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3 years ago

Point S is on line segment RT given ST=3x-8, RT = 4x, and RS = 4x - 7, determine the numerical length of RT

Mathematics

1 answer:

seraphim [82]3 years ago

8 0

Answer:

Step-by-step explanation:

Segment ST is half and RS is the other half. RT is the whole line so adding ST and RS will get you RT. 4x-7+3x-8=4x. solve for x which will get you 5. Replace the x with 5 in 4x (for segment RT) will get you an answer of 20 for the whole line.

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A lift driver charges $5.25 for the first mile of the trip and$1.25 each mile after that. He charges the customer $24 for the ri

WARRIOR [948]

Answer: 15 miles

Step-by-step explanation:

The equation is 5.25+1.25x=24 where x is each additional mile so to solve for x it would be 1.25x=18.75 and divide both sides to solve for x

3 0

3 years ago

Read 2 more answers

I'm having trouble with #2. I've got it down to the part where it would be the integral of 5cos^3(pheta)/sin(pheta). I'm not sur

Butoxors [25]

$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

Setting $x=5\sin\theta$ , you have $\mathrm dx=5\cos\theta\,\mathrm d\theta$ . Then the integral becomes

$\displaystyle\int\frac{\sqrt{25-(5\sin\theta)^2}}{5\sin\theta}5\cos\theta\,\mathrm d\theta$
$\displaystyle\int\sqrt{25-25\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{1-\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

Now, $\sqrt{x^2}=|x|$ in general. But since we want our substitution $x=5\sin\theta$ to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means $\theta=\sin^{-1}\dfrac x5$ , which implies that $\left|\dfrac x5\right|\le1$ , or equivalently that $|\theta|\le\dfrac\pi2$ . Over this domain, $\cos\theta\ge0$ , so $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

Long story short, this allows us to go from

$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

to

$\displaystyle5\int\cos\theta\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\dfrac{\cos^2\theta}{\sin\theta}\,\mathrm d\theta$

Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

$\dfrac{\cos^2\theta}{\sin\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}=\csc\theta-\sin\theta$

Then integrate term-by-term to get

$\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)$
$=-5\ln|\csc\theta+\cot\theta|+\cos\theta+C$

Now undo the substitution to get the antiderivative back in terms of $x$ .

$=-5\ln\left|\csc\left(\sin^{-1}\dfrac x5\right)+\cot\left(\sin^{-1}\dfrac x5\right)\right|+\cos\left(\sin^{-1}\dfrac x5\right)+C$

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

$=-5\ln\left|\dfrac{5+\sqrt{25-x^2}}x\right|+\sqrt{25-x^2}+C$

4 0

2 years ago

Read 2 more answers

What is 5/8 times 1/2times

konstantin123 [22]

5/16

this is the fraction

You choose

6 0

3 years ago

Someone help me asap pls

Makovka662 [10]

Answer:

For the graph in the top-left corner, the ?? = 0.25

This can be found using a simple slope equation:

m = (y2-y1)/(x2-x1)

m = slope

You take two coordinates, in this case (8, 2) and (4, 1), label one as #1 and the other as #2, and plug in the values so:

slope = (2-1)/(8-4)

slope = 1/4 or 0.25

The equation of a line is y = mx + b and if you were to place 0.25, or 1/4, in place of m (the slope) and 1 in the place of x since it is the x value, and multiply, you would end up with 0.25.

This also gives you the answer to your next two questions.

The one in the top-right corner is $0.25 per pencil.

The answer to the question just below it is y = 0.25x.

b in the equation would equal 0 since b is the y-intercept (where the line crosses the y-axis)

As for the last one, you simply have to multiply 30 by each number in the left column since you already know 30 miles are travelled in 1 hour, giving you your rate or the equation of the line, y=x.

The missing values of the table are as follows:

0, 60, 150, 240, 330, 1470

Finally, the last box:

Miles = 30 * hours

y = 30x

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3 years ago

Find the value of each variable and show which property is used.

mojhsa [17]

7y-2=5y+4
+2 +2
__________
7y= 5y + 6
-5y -5y
__________
2y= 6

Y=3

3x+2=23
3x =21
x= 7

7(3) -2= 5(3)+4
19=19
x=19

3(7)+2=23
23= 23
Y=23

Adding and subtracting property

6 0

3 years ago