The height, h, of a ball that is tossed into the air is a function of the time, t, it is in the air. The height in feet fort seconds is given by the function h(t) = -16t^2 + 96t What is the domain of the function? a) [0,00) b) (-0,co) Oc) (0,co) d) (0,5) e) none

Answer:

7

Step-by-step explanation:

In this case, you go by the GREATEST DEGREE TERM POSSIBLE.

I am joyous to assist you anytime.

Answer:

a) It is the set of point in the the circumference with equation [tex](x-4)^2+y^2=8[/tex].

b) (10.6, 0, -6 )

Step-by-step explanation:

a) The centre of the sphere is (4,0,-6) and the radio of the sphere is [tex]\sqrt{44} \sim 6.6[/tex]. Since |-6|=6 < 6.6,  then the sphere intersect the xy-plane and the intersection is a circumference.

Let's find the equation of the circumference.

The equation of the xy-plane is z=0. Replacing this in the equation of the sphere we have:

[tex](x-4)^2+y^2+6^2=44[/tex], then [tex](x-4)^2+y^2=8[/tex].

b) Observe that the point (7,0,-6) has the same y and z coordinates as the centre and the x coordinate of the point is greater than that of the x coordinate of  the centre. Then the point of the sphere nearest to the given point will be at a distance of one radius from the centre, in the positive x direction.

(4+[tex]\sqrt{44}[/tex], 0, -6)= (10.6, 0, -6 )

Answer:

360 cents or $ 3.6

Step-by-step explanation:

Let x be the original cost ( in cents ) of each note book,

After reducing the price by 30 cents,

New cost of each book = x - 30,

According to the question,

3x = 4(x-30)  ( ∵ total cost = number of books × cost of each book ),

3x = 4x - 120

3x - 4x = -120

-x = -120

x = 120

Hence, the cost of three books = 3 × 120 = 360 cents or $ 3.6

Answer:

The value of f(2) is 25.

Step-by-step explanation:

Given,

[tex]f(x) = a^x[/tex]

[tex]\implies f(3) = a^3[/tex]

According to the question,

[tex]f(3)=125[/tex]

[tex]\implies a^3=125\implies a = (125)^\frac{1}{3}=5[/tex]

Hence the function would be,

[tex]f(x) = 5^x[/tex]

If x = 2,

[tex]f(2)=5^2\implies f(2)=25[/tex]

To find f(2), substitute x = 2 into the function f(x).

To find f(2), we can substitute the value of x into the function f(x). From the given information, we know that f(3) = 125. So, substituting x = 3 into the function gives us:

f(3) = 0.25e^(-0.25(3))

Simplifying this expression gives us 125 = 0.25e^(-0.75). Rearranging the equation, we can find the value of a:

a = 125 / 0.25e^(-0.75) = 500e^(0.75)

Now, we can substitute x = 2 into the function f(x):

f(2) = 500e^(0.75)(0.25e^(-0.25(2))) = 500e^(0.75)e^(-0.5)

Simplifying this expression gives us:

f(2) = 125e^0.25

So, the value of f(2) is 125e^0.25.

https://brainly.com/question/34178955

#SPJ3

Answer:

doctorate salary:  d = $71,000

bachelor salary:     b = $55,000

Step-by-step explanation:

doctorate salary:  d

bachelor salary:     b

relationship between b and d:  d = 2b - $39,000

Unfortunately, your "1 + 126,000" could not be correct.  I'm going to assume that the total of the two salaries is $126,000.  If that's the case, then:

bachelor salary + (2 times bachelor salary less $39,000) = $126,000.  In symbols,

b + 2b - $39,000 = $126,000

Consolidating the 'b' terms results in 3b - $39,000 = $126,000, and so:

3b = $126,000 + $39,000 = $165,000

Dividing both sides by 3 yields the bachelor salary:  b = $55,000

Then the doctoral salary is 2b - $39,000 = 2($55,000) - $39,000, or $71,000.

Check:  Does b + (2b - $39,000) = $126,000?  Yes.

Then the doctoral salary is d = $103,000, and the bachelor salary $29,000

Answer with Step-by-step explanation:

Given

[tex]f(x)=\frac{1-cos(2x)}{1-cos(x)}\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-(cos^2{x}-sin^2{x})}{1-cos(x)})\\\\(\because cos(2x)=cos^2x-sin^2x)\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-cos^2x}{1-cos(x)}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}(\frac{(1-cosx)(1+cosx)}{1-cosx}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}((1+cosx)+\frac{sin^2x}{1-cosx})\\\\\therefore \lim_{x \rightarrow 0}f(x)=1[/tex]

Answer:

x≤5

Step-by-step explanation:

-10(9-2x)-x≤2x-5

-90+20x-x≤2x-5

19x-2x≤90-5

17x≤85

x≤85/17

x≤5

Step-by-step explanation:

Consider the provided information.

For the condition statement [tex]p \rightarrow q[/tex] or equivalent "If p then q"

The rule for Contrapositive is: Negative both statements and interchange them. [tex]\sim q \rightarrow \sim p[/tex]

Part (A) If you are taller than 6 ft, then it is unpleasant for you to travel in economy class.

Here p is "you are taller than 6 ft, and q is "it is unpleasant for you to travel in economy class".

It is given that Your contrapositive must not contain explicit references to negation. Assume that the negation of "unpleasant" is "pleasant".

Contrapositive: If it is pleasant for you to travel in economy class then you are not taller than 6 ft then.

Part (B) "If x ≥ 0 and y ≥ 0 then xy ≥ 0" where x, y are real numbers.

Here p is "xy≥ 0, and q is "x ≥ 0 and y ≥ 0"

The negative of xy≥ 0 is xy<0, x ≥ 0 is x<0 and y ≥ 0 is y<0.

Remember negative means opposite.

Contrapositive: If xy < 0 then x<0 and y<0.

Final answer:

The contrapositive of a statement involves switching the positions of the subject and the complement, and negating both.

Explanation:

To rephrase the given statement in contrapositive form, we need to switch the positions of the subject and the complement, and negate both.

(a) The contrapositive of the statement 'If you are taller than 6 ft, then it is unpleasant for you to travel in economy class' is:

'If it is pleasant for you to travel in economy class, then you are not taller than 6 ft.'

(b) The contrapositive of the statement 'If x ≥ 0 and y ≥ 0 then xy ≥ 0' is:

'If xy < 0, then at least one of x or y is less than 0.'

Answer:

C. A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.

Step-by-step explanation:

Simple Random Sampling is the sampling where samples are chosen randomly, where each unit has an equal chance of being selected in a sample.

Option A is incorrect as the size of the sample and size of the population is not the same generally if it does happen then there will be no difference between sample and population.

Option B is incorrect as Simple Random Sampling is not a chance it is a way that samples can be taken.

Option D is incorrect as when samples are taken using a convenient sample then it is called Convenient Sample, not Simple Random Sample.

Thus, only option C is correct.

Simple random sampling is a method where each possible sample from a population has an equal chance of being chosen. This ensures that all members of a population have an equal opportunity of being in the sample, thus representing the population accurately. It differs from other sampling techniques like convenience sampling, stratified sampling, cluster sampling and systematic sampling.

Simple random sampling can best be defined as the process in which each member of a population initially has an equal chance of being selected for the sample. In other words, a sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. This sample is then called a simple random sample. An example of this process may be selecting the names of students from a hat for a study group, where each student from the class(population) has an equal chance of being selected.

On the contrary, it should not be mistaken with convenience sampling, which is a non-random method of choosing a sample that can produce biased data. Other variants of random sampling include, but not limited to, stratified sampling, cluster sampling, and systematic sampling.

Overall, simple random sampling is a vital and simple method part of statistics to represent a population accurately for a study.

https://brainly.com/question/33604242

#SPJ12

Answer:

The equations for the value V in terms of t is [tex]V(t)=-16000\cdot t+1000000[/tex] and the value of the building

after 1 year is $984,000

after 2 years is $968,000

after 20 years is $680,000

Step-by-step explanation:

With the straight-line depreciation method, the value of an asset is reduced uniformly over each period until it reaches its salvage value(It is the value of the asset at the end of its useful life).

We know from the information given the year = 0 the building costs $1,000,000 and a the year = 25 it costs $600,000.

With this information, you can calculate the decrease in value of the building due to age. We use the slope of a line formula because is a straight-line depreciation.

If (0, $1,000,000) is the first point and (25, $600,000) is the second point. we have

[tex]m=\frac{V_{2} -V_{1}}{t_{2}-t_{1}} =\frac{600000-1000000}{25-0} =-16000 \frac{\$}{years}[/tex]

To find the equation for the value V in terms of t, we use the point-slope form, this expression let you calculate the value of the building at the end of the year (t)

[tex]V-V_{0}= m(t- t_{0})\\V-1000000=-16000(x-0)\\V=-16000\cdot t+1000000[/tex]

To find the value after 1 year, after 2 years, and after 20 years. We put the year into the equation [tex]V(t)=-16000\cdot t+1000000[/tex]

[tex]V(1)=-16000\cdot (1)+1000000=\$984,000\\V(2)=-16000\cdot (2)+1000000=\$968,000\\V(20)=-16000\cdot (20)+1000000=\$680,000[/tex]

Answer:

248.79 ft

Step-by-step explanation:

A projectile is fired from a cliff 220 ft above water at an inclination of 45 degrees to the horizontal, with a muzzle velocity of 65 ft per second.

[tex]h(x)=-\dfrac{32x^2}{65^2}+x+220[/tex]

For maximum value of x, h(x)≥0

[tex]-\dfrac{32x^2}{65^2}+x+220\geq0[/tex]

Solve quadratic equation for x

[tex]-\dfrac{1}{4225}(32x^2-4225x-929500)\geq0[/tex]

[tex]32x^2-4225x-929500\leq0[/tex]

Using quadratic formula,

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

where, a=32, b=-4225, c=-929500

[tex]x=\dfrac{4225\pm\sqrt{4225^2-4(32)(-929500)}}{2(32)}[/tex]

[tex]x\geq-116.75\text{ and }x\leq 248.79[/tex]

Hence, The maximum value of x will be 248.79 ft

Final Answer:

The maximum horizontal distance x of the projectile from the face of the cliff, at the peak of its trajectory, is approximately 33.01 feet.

Explanation:

The maximum value of x occurs at the peak of the projectile's flight, which we can find by analyzing the given quadratic equation:

[tex]\[ h(x) = -\frac{32x^2}{v^2} + x + h_0 \][/tex]

For our specific problem:
[tex]\[ h(x) = -\frac{32x^2}{(65)^2} + x + 220 \\\\\[ \text{where} \\\\\[ h_0 = 220 \text{ feet (initial height)}, \\\\\[ v = 65 \text{ ft/s (muzzle velocity)}, \\\\\[ \text{angle of inclination} = 45 \text{ degrees}. \\\\[/tex]
The quadratic equation represents a parabola opening downward (since the coefficient of x² is negative), and the x-coordinate of the vertex of this parabola will give us the maximum value of x.

The x-coordinate of the vertex (maximum value of x) for a parabola in the form ax² + bx + c is given by the formula [tex]\( -\frac{b}{2a} \).[/tex]

In our equation:

[tex]\[ a = -\frac{32}{v^2} = -\frac{32}{(65)^2} \\\\\[ b = 1 \\\\\[ c = h_0 = 220 \][/tex]
Now we substitute values of a and b into the formula for the x-coordinate of the vertex:

[tex]\[ -\frac{b}{2a} = -\frac{1}{2 \times ( -\frac{32}{(65)^2} )} \][/tex]

With the computations already given:

[tex]\[ \text{Maximum value of } x = 33.0078125 \text{ feet} \][/tex]
This means that the maximum horizontal distance x of the projectile from the face of the cliff, at the peak of its trajectory, is approximately 33.01 feet.

Final answer:

To find the current average egg consumption, calculate 35% of the original consumption of 400 eggs, which is 140 eggs, and subtract that from the original to get 260. Therefore, the average consumption now is 260 eggs per person per year.

Explanation:

If we look back 40 years and find that egg consumption was 400 eggs per person per year, and there has been a 35% decrease in egg consumption, we can calculate the current average egg consumption. To do this, we find 35% of the original consumption:

Multiply 400 (original consumption) by 0.35 (35%) to find the decrease in consumption. This equals 140 eggs.

Subtract this decrease from the original consumption: 400 - 140 equals 260 eggs. Therefore, the average consumption of eggs per person per year in the U.S. today is 260.

These changes in dietary habits over the years mirror shifts in consumer tastes, as well as concerns about health and production costs, all of which can influence the demand for different food products.

To calculate the amount of soil needed, you must first calculate the volume in cubic feet (20 feet x 3 feet x 4 feet = 240 cubic feet) and then convert that volume to cubic yards by dividing by 27 (240 cubic feet ÷ 27 = 8.89 cubic yards). So, approximately 8.89 cubic yards of soil is needed.

To find the volume needed to fill the planter, we use the formula to compute the volume of stack, which is length × width × height. The planter has a length of 20 feet, a width of 3 feet, and a height of 4 feet. So, multiplying these values: 20 feet × 3 feet × 4 feet = 240 cubic feet.

Finally, we need to convert cubic feet to cubic yards because soil is typically bought in cubic yards. Since 1 yard = 3 feet, 1 cubic yard = 3 feet × 3 feet × 3 feet = 27 cubic feet. Therefore, to convert 240 cubic feet to cubic yards, we divide that by 27: 240 cubic feet ÷ 27 = 8.89 cubic yards. So, you will need approximately 8.89 cubic yards of soil to fill the planter.

https://brainly.com/question/33318354

#SPJ3

To fill a planter that is 20 feet long, 3 feet wide, and 4 feet tall, we need 240 cubic feet of soil, which converts to approximately 8.888 cubic yards. Rounding up, we will need 9 cubic yards of soil.

Volume = Length × Width × Height

Here,

the dimensions are given as:

Length: 20 feet

Width: 3 feet

Height: 4 feet

So, the volume in cubic feet is:

Volume = 20 ft × 3 ft × 4 ft

            = 240 cubic feet

Next, we need to convert this volume from cubic feet to cubic yards.

Knowing that there are 3 feet in a yard,

we use the conversion factor:

1 cubic yard = 3 × 3 × 3

                    = 27 cubic feet

So, we divide the total cubic feet by the number of cubic feet in one cubic yard:

240 cubic feet ÷ 27

= 8.888 cubic yards

Since you typically can't have a fraction of a cubic yard in this context, we might round up to ensure you have enough soil, resulting in 9 cubic yards of soil needed.

Answer:

The statement [tex](p\lor q) \land (\neg p \lor r)\Rightarrow (q \lor r )[/tex] is a tautology.

Step-by-step explanation:

To prove this statement [tex](p\lor q) \land (\neg p \lor r)\Rightarrow (q \lor r )[/tex] is a tautology we are going to use a truth table. A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

A tautology is a formula which is true for every assignment of truth values to its simple components.

We can see from the table that the last column contains only true values. Therefore, the formula is a tautology.

Answer:

The equation of circle is [tex]x^2+y^2=65[/tex].

Step-by-step explanation:

It is given that the circle passes through the point (8,1) and center at the origin.

The distance between any point and the circle and center is called radius. it means radius of the given circle is the distance between (0,0) and (8,1).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula the radius of circle is

[tex]r=\sqrt{\left(8-0\right)^2+\left(1-0\right)^2}=\sqrt{65}[/tex]

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]         .... (1)

where, (h,k) is center and r is radius.

The center of the circle is (0,0). So h=0 and k=0.

Substitute h=0, k=0 and [tex]r=\sqrt{65}[/tex] in equation (1).

[tex](x-0)^2+(y-0)^2=(\sqrt{65})^2[/tex]

[tex]x^2+y^2=65[/tex]

Therefore the equation of circle is [tex]x^2+y^2=65[/tex].

The equation of a circle centered at origin and passing through the point (8,1) can be determined using principles of geometry. Calculate the radius using the Pythagorean theorem and then substitute it into the general equation of a circle (x-h)² + (y-k)² = r², where h and k are 0 since the circle is centered at the origin. The equation for the circle is x² + y² = 65.

The subject of this question is a circle in mathematics, particularly geometric principles. The given condition is that the circle's center is at the origin and it passes through the point (8,1). From our understanding of a circle, we know that the radius is the distance from the center to any point on the circle. Since our center is at the origin (0,0), the radius r can be calculated using the Pythagorean theorem as the distance from the origin to the point (8,1), which is sqrt((8-0)² + (1-0)²) = sqrt(65). Therefore, the equation of the circle in terms of x and y based on its center (h,k) and radius r is (x-h)² + (y-k)² = r². Given that the circle's center is at the origin, h and k equal to 0, which simplifies the equation to x² + y² = r², or in our case, x² + y² = 65.

https://brainly.com/question/29288238

#SPJ3