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exis [7]
3 years ago
13

A punch recipe serves 24 people calls for 4 L of lemonade soda 2 pints of sherbet and 6 cup of ice how much of each ingredient w

ould you need to make an identical recipe that serves 36 people?
Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
4 0
punch recipe serves 24 people
4 L of lemonade soda
2 pints of sherbet and
6 cup of ice

how much of each ingredient would you need to make an identical recipe that serves 36 people?
36-24=12 (12 is half of 24, increase by 1/2)

4 L of lemonade soda (increase to 6L)
2 pints of sherbet (increase to 3 pints)
6 cup of ice (increase to 9 cups)

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3 years ago
The given function models the number of cars that are put through a quality control test each hour at a car production factory.
Annette [7]

hours each day.

Step-by-step explanation:

The given function models the number of cars that are put through a quality control test each hour at a car production factory.

The given function is

We need to find the number of hours does the quality control facility operate each day.

Rewrite the given function it factored form.

Taking out the common factors from each parenthesis.

The factored form of given function is c(t)=-(t-10)(t+2).

Equate the function equal to 0 to find the x-intercept.

Number of hours cannot be negative. So from t=0 to t=10 quality control facility operate the cars.

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7 0
3 years ago
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PLEASE HELP!!
PSYCHO15rus [73]

<u><em>Answer:</em></u>

The bird is approximately 9 ft high up in the tree

<u><em>Explanation:</em></u>

The required diagram is shown in the attached image

Note that the tree, the cat and the ground form a right-angled triangle

<u>Therefore, we can apply special trigonometric functions</u>

<u>These functions are as follows:</u>

sin(\alpha)=\frac{opposite}{hypotenuse} \\ \\ cos(\alpha)=\frac{adjacent}{hypotenuse} \\ \\tan(\alpha)=\frac{opposite}{adjacent}

<u>Now, taking a look at our diagram, we can note the following:</u>

α = 25°

The opposite side is the required height (x)

The adjacent side is the distance between the cat and the tree = 20 ft

Therefore, we can use the <u>tan function</u>

<u>This is done as follows:</u>

tan(\alpha)=\frac{opposite}{adjacent}\\ \\ tan(25)=\frac{x}{20}\\ \\x=20tan(25) = 9. 32 ft which is 9 ft approximated to the nearest ft

Hope this helps :)

5 0
3 years ago
An object is launched from a launching pad 144 ft. above the ground at a velocity of 128ft/sec. what is the maximum height reach
ollegr [7]

Answer:

18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144

b. The maximum height = 400 feet

c. Attached graph

19) The rocket will reach the maximum height after 4 seconds

20) The rocket hits the ground after 9 seconds

Step-by-step explanation:

* Lets study the rule of motion for an object with constant acceleration

# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time

  and a is the acceleration of gravity

# The vertical distances h in x second is h(x) - h(0), where h(0)

   is the initial height of the object above the ground

∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial

  velocity, a is the acceleration of gravity (32 feet/second²) and x

  is the time

18)a.

∵ The value of a = -32 ft/sec² ⇒ negative because the direction

   of the motion

  is upward

∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16

∴ h(x) = vx - 16x² + h(0)

∴ h(x) = -16x² + vx + h(0) ⇒ proved

* Find the height of the object after x seconds from the ground

∵ h(0) = 144 and v = 128 ft/sec

∴ h(x) = -16x² + 128x + 144

b.

* At the maximum height h'(x) = 0

∵ h'(x) = -32x + 128

∴ -32x + 128 = 0 ⇒ subtract 128 from both sides

∴ -32x = -128 ⇒ ÷ -32

∴ x = 4 seconds

- The time for the maximum height = 4 seconds

- Substitute this value of x in the equation of h(x)

∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet

c. Attached graph

19)

- The object will reach the maximum height after 4 seconds

20)

- When the rocket hits the ground h(x) = 0

∵ h(x) = -16x² + 128x + 144

∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16

∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x

∵ x² - 8x - 9 = 0

∴ (x - 9)( x + 1) = 0

∴ x - 9 = 0 OR x + 1 = 0

∴ x = 9 OR x = -1

- We will rejected -1 because there is no -ve value for the time

* The time for the object to hit the ground is 9 seconds

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Answer: Should be "the sum of 3 and the quotient of y and 2"

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2 years ago
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