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3 years ago

Graph the following. F(x)=4|x+2|-3

Mathematics

1 answer:

liberstina [14]3 years ago

3 0

Answer:

Step-by-step explanation:

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Please help me out! its urgent!

sineoko [7]

Answer:

Step-by-step explanation:

ΔBCA ~ ΔECD ⇒ the corresponding sides are proportional.

$\frac{AC}{DC}$ = $\frac{AB}{DE}$

AC = 4 + 6 = 10 cm

$\frac{10}{6}$ = $\frac{x+5}{x}$ ⇔ 10x = 6(x + 5) ⇒ <em>x = 7.5 cm</em>

5 0

3 years ago

A quantity q varies directly with a quantity p. When q = 42 and p = 21, what is the constant of proportionality

Kay [80]

42 and 21 are constants their numbers

7 0

3 years ago

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

3 years ago

Δ ABC was dilated from point A to get Δ ADE. Find the length of AD given a scale factor of 2.

liraira [26]

Answer:

2x+4

Step-by-step explanation:

if you double the triangle, than the sides double as well meaning you use distributive property to multiply two to each integer.

6 0

3 years ago

How can I solve this problem?

HACTEHA [7]

Answer:

25*pi or

78.5 square units.

Step-by-step explanation:

If there was no shaded area, the area of the circle would be pi * r^2

r = 10

Area = pi * 10^2

Area = 100 * pi

Since there is a shaded area, the shaded part looks to be 1/4 of the whole. There's no indication of what it actually is, but 1/4 should be close enough.

Area_shade = 1/4 (100*pi)

Area_shade = 25 * pi

That's one answer.

Another is 25 * 3.14 = 78.5 square units

7 0

3 years ago