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2 years ago

5-1.

Mathematics

1 answer:

liq [111]2 years ago

6 0

Answer:

If you mean y = 4x + 5, then the answer is 5 (the height would be 5 feet)

Step-by-step explanation:

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Rewrite the parametric equations by eliminating the parameter:

Elodia [21]

I believe the answer is c. I hope that’s right! Good luck!

6 0

3 years ago

Read 2 more answers

Factor please.<br> m^2 - 64n^2

rewona [7]

Answer:

(n - 8n)(m+8n)

Step-by-step explanation:

x² - y² = (x - y)(x + y)

In this situation, the "x" = m and the "y" = 8n

So,

m² - 64n² = (n - 8n)(m+8n)

5 0

2 years ago

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Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

2 years ago

PLEASE HELP QUICKLY!!! A student's parents offer him one of two options to receive scholarship money for college.

emmainna [20.7K]

Answer:

A = $47,500.00, B = $65,536.00; B, because he receives $18,036.00 more

Step-by-step explanation:

Option A Versus Option B

Option A Option B

Day Amount Deposited Day Amount Deposited

0 $40,000.00 0 $1.00

1 $40,250.00 1 $2.00

2 $40,500.00 2 $4.00

...

30 $47,500 16 $65,536.00

Answer:

A = $47,500.00, B = $65,536.00; B, because he receives $18,036.00 more

7 0

2 years ago

The numerator of a given fraction is 4 less than the denominator. if 3 is subtracted from the numerator and 5 is added to the de

Sergeu [11.5K]

Answer:

Step-by-step explanation:Given that the numerator of a given fraction is 4 less than its denominator.

Also given that 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth .

Let the fraction be

Since the numerator of a given fraction is 4 less than its denominator we have,

Numerator=Denominator-4

⇒ a=b-4

Since 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth we have

4(a-3)=1(b+5)

4a-12=b+5

4a-b=17

4(b-4)-b=17 ( ∵ a=b-4)

4b-16-b=17

3b=17+16

3b=33

⇒ b=11

Now put b=11 in a=b-4 we get

a=11-4

⇒ the fraction is a/b=7/11

3 0

2 years ago