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2 years ago

PLEASE HELP, WILL MARK BRAINLIEST

Mathematics

1 answer:

Advocard [28]2 years ago

5 0

Answer:

A, B, D

Step-by-step explanation:

25% of 37

= 25/100 × 37

= 1/4 × 37

= 0.25 × 37

= 9.25

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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

Gregory’s age is 5 years greater than of Amanda’s age. Gregory is 17 years old. If Amanda’s age is denoted by x, which equation

Mariana [72]

Let Amanda's age = x.
Gregory's age = x + 5.

Since Gregory is 17 years old.
17 = x + 5
x = 17 - 5
x = 12

Amanda is 12 years old.

4 0

2 years ago

A frame shop owner is working with her apprentice, who takes four times as long as

Lunna [17]

Answer:

1 hour

Step-by-step explanation:

25min=1 poster for the shop owner

25×4=100

100×8=800

800÷25=32 posters in 8hrs for the shop owner

1hr×8=8 posters for the apprentice

thus 40 in total

6 0

3 years ago

Please solve the underlined question thank you!

notsponge [240]

Answer:

Step-by-step explanation:

Take out a 2 to begin with.

2(25x^2 - 36) This is the difference of squares (inside the brackets). Factor.

2*(5x - 6)(5x + 6)

5 0

2 years ago

Read 2 more answers

Help me out yall!!!! I need answers ASAP

Paha777 [63]

Answer:

199

Step-by-step explanation:

Ok, lets do the math, 41,790 is going to be the number we divide by, and than we use 210 to divide it with, meaning the final answer is 199.

5 0

2 years ago