an arrow is fired directly horizontal off a cliff that is 10 meters tall with a velocity of 65.5m/s.

A. How long is the arrow in the air?
B. What is the range of the arrow?

Answer:

D)  $ 300

Step-by-step explanation:

Here, the cost ( in dollars ) of x products is defined by the function,

[tex]C=0.25x^2-80x+300[/tex]

Since, if the no units are produced,

x = 0,

Hence, the cost would be,

[tex]C=0.25(0)^2-80\times 0+300[/tex]

[tex]=0-0+300[/tex]

[tex]=\$ 300[/tex]

Option D is correct.

The cost is $300 if no units are produced.

To find the cost when no units are produced, which are shown by x and we need to evaluate the cost function C at x = 0. The cost function is given by [tex]C = 0.25x^2 - 80x + 300.[/tex]

Let's substitute x = 0 into the function:

[tex]C(0) = 0.25(0)^2 - 80(0) + 300[/tex]

[tex]C(0) = 0 - 0 + 300[/tex]

[tex]C(0) = 300[/tex]

Therefore, the cost when no units are produced is $300.

This corresponds to the constant term in the cost function, which represents the fixed costs that are incurred regardless of the number of units produced.

134.235 cube inches is the volume of a cylinder with a radius of 1.5 inches and a height of 19 inches.

Volume = base area x height

Radius of cylinder (r) = 1.5 inches

Height of cylinder (h) = 19 inches

Value of π = 3.14

To Find :

The volume of a cylinder.

Explanation :

Let, volume of a cylinder be "R".

We know that,

Volume of a cylinder = πr²h

[ Put the values ]

↪ R = 3.14 × (1.5)² × 19

↪ R = 3.14 × 2.25 × 19

↪ R = 7.065 × 19

↪ R = 134.235 cube inches

Therefore,

The volume of a cylinder is 134.235 cube inches.

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The diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.

To find the rate at which the diameter is increasing, we need to differentiate the formula for the volume of a sphere with respect to time:

V = (4/3)πr^3

Where V is the volume and r is the radius.

Let's differentiate V with respect to t:

dV/dt = (4/3)π(3r^2)(dr/dt)

We know dV/dt = 100 cm^3/s and r = 5 cm, so plug in these values:

100 = (4/3)π(3(5^2))(dr/dt)

Simplifying the equation gives us:

dr/dt = 100 / (4π(3(5^2)))

dr/dt ≈ 100 / 300π

So, the diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.

Final answer:

Using equivalent ratios is like adding fractions with unlike denominators as it involves finding a common value to work with.

Explanation:

Using equivalent ratios is similar to adding fractions with unlike denominators because both involve finding a common value to work with. When adding fractions, we look for a common denominator so that we can add the numerators. With equivalent ratios, we find a common multiplier to scale the ratios, which allows us to compare or combine the quantities represented by the ratios.

Here's a step-by-step process:

Convert the given ratios to fractions by writing them as a fraction with the given quantities as the numerator and denominator.

Find a common denominator for the fractions. This involves identifying the least common multiple (LCM) of the denominators.

Multiply the numerators and denominators of the fractions by the appropriate multiples to get equivalent fractions with the same denominator.

Compare or combine the quantities represented by the equivalent fractions.

The expression for the width of a rectangle when the width is given by the algebraic expression 2x3 - 8x2 + 2x + 12.is already stated in its complete form.

The student is asking about finding an expression for the width of a rectangle with given algebraic expressions for length and width. Since the student has provided the expressions for both length and width, we do not need to perform any calculations or manipulations to answer the question directly. The length of the rectangle is given as x-2, and the width of the rectangle is given by the expression 2x3 - 8x2 + 2x + 12. There are no further instructions to simplify or modify, so the expression for the width as provided is complete.

Answer:

6(x+20)

Step-by-step explanation:

6x:  2*3

120:  2*2*3*5

The GCF of 6x*120 is 2*3

so the factored expression is 6(x+20)

Answer:

Its a triangle

The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 15 are 1, 3, 5, and 15.

To find the factors of 12 and 15, you need to identify the numbers that can evenly divide these two numbers without leaving a remainder. Here's how you can find the factors:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 15: 1, 3, 5, 15.

The beam reaches approximately 23 feet up the wall.

Given that, a wooden beam is 24 feet in length and makes an angle of 71° with the ground.

We need to determine how high does it touches the wall,

To find the height up the wall reached by the wooden beam, we can use trigonometry.

Let's denote the height as "h".

In a right triangle formed by the wooden beam, the height "h" represents the opposite side, and the length of the beam (24 feet) represents the hypotenuse.

The angle between the ground and the beam is given as 71°.

We can use the sine function to solve for "h" since sine is defined as the ratio of the opposite side to the hypotenuse in a right triangle.

sin(71°) = h / 24

To find "h," we rearrange the equation:

h = sin(71°) × 24

Calculating this, we get:

h ≈ 0.9511 × 24 ≈ 22.8264

Rounding to the nearest foot, the beam reaches approximately 23 feet up the wall.

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Answer: The solution is g = 4, -8.

Step-by-step explanation: We are given to solve the following algebraic equation.

[tex]g^2+4g-32=0.[/tex]

Since the above algebraic equation is quadratic, so it will have two solutions.

The solution by the method of factorization is as follows:

[tex]g^2+4g-32=0\\\\\Rightarrow g^2+8g-4g-32=0\\\\\Rightarrow g(g+8)-4(g+8)=0\\\\\Rightarrow (g-4)(g+8)=0\\\\\Rightarrow g-4=0,~~~g+8=0\\\\\Rightarrow g=4, -8.[/tex]

Thus, the required solution is  g = 4, -8.

The value of x from the given circle is 4.6 units.

From the given figure, the radius is 9.7 units.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Here,

9.7 =5.1+x

⇒ x=9.7-5.1

⇒ x=4.6 units

Therefore, the value of x from the given circle is 4.6 units.

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Answer:

The decimal of the fraction rounded to the nearest hundredth is

[tex]\frac{43}{14}=3.07[/tex]  

Step-by-step explanation:

Given : Expression [tex]\frac{43}{14}[/tex]  

To find : What is the decimal of the fraction rounded to the nearest hundredth?

Solution :

Step 1 - Write the fraction

[tex]\frac{43}{14}[/tex]  

Step 2 - Divide the numerator by denominator,

[tex]\frac{43}{14}=3.071[/tex]  

Step 3 - Convert to the nearest hundredth,

[tex]3.071\approx 3.07[/tex]

Therefore, The decimal of the fraction rounded to the nearest hundredth is

[tex]\frac{43}{14}=3.07[/tex]  

4.32*10^5

To write scientific number must be greater than one but less than 10

Answer:

Option B. $155

Step-by-step explanation:

Jay Ward has already been taxed on his earning on $107,600.

So on this paycheck only  ($110,100 - $107,600) = $2,500 of his earnings are taxable for social security tax.

Social security tax rate = 6.2%

Hence, social security tax amount = 6.2% × 2500

                                                         = 0.062 × 2500

                                                         = $155

Option B. $155 is the answer.

The baby meerkat weighs 29 grams.

First, we need to ensure our units are the same, so we'll convert 776 grams to kilograms.

There are 1,000 grams in a kilogram, so 776 grams is equivalent to 0.776 kilograms.

Given that the adult meerkat is 0.747 kilograms heavier than the baby meerkat, we can calculate the baby meerkat's weight by subtracting.

Baby meerkat weight = Adult meerkat weight - Additional weight

Baby meerkat weight = 0.776 kg - 0.747 kg

Baby meerkat weight = 0.029 kg

To express this in grams, we multiply by 1,000:

Baby meerkat weight in grams = 0.029 kg × 1000

= 29 grams

Answer:

WrItE wHaT yOu FeElLlLlL

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

The answer is blue i just took the test.