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2 years ago

What is the value of c? ______ units

Mathematics

2 answers:

Shalnov [3]2 years ago

8 0

The answer is 5, C = 5 units.

AnnyKZ [126]2 years ago

8 0

Answer:

The value of c is 5 units.

Step-by-step explanation:

Now by using the pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

As in Δ WYZ.

WZ² = ZY² + WY²

Hypotenuse = WZ = c

Perpendicular = WY = 4 units

Base = ZY = 3 units

Put in the above

c² = 4² + 3²

c² = 16 + 9

c² = 25

$c = \sqrt{25}$

c = 5 units

Therefore the value of c is 5 units.

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Lisa paid 43.95 for 16.1 gallon of gasoline. What was that cost per gallon rounded to the nearest hundredth

djverab [1.8K]

Answer:

2.73

Step-by-step explanation:

It is given that Lisa paid 43.95 for 16.1 gallons of gasoline.

So, the cost of 16.1 gallons of gasoline is 43.95.

Hence, the cost of gasoline per gallon is 43.95/16.1 = 2.7304347.

Now, it is required to round this value to the nearest hundredth.

Therefore, the cost of gasoline per gallon rounded to the nearest hundredth is 2.73. (Answer)

3 0

3 years ago

Can someone please help me in this question

Pie

Step-by-step explanation:

a) Let y = f(x) = 3x - 2x^2

f(-2) = 3(-2) - 2(-2)^2 = p

= -6 - 8

= -14

= p

f(2.5) = 3(2.5) - 2(2.5)^2 = q

= 7.5 - 12.5

= -5

= q

b) graphing

c) From the graph, you should be able to verify the following:

i) f(0.5) = 3(0.5) - 2(0.5)^2 = 1

ii) 0.5 = 3x - 2x^2 or x = 1.3, 0.2

iii) the maximum occurs at

f(0.75) = 1.125

d) the equation for the line of symmetry is x = 0.75

4 0

2 years ago

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

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Write 0.00605 in scientific notation.

vichka [17]

How many jumps is it from the decimal point to the position to the right of the 6

The answer to that is 3 jumps. Since the move of the decimal made the number larger than it really is, it will take a negative value to put it back where it belongs.

So A) is the correct answer. It is in scientific notation and if you move the decimal back 3 place you get the number you stared with.

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3 years ago

The sum of the ages of two siblings is 29. The brother is eleven more than half the age of his sister. How old is each sibling

mina [271]

Answer: the brother is 20 and the sister is 9

Step-by-step explanation:

29 - 11 = 18 18 divided by 2 is 9

9+11 is 20 the brothers age so the sister is 9

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2 years ago

Read 2 more answers