Find the slope of the line that passes through (4.4) and (5,3)

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

7 0

Answer:

- 1

Step-by-step explanation:

Slope of the line

$= \frac{3 - 4}{5 - 4} \\ \\ = \frac{ - 1}{1} \\ \\ = - 1$

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An old-fashioned bicycle has two differently sized wheels. The circumference of the front wheel is 9 feet larger than the circum

Lady_Fox [76]

So, the bicycle looks like the one in the picture below.

now, the circumference of the smaller wheel, will just be C = 2πr, with a radius of "r".

we also know that the large wheel has a circumference that is 9 feet larger than the small one, so, since the small one has a circumference of 2πr, then the large one will have a circumference of 2πr + 9.

after Thomas cycled for a while, the large did 500 revolutions, or times around, whilst the small one did 1400, since it's smaller. On that time, they covered however, the same amount of ground, since they're on the same bike.

The amount covered by the small one in 1400 cycles, is 1400(2πr), that's how much ground it covered.

The amount covered by the large one in 500 cycles, is 500(2πr + 9).

And we know that ground covered, is the same for both, therefore, we also know that 1400(2πr) = 500(2πr + 9).

$\bf \stackrel{small~wheel}{1400(2\pi r)}~~=~~\stackrel{large~wheel}{500(2\pi r+9)}\implies 14(2\pi r)=5(2\pi r+9)
\\\\\\
28\pi r=10\pi r+45\implies 18\pi r=45\implies r=\cfrac{45}{18\pi }
\\\\\\
\boxed{r=\cfrac{5}{2\pi }}$

so, how much ground did they cover anyway?

well, we could use either, since we know what the radius is, hmmmm let's use say the small wheel's circumference,

$\bf 1400(2\pi r)\implies 1400\left(\underline{2\pi }\cdot \cfrac{5}{\underline{2\pi }} \right)\implies 1400(5)\implies \stackrel{feet}{7000}$

8 0

3 years ago

Read 2 more answers

Find f if f ''(x) = 12x2 + 6x − 4, f(0) = 5, and f(1) = 4.

Taya2010 [7]

This is a differential equations problem. We are to work backwards and determine the function f(x) when given f "(x) and initial values.

<span>f ''(x) = 12x^2 + 6x − 4, when integrated with respect to x, yields:

x^3 x^2
f '(x) = 12------ + 6----- - 4x + C, or 4x^3 + 3x^2 - 4x + C, and
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x^4 x^3 x^2
f(x) = 4------- + 3------- - 4------ + Cx + D, or f(x)=x^4 + x^3 - 2x^2 + Cx + D
4 3 2

Now, because f(0)=5, 5=0^4 + 0^3 -2(0)^2 + C(0) + D, so that D=5.
Determine D in the same manner: Let x=1 and find the value of C.

Then the solution, f(x), is x^4 + x^3 - 2x^2 + Cx + 5. Replace C with this value and then you'll have the desired function f(x).</span>

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3 years ago

A states division of motor vehicles claims that 60% of teens pass their drivers test on the first attempt. an investigative repo

____ [38]

Answer: There is convincing evidence at the the significance level that the DMV's claim is incorrect.

Step-by-step explanation:

Since we have given that

Hypothesis:

$H_0:p=0.6\\\\H_a:p\neq 0.6$

Probability of teens pass their drivers test on the first attempt = 60% = 0.60

Number of teens = 125

Number of them passed the tests on their first try = 86

$\hat{p}=\dfrac{86}{125}=0.688$

So, the value of test statistic would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.688-0.60}{\sqrt{\dfrac{0.6\times 0.4}{125}}}\\\\z=\dfrac{0.088}{0.0438}\\\\z=2.009\\\\z\approx 2.01$

At α = 0.05% level of significance, critical value = 1.645

Since 1.645 < 2.01

So, we will reject the null hypothesis.

Hence, there is convincing evidence at the the significance level that the DMV's claim is incorrect.

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3 years ago

An empty cup in the shape of a cylinder is being filled with water . The cup is filled at constant rate . The table below shows

KatRina [158]

<h2>Explanation:</h2><h2></h2>

Hello! Remember you have to write complete questions in order to get good and exact answers. I'll help you to understand this problem, but I have to assume some things.

We know that the empty cup in the shape of a cylinder is being filled with water. Suppose the volume of this cylinder is:

$V=450cm^3$