What’s the volume of a cone with the radius of 45 cm and a height of 55 cm

Find an equation in rectangular coordinates for the cylindrical equation r = 2sintheta

frutty [35]

Answer:

$x^2+(y-1)^2=1$

Step-by-step explanation:

The given cylindrical equation is

$r=2\sin \theta$

Multiply both sides by r.

$r^2=2r\sin \theta$ .... (1)

The required formulas are

$x=r\cos \theta,y=r\sin \theta,r^2=x^2+y^2$

Substitute $r\sin \theta =y,r^2=x^2+y^2$ in equation (1).

$x^2+y^2=2y$

$x^2+y^2-2y=0$

Add 1 on both sides.

$x^2+(y^2-2y+1)=1$

$(x-0)^2+(y-1)^2=1^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

It is the equation of a circle centered at (0,1) with radius 1.

Therefore, the equation in rectangular coordinates is $x^2+(y-1)^2=1$ .

3 0

3 years ago

there are 24 apple trees in my orchard. if i can harvest the fruit from 2 and 2 thirds trees each day, how many days will it tak

valentina_108 [34]

Answer: 9 days.

Step-by-step explanation:

2 2/3 is the amount able to be harvested, you want to find days. So, 2 2/3(d)=9. You need to solve for days (d) which equals 9.

8 0

3 years ago

-8z+(4.5)+3.5z+7y-1.5

bogdanovich [222]

Answer:

$\boxed{\sf{7y+3-4.5z}}$

Step-by-step explanation:

In order to combine like terms, you have to isolate x and y from one side of the equation.

$\sf{-8z+\left(4.5\right)+3.5z+7y-1.5}$

First, thing you do is remove parentheses.

$\Longrightarrow: \sf{-8z+4.5+3.5z+7y-1.5}$

Solve.

Then, you combine like terms.

$\Longrightarrow:\sf{-8z+3.5z+7y+4.5-1.5}$

Add/subtract the numbers from left to right.

-8z+3.5z=-4.5z

Rewrite the problem down.

$\Longrightarrow: \sf{-4.5z+7y+4.5-1.5}$

Solve.

4.5-1.5=3

$\Longrightarrow: \boxed{\sf{7y+3-4.5z}}$

Therefore, the correct answer is 7y+3-4.5z.

I hope this helps, let me know if you have any questions.

6 0

1 year ago

Linda owns 4 shares of a certain stock. Yesterday the total value of her shares went down by 32 dollars. What was the change in

Annette [7]

Answer:

The value of each share decreased by $8.

Step-by-step explanation:

Number of shares of a certain stock Linda owned = 4

Total value of shares went down by = $32

So find the change in value of each share.

Solution:

Let the total value of each share in dollars be = $x$

Value of 4 shares in dollars will be = $4x$

The total value of shares went down by $32

So, new value of 4 shares = $4x-32$

New value of each share = $\frac{New\ value\ of\ total\ shares}{4}$

⇒ $\frac{4x-32}{4}$

Splitting the denominators.

⇒ $\frac{4x{{4}-\frac{32}}{4}$

⇒ $x-8$

Original value of each share in dollars was = $x$

New value of each share in dollars = $x-8$

Thus, we can see that the value of each share decreased by $8.

6 0

3 years ago

Tristan is building steps up to a deck that is 156 5 6 yards above the ground. The steps must all be the same height. If he want

ss7ja [257]

Answer:

The height of each step is 1957 yard

Step-by-step explanation:

we are given

Tristan is building steps up to a deck that is 15656 yards above the ground

so, total height =15656 yards

Number of steps =8

now, we can use formula

Height of each step = ( total height)/( number of steps)

now, we can plug these values

and we get

Height of each step is

$=\frac{15656}{8}yards$

$=1957yards$

8 0

3 years ago