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3 years ago

Their are 40 coin of dimes and quaters and they make $4.90 how much of each coin is their

1 answer:

8 0

1 dime = 10 cents
1 quarter = 25 cents

$4.90 = 490 cents

let q = quaters
let d = dimes

d + q = 40 ----- equation 1
10d + 25q = 490 ----- equation 2

10d+ 10q = 400 ---- equation 1 multiplied by 10
10d + 25q = 490 ---- equation 2 multiplied by 1

-15q = -90
q = 90/15
q = 6

plug q into any one of the equations

d + q = 40
d + 6 = 40
d = 40 - 6
d = 34

34 dimes and 6 quaters

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Find the slope of the line that passes through the two given points:

elixir [45]

Answer:

$\frac{ - 1}{6}$

Step-by-step explanation:

$slope \: = \frac{y2 - y2}{x2 - x1} \\ slope = \frac{3 - 4}{5 - - 1} \\ sope = \frac{ - 1}{ \: \: \: 6}$

4 0

2 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

4 years ago

What is 19 × 10 I need help please

AleksAgata [21]

It's 190 it's easy bro

3 0

3 years ago

Read 2 more answers

Jamarie owns a tomato farm. Each season, she collects about 3,500 tomatoes. This can vary by as many as 425. What is the maximum

olga55 [171]

Answer:

max: 3,925

min: 3,075

Step-by-step explanation:

3,500-425=3,075 minimum

3,500+425=3,925 maximum

3 0

3 years ago

An arc on a circle measures 295Â°. The measure of the central angle

marishachu [46]

Answer:

59/36π

Step-by-step explanation:

We know that an angle is measured in either degrees or radians and The arc's angle measurement, taken at the center of the circle the arc is part of, is measured in degrees (or radians)

Let's convert 90 degrees into radians

295Â° = 295 * π/180 = 59/36π

4 0

3 years ago