All categories

3 years ago

1+sec^2xsin^2x=sec^2x

Mathematics

2 answers:

lina2011 [118]3 years ago

5 0

1+sec^2(x)sin^2(x)=sec^2(x)
Then you final answer is 1=1

Sholpan [36]3 years ago

4 0

1 + sec^2(x)sin^2(x) = sec^2(x)
This becomes
1+tan^2(x) = sec^2(x) which is an identity
You could
1 + sin^2(x)/cos^2(x) = sec^2(x)
then
cos^2(x) + sin^2(x) = cos^2(x)sec^2(x)
1 = 1

You might be interested in

Given 4/ (-2 - 6sin(theta)) What type of directrix does this conic have?

atroni [7]

Answer:

a horizontal line

Step-by-step explanation:

The hyperbola opens vertically, so the directrix is a horizontal line (a different one for each branch).

6 0

3 years ago

The letter a represents a nonzero constant. Solve x + a = 3/4<br> for x

sveticcg [70]

x+a=3/4

Move a to the other side. Sign changes from +a to -a.

x+a-a=3/4-a

x=3/4-a or x=-a+3/4

Answer: x=3/4-a or x=-a+3/4

4 0

2 years ago

Read 2 more answers

Find the center and radius of the sphere whose equation is given by x2+y2+z2−2x−4y+8z+17=0x2+y2+z2−2x−4y+8z+17=0.

Vedmedyk [2.9K]

We know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²
where (h,k,l) is the center and r is the radius

we have
x²+y²+z²<span>−2x−4y+8z+17=0
</span>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x²+2x)+(y²-4y)+(z²+8z)=-17
<span>Complete the square. Remember to balance the equation by adding the same constants to each side
</span>(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=-17+1+4+16
(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=4

Rewrite as perfect squares

(x+1)²+(y-2²)+(z+4)²=4

(x+1)²+(y-2²)+(z+4)²=2²

the center is the point (-1,2,-4) and the radius is 2 units

4 0

2 years ago

Can someone please help me understand

Mnenie [13.5K]

Stop being like that I helped u

7 0

2 years ago

The hopper bin in the picture below is modeled by the two-dimensional figure beside it. The hopper bin is

Zepler [3.9K]

The volume of the hopper bin is the amount of feed in it

The volume of the hopper bin is 35974 cubic feet
The carnival tent can be filled to 85% of its volume and not exceed the weight limit

<h3>The volume of the hopper bin</h3>

The given parameters are:

Height of cylinder, H = 20 ft
Diameter of cylinder, D = 36 feet
Angle, θ = 52°

Start by calculating the radius (r) of the cones.

r = D/2 -------- because the cones and the cylinder have equal diameters.

So, we have:

r = 36/2 = 18

The height (h) of the cones is:

tan(θ) = h/r

This gives

tan(52) = h/18

Make h the subject

h = 18 * tan(52)

Evaluate

h = 23.04

The volume is then calculated as:

Volume = Volume of cylinder + 2 * Volume of cone

This gives

Volume = πr^2H + 2 * 1/3πr^2h

Volume = πr^2H + 2/3πr^2h

Factor out πr^2

Volume = πr^2(H + 2/3h)

Substitute known values

Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)

Evaluate

Volume = 35973.85 cubic feet

Hence, the volume of the hopper bin is 35974 cubic feet

<h3>The weight limit of the hopper bin</h3>

The given parameters are:

Maximum weight = 500000 pounds
Feed weight = 22 pounds per cubic feet

For a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:

Weight = 22 * 35974 pounds

Weight = 791428 pounds

At 85% full, the weight wuld be:

Weight = 85% * 791428 pounds

Weight = 672713.8 pounds

672713.8 pounds is greater than the weight limit of 500000 pounds.

Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit