric sequence is

<em>S</em> = <em>b</em> + <em>br</em> + <em>br</em> ² + … + <em>br</em> ¹⁰

Multiply both sides by <em>r</em> :

<em>rS</em> = <em>br</em> + <em>br</em> ² + <em>br</em> ³ + … + <em>br</em> ¹¹

Subtract this from <em>S</em>, then solve for <em>S</em> :

<em>S</em> - <em>rS</em> = <em>b</em> - <em>br</em> ¹¹

(1 - <em>r</em> ) <em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹)

<em>S</em> = <em>b</em> (1 - <em>r</em> ¹¹) / (1 - <em>r</em> )

Plug in <em>b</em> = 1/32 and <em>r</em> = 1/2 to get the sum :

$S = \dfrac1{32}\cdot\dfrac{1-\dfrac1{2^{11}}}{1-\dfrac12} = \boxed{\dfrac{2047}{32768}}$

6 0

3 years ago

$15,074 is invested, part at 14% and the rest at 5%. If the interest earned from the amount invested at 14% exceeds the interest

Flauer [41]

The rate at 14% and 5% are $12, 883 and $2191 respectively.

<h3>How to determine the rate</h3>

Given that;

Invested amount = $ 15, 074 at 14% and 5%

Let rate at 14% = x

rate at 5% = y

We have rate at 9% exceeds that of 5% by $1694. 07

Hence,

0. 14x = 0. 05y + $1694. 07 ⇒ equation 1

x + y = $15, 074 ⇒ equation 2

Make 'x' the subject

x = $15, 074 - y$

Substitute in equation 2

$0. 14(15, 074 - y) = 0. 05y + $1694. 07$

Expand the expression

$2, 110. 36 - 0. 14y = 0.05y + 1694. 07$

Collect like terms

$416. 29 = 0. 19y$

Make 'y' the subject

y = $\frac{416. 29}{0. 19}$

y = $$2, 191$

Substitute the value in equation 2

x + y = $15, 074

x = $15, 074 - y

x = $$15, 074 - 2191$

x = $12, 883

Therefore , the rate at 14% and 5% are $12, 883 and $2191 respectively.

Learn more about simultaneous equations here:

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4 0

2 years ago

Answer choices :<br> A-90<br> B-360

vladimir1956 [14]

Answer:

Step-by-step explanation:

Re-read

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3 years ago

There are 283 students and Wiley school and 59 of them are in the sixth grade. What is the approximate percent of six graders at

Paladinen [302]

20% are in 6th grade

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3 years ago

Read 2 more answers

Find the area of the following shape:

lara31 [8.8K]

9514 1404 393

Answer:

77 in²

Step-by-step explanation:

The area of a triangle is given by the formula ...

A = (1/2)bh

For your triangle, with its base of 14 inches and height of 11 inches, the area is ...

A (1/2)(14 in)(11 in) = 77 in²

_____

<em>Additional comment</em>

The side lengths added to the figure are incorrect. If we take the 11.5 to be correct, then the left side is about 15.3.

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3 years ago