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3 years ago

Someone help me answer this one

Mathematics

1 answer:

Verdich [7]3 years ago

6 0

Hey again...
So the first angle is angle C.
The first side is FC
and the second side is CG.
There you go and hope this helps!

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + se

sertanlavr [38]

Answer:

The volume of the solid is: $\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

Step-by-step explanation:

GIven that :

$y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2$

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid can be calculated as follows:

$V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx$

$V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ]$

$\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}$

7 0

3 years ago

In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third side, AB o

Luden [163]

You can use the Pythagorean Theorem to find the length of the third side AB (Identified as "x" in the figure attached in the problem), which says that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
a² = b²+c²
As we can see the figure, the triangle does not have an angle of 90°, but it can be divided into two equal parts, leaving two triangles with a right angle. We already have the values of the hypotenuse and a leg in triangle "A" , so we can find the value of the other leg:
b = √(a²-c²) b = √(10²-4²) b = 9.16
With these values, we can find the hypotenuse in the triangle "B": x = √b²+c² x = √(9.16)²+(4)² x = 10

3 0

3 years ago

Read 2 more answers

Li can walk 2 miles in 45 minutes.At that rate,how far can she walk in 135 minuets.

Zielflug [23.3K]

Li can walk 6 miles. if you divide 135 and 45, you'll get 3. finally, if you multiply 2 and 3, you'll get 6. So, in total, Li walks 6 miles.

8 0

3 years ago

Bill Baxter has 28,000 to invest for a year. You can lend it to a sister who has agreed to pay 8% simple interest for the year.

Firdavs [7]

Answer: Additional interest of $521.82 with a simple interest loan to sister generate.

Step-by-step explanation:

Since we have given that

Principal = $28000

Rate of interest at simple interest = 8%

Number of year = 1

so, Interest becomes,

$\dfrac{28000\times 8\times 1}{100}\\\\=280\times 8\\\\=\$2240$

Rate of interest compounded quarterly = 6%

Amount becomes,

$A=P(1+\dfrac{r}{400})^{4n}\\\\A=28000(1+\dfrac{6}{400})^4\\\\A=28000(\dfrac{406}{400})^4\\\\A=\$29718.18$

So, Interest would be

$Amount-Principal\\\\=29718.18-28000\\\\=\$1718.18$

Hence, Additional interest is given by

$2240-1718.18\\\\=\$521.82$

Hence, Additional interest of $521.82 with a simple interest loan to sister generate.

4 0

3 years ago

When x = 1 ; (1) - y = 1

ioda

I don't speak the language; I'm not even sure what language that is. I went to Indonesia in 1991 but all I can say now is "saya mau beli mango."

But math is math. It says "graf"; this is probably making a table to help draw the graph.

It looks like the curve we're trying to graph is

$x - y = 2$

That's

$y = x - 2$

That's a fairly straightforward table to make; unfortunately our first entry isn't consistent with the above equation. I'll assume the equation is correct and make a vertical table; that's easier to type:

x y (x,y)

0 -2 (0,-2)

1 -1 (1,-1)

2 0 (2,0)

3 1 (3,1)

4 2 (4,2)

5 3 (5,3)

3 0

3 years ago