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zysi [14]
3 years ago
12

Solve for x: −2x − 4 > 8 x < −6 x > −6 x < −2 x > −2

Mathematics
1 answer:
ivann1987 [24]3 years ago
5 0

Step-by-step explanation:

first remove this -4

so add 4 on both side

-2x-4+4>8+4

-2x>12

then remove -2

so divide both side by - 2 if we multiply or divide by negative number so sign will reverse

x<-6

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Answer:

23°

Step-by-step explanation:

Let the missing angle be x

Reference angle = missing angle = x

Opposite side to x = 14

Hypotenuse = 36

Applying trigonometric ratio, we have:

sin(x) = \frac{14}{36}

x = sin^{-1}(\frac{14}{36})

x = 23° (to the nearest degree)

3 0
3 years ago
Find the equation of the line passing<br> through the points (3,-2) and (4, 6).<br> y = [? ]x + [ ]
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Step-by-step explanation:

4 0
3 years ago
a. Calculate the volume of the solid of revolution created by rotating the curve y = 3 + 3 exp(-5 x) about the x-axis, for x bet
miskamm [114]

Answer:

A) The volume of solid is 18π cubic unit.

B) The volume of sphere is \dfrac{4}{3}\pi r^3

    a = -r , b = r , f(x)=\sqrt{r^2-x^2} and V=\dfrac{4}{3}\pi r^3

Solution A)

The given curve, y=3+3e^{-5x} rotate about x-axis between 2 to 4.

Please find attachment for solid figure or rotation.

Using disk method to find the volume rotation about x-axis

V=\int_a^b\pi R^2dx  

where, a = 2, b= 4 , R=y=3+3e^{-5x} and dx is thickness of disk.

V=\int_2^4\pi (3+3e^{-5x})^2dx

V=9\pi\int_2^4(1+e^{-10x}+2e^{-5x})dx

V=9\pi(x-\dfrac{1}{10}e^{-10x}-\dfrac{2}{5}e^{-5x})|_2^4)

V=9\pi(4-\dfrac{1}{10}e^{-40}-\dfrac{2}{5}e^{-20}-2+\dfrac{1}{10}e^{-20}-\dfrac{2}{5}e^{-10}))

V=9\pi (2-0)

V=18\pi

Hence, the volume of solid is 18π cubic unit

Solution B)

The equation of circle of radius r and centered at origin (0,0).

x^2+y^2=r^2

y=\sqrt{r^2-x^2}

The solid form is sphere of radius r.

Using disk method, to find volume of solid

V=\int_a^b\pi R^2dx  

where, a = -r, b = r , R=y=\sqrt{r^2-x^2} and dx is thickness of disk.

V=\int_{-r}^r\pi (r^2-x^2)dx

V=\pi(r^2x-\dfrac{x^3}{3})|_{-r}^r

V=\pi(2r^3-\dfrac{2r^3}{3})

V=\dfrac{4}{3}\pi r^3

Hence, the volume of sphere is \dfrac{4}{3}\pi r^3

4 0
4 years ago
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tekilochka [14]

Answer:

I think Its B

Step-by-step explanation:

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3 years ago
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