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3 years ago

What is the distance between P(0,4) and Q(3,0)

Mathematics

2 answers:

igor_vitrenko [27]3 years ago

6 0

Plot this out on a graph and you'll get your answer of 5.

bixtya [17]3 years ago

4 0

Hey!
The distance formula is the:
$\sqrt{(x_2}- x_{1})^2 + {(y_2}- y_{1})^2$
so 3-0 is 3 and squared is 9
0-4 is -4 and squared it is 16
add those and you get 25
the square root of 25 is 5
5 is the distance
Hope this helps!

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What is the length of the missing leg?

Crank

Answer:

$a=\sqrt{609}\\\\a\approx 24.67793$

Step-by-step explanation:

To solve for the leg of the missing right triangle, one must use the Pythagorean theorem. The Pythagorean theorem states the following,

$a^2+b^2=c^2$

Where (a) and (b) are the sides adjacent to or next to the right angle. (c) is the side opposite the right angle. Substitute in the given values and solve for the unknown,

$a^2+b^2=c^2\\$

Substitute,

$a^2+40^2=47^2\\$

Simplify,

$a^2+1600=2209\\$

Inverse operations,

$a^2=609$

$a=\sqrt{609}\\\\a\approx 24.67793$

8 0

3 years ago

Read 2 more answers

Verify cot x sec^4x=cotx +2tanx +tan^3x

Tanzania [10]

Answer:

See explanation

Step-by-step explanation:

We want to verify that:

$\cot(x) \: { \sec}^{4} x = \cot(x) + 2 \tan(x) + { \tan}^{3} x$

Verifying from left, we have

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { \tan}^{2} x )^{2}$

Expand the perfect square in the right:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { 2\tan}^{2} x + { \tan}^{4} x)$

We expand to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + \cot(x){ 2\tan}^{2} x +\cot(x) { \tan}^{4} x$

We simplify to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + 2 \frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{2} x}{{ \cos}^{2} x} +\frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{4} x}{{ \cos}^{4} x}$

Cancel common factors:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + 2 \frac{{ \sin}x}{{ \cos}x} +\frac{{ \sin}^{3} x}{{ \cos}^{3} x}$

This finally gives:

$\cot(x) \: { \sec}^{4} x = \cot(x) + 2 \tan(x) + { \tan}^{3} x$

3 0

3 years ago

Suppose a population of honey bees in Ephraim, UT has an initial population of 2300 and 12 years later the population reaches 13

Rama09 [41]

Answer:

common ratio: 1.155

rate of growth: 15.5 %

Step-by-step explanation:

The model for exponential growth of population P looks like: $P(t)=P_i(1+r)^t$

where $P(t)$ is the population at time "t",

$P_i$ is the initial (starting) population

$(1+r)$ is the common ratio,

and $r$ is the rate of growth

Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:

$P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\$

This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155

We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:

$1+r=1.155273\\r=1.155273-1=0.155273$

So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %

6 0

3 years ago

Yoki is running a 10-mile race. She runs at a steady speed and then slows down, stops to get a drink of water, and

kondor19780726 [428]

Do you have any pictures to choose from anything to show what im looking at?

4 0

3 years ago

Read 2 more answers

Darius counted that he walks 864 steps from his house to the bookstore. If Darius takes 52 steps each minute, about how long wil

MakcuM [25]

Answer:

It would take him approximately 16.62 minutes to reach the bookstore

Step-by-step explanation:

Total steps to the bookstore=Number of steps per minute×number of minutes

where;

Total steps to the bookstore=864 steps

Number of steps per minute=52

Number of minutes=t

Replacing;

864=52×t

t=864/52

t=16.62 minutes

It would take him approximately 16.62 minutes to reach the bookstore

3 0

3 years ago