Solve 4x^2 - 4x - 24 = 0 for x. Using quadratic formulas

A cone with radius 5 units is shown below. Its volume is 105 cubic units. Find the height of the cone.

Ainat [17]

Answer:

height of the cone = 4.01273885 units

Step-by-step explanation:

Volume of a cone(V) is given by:

$V = \frac{1}{3} \pi r^2h$ ....[1]

where,

r is the radius and h is the height of the cone.

As per the statement:

A cone with radius 5 units and ts volume is 105 cubic units

⇒r = 5 units and V = 105 cubic units

Substitute these given values and use $\pi = 3.14$ in [1] we have;

$105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h$

Multiply both sides by 3 we have;

⇒ $315 = 78.5 \cdot h$

Divide both sides by 78.5 we have;

$4.01273885 = h$

or

h = 4.01273885 units

Therefore, the height of the cone is, 4.01273885 units

6 0

4 years ago

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What is the solution to the system of equations?

Dovator [93]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}x+3y+2z=8&(1)\\3x+y+3z=-10&(2)\\-2x-2y-z=10&(3)\end{array}\right\qquad\text{subtract both sides of the equations (1) from (2)}\\\\\underline{-\left\{\begin{array}{ccc}3x+y+3z=-10\\x+3y+2z=8\end{array}\right }\\.\qquad2x-2y+z=-18\qquad(4)\qquad\text{add both sides of the equations (3) and (4)}\\\\\underline{+\left\{\begin{array}{ccc}-2x-2y-z=10\\2x-2y+z=-18\end{array}\right}\\.\qquad-4y=-8\qquad\text{divide both sides by (-4)}\\.\qquad\qquad y=2\qquad\text{put the value of y to (1) and (3)}$

$\left\{\begin{array}{ccc}x+3(2)+2z=8\\-2x-2(2)-z=10\end{array}\right\\\left\{\begin{array}{ccc}x+6+2z=8&\text{subtract 6 from both sides}\\-2x-4-z=10&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+2z=2&\text{multiply both sides by 2}\\-2x-z=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+4z=4\\-2x-z=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad3z=18\qquad\text{divide both sides by 3}\\.\qquad\qquad z=6\qquad\text{put the value of z to the first equation}$

$x+2(6)=2\\x+12=2\qquad\text{subtract 10 from both sides}\\x=-10$

4 0

3 years ago

What is the number of possible outcomes when a coin is tossed one time

Salsk061 [2.6K]

Answer:

2.

Step-by-step explanation:

the coin could be heads or tails, but knowing me prolly 3 because I would lose the coin when I flip it.

6 0

3 years ago

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Judy is a single woman, 25 years old. Her take home pay is $2314.92/month. She also earns $48 interest per month on her savings

Leni [432]

The monthly budget plan for Judy includes all of her income and expenses, the total balance is $ 2362.92 and she spends $ 1083.

<h3>What is the monthly budget?</h3>

A monthly budget is a personal spending plan that you use to track your monthly income and costs.

The given data in the problem is;

Home pay = $2314.92/month.

Interest earned = $48 / month

House rent = $825/month

EMI of student loan = $258/month

Total earning per month = $2314.92 + $48

Total earning per month = $ 2362.92

Amount she spends per month = $825/month + $258

Amount she spends per month = $ 1083

Hence, the total balance will be $ 2362.92 and she spend $ 1083.

To learn more about the monthly budget refer to:

brainly.com/question/570904

#SPJ1

3 0

2 years ago

Which counterexample shows that the conjecture "All animals that can fly are birds" is false?

QveST [7]

It seems like you forgot to post the answer choices. However, bats are one animal where they can fly but they aren't birds. So this is one counter-example to prove the claim false. Another example would be any flying insects.

3 0

4 years ago

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