Answer the following correct

Answer:

h = 2.25 m

Step-by-step explanation:

Given:

Speed = v = 12 ft/sec

Acceleration due to gravity = g = 32 ft/sec²

Required:

Height = h = ?

Formula:

v = \(\sqrt{2gh}\)

Solution:

For h, the formula will be:

=> h = \(\frac{v^2}{2g}\)

=> h = \(\frac{(12)^2}{2(32)}\)

=> h = \(\frac{144}{64}\)

=> h = 2.25 m

The limit as x approaches 7 of the absolute value of (7 - x) divided by (7 - x) exists and is equal to 1.

To evaluate the given limit, we need to analyze the behavior of the expression as x approaches 7. The absolute value function ensures that the numerator, |7 - x|, is always positive or zero.  

When x approaches 7 from the left side, the expression simplifies to (-1)/(7 - x), which approaches -1 as x gets closer to 7. Similarly, when x approaches 7 from the right side, the expression simplifies to (1)/(7 - x), which approaches 1 as x gets closer to 7.

Since the limit of the numerator is always positive or zero, and the limit of the denominator is always positive or zero as well, we can conclude that the limit of the entire expression is the same from both sides. Thus, the limit as x approaches 7 of |7 - x|/(7 - x) exists, and its value is 1.

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I guess you're missing some plus signs, so that

\(\vec f(x, y, z) = z \, \vec\imath + y \, \vec\jmath + zx \, \vec k\)

You're also missing the plane that defines the tetrahedron, but no big deal; I'll use the general equation \(ax+by+cz = 1\), where each of a, b, and c are positive. Then S is the boundary of the region R, where

\(R = \left\{ (x, y, z) : 0 \le x \le \dfrac1a \text{ and } 0 \le x \le \dfrac{1-ax}b \text{ and } 0 \le z \le \dfrac{1-ax-by}c \right\}\)

By the divergence theorem, the flux of \(\vec f\) across S is

\(\displaystyle \iint_S \vec f \cdot d\vec s = \iiint_R \mathrm{div}(\vec f) \, dV\)

We have

\(\mathrm{div}(\vec f) = \dfrac{\partial(z)}{\partial x} + \dfrac{\partial(y)}{\partial y} + \dfrac{\partial(zx)}{\partial z} = 1 + x\)

Then the flux is equal to the volume integral,

\(\displaystyle \iiint_R (1 + x) \, dV = \int_0^{1/a} \int_0^{(1-ax)/b} \int_0^{(1 - ax - by)/c} (1 + x) \, dz \, dy \, dx \\\\ = \frac1c \int_0^{1/a} \int_0^{(1-ax)/b} (1 + x) (1 - ax - by) \, dy \, dx \\\\ = \frac1{2bc} \int_0^{1/a} (1 + x) (1 - ax)^2 \, dx \\\\ = \frac1{6abc} \left(\frac1{4a} + 1\right) = \boxed{\frac{1+4a}{24a^2bc}}\)

Both Andre and Elena are correct, but they have used different properties of exponents to simplify the expression.

Andre used the property that when multiplying powers with the same base, the exponents can be added. So, he added the exponents of 10^2, which is 2, to get 2+2+2 = 6. Therefore, his answer of 10^6 is correct.

Elena used the property that when a power is raised to another power, we can multiply the exponents. So, she rewrote 10^2 • 10^2 • 10^2 as (10^2)^3, and then multiplied the exponents of 10^2, which is 2, by 3 to get 2*3 = 6. Therefore, her answer of 10^5 is also correct.

Both methods are valid and result in the same answer, so it's a matter of personal preference which method to use.

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Answer:

To calculate the vertex you can use the vertex form ( i searched about the vertex and found it) but i don't know how to use it so i used another method.

The vertex is where the function inverts (y values) so it is going to be or a maximum or a minimum of the function. To calculate the min/max you derivate the function and then equal it to zero.

1) y  = -3x^2 -12x -10

the derivative of y is y' = -6x -12 = -6(x+2)

y'=0 <=>  -6(x+2) = 0 <=> x+2=0 <=> x=-2

y(-2) = -3(-2)^2 -12*(-2) -10 = 2

So the vertex is the point (-2,2) .

Because the slope of the equation is negative that means that the vertex is going to be the maximum , so the maximum is (-2,2) .

To find another 4 points you just have to pick values of x and replace them in the equation y  = -3x^2 -12x -10  to find y.

2) y = -2x^2 -12x -16

Do the same thing we did in point 1

y'= -4x-12 = -4(x+3)

y'=0 <=>  -4(x+3) = 0 <=> x+3=0 <=> x=-3

y(-3) = -2(-3)^2 -12*(-3) -16 = 2

So the vertex is the point (-3,2) .

Answer:

5y=7

y=7/5

Step-by-step explanation:

6x+6y=-6

6x+y=-3

eliminate the 6x

then subtract y from 6y

then subtract -3 from -6

6y-y=5y

-6-(-13)=7

5y=7

divide 5 from both sides

y=7/5

then you eliminate the y and do the same thing :)

x=-12/5

Answer:

(x,y)=(-12/5,7/5)

Step-by-step explanation:

6x+6y=-6

6x+y=-13 First, subtract 1 from 2

6x-6x+6y-y=-6--13

5y=7 Divide by 5

5y/5=7/5

y=7/5

y=1.2

6x+6(7/5)=-6

6x+42/5=-6 subtract 42/5

6x=-14 2/5

6x=-14.4 divide by 6

x=-2.4

x=-2 2/5

x=-12/5

(x,y)=(-12/5,7/5)

Hope this helps plz hit the crown :D

The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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Answer:

a. 7.78%

b.

c. lower

Step-by-step explanation:

Answer:

mean gives you the average of the information, median gives the perfect number. brainliest please

The percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.

Given that, there were 500 lions in an African nature reserve. 3 years later there were 864 lions in the same nature reserve.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let the percentage increase per year be x.

a) According to the question,

500(1+x)³=864

⇒ (1+x)³=864/500

⇒ (1+x)³=1.728

⇒ 1+x= 1.2

⇒ x =0.2

In percentage 20%

b) \(500(1+0.2)^1\)

= $600

Hence, the percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.

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The probability that exactly one of the coins is a 10p piece is 1/2.

To find the probability that exactly one of the coins is a 10p piece, we can consider the possible outcomes.

There are two coins, and each coin can be either a 10p piece or a non-10p piece. Let's consider the four possible outcomes:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece.

3. Both Erin's and Jack's coins are 10p pieces.

4. Both Erin's and Jack's coins are non-10p pieces.

Since the total amount of the two coins is less than 50p, we can eliminate the third possibility (both coins being 10p pieces).

Now, let's calculate the probability for each of the remaining possibilities:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece:

The probability of Erin having a 10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece:

This is the same as the previous case, so the probability is also 1/4.

3. Both Erin's and Jack's coins are non-10p pieces:

The probability of Erin having a non-10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

Now, we sum up the probabilities of the two cases where exactly one of the coins is a 10p piece:

1/4 + 1/4 = 2/4 = 1/2.

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Answer:45 x 12 = 450

15 x 10 = 150

35 x 15 = 525

43 x 14 = 602

Step-by-step explanation:

Answer:

488000

(real number)

= 4.88 × 105

(scientific notation)

= 4.88e5

(scientific e notation)

number of significant figures: 3

Step-by-step explanation:

\(x = y \\ 2 \sqrt{14} = x \sqrt{2} \)

\(x = 2 \sqrt{7} \)

\(x = y = 2 \sqrt{7} \)

Step-by-step explanation:

Here,

x -20 < 35

or, X<35+20

•X<55

The slope of AB is (0-4)/(-2-0)=2, so since perpendicular lines have negative reciprocal slopes, the slope of the perpendicular line is -0.5.

So, the equation of the line is:

y + 1 = -0.5(x - 5)

y + 1 = -0.5x + 2.5

y = -0.5x + 1.5

Answer:

a, d

Step-by-step explanation:

Answer:

\(y=x*2^x (3,5)+y\)

Step-by-step explanation:

The new exchange rate is 12.5 SEK: $1.

The Swedish krona trades at 10 SEK: $1. If the kroner weakens by 20% vs. the USD, the new exchange rate will be 12.5 SEK : $1.

Since we are looking for the exchange rate between Swedish krona and the dollar, let us find how many dollars we can buy with one Swedish krona initially.

10 SEK: $1 is the exchange rate. One can buy 1 dollar for every 10 SEK.

20% weakening of SEK would imply that one needs to spend more SEK to purchase the same amount of USD.

Since we have 20% depreciation, 1 dollar should now cost more than 10 SEK.

20% of 10 is 2, which means 2 SEK is now lost.

10 SEK - 2 SEK = 8 SEK

Now, 1 dollar is worth 8 SEK. Now we will reverse the ratio for the new exchange rate: 1/8 = 0.125, which means that 1 USD is worth 0.125 SEK.

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You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.

A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.

The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.

The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.

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Answer: (1,2)

Step-by-step explanation:

1)

x+y=3

y=-x+3

x | 0 | 3 |

y | 3 | 0 |

2)

3x+y=5

y=-3x+5

x | 0 | 2 |

y | 5 | -1 |

A histogram with a symmetric distribution looks like this:

Leaving aside the quality of the drawing, the left and the right side of the histogram are identical if we split it by the red line. Is like having a reflexion axis.

Now, we have to discuss what of the 2 data sets may have such an histogram. This means that we must think which of them may have the same number of ocurrences for very short and very long durations, for regular to short and regular to long durations, and so on and so furth.

Pop album tracks:

In the same album we may have arround 12 tracks (small number), all of them with a duration of arround 3 minutes. We could imagine a histogram like the following:

All the songs last between 170 and 190 seconds, and one or two last a little bit more.

Phone talks:

In this case, we can think that there are some calls to say something like "mom, I'm on my way home" and other like "let me tell you the hole movie I saw yesterday night", so very short and very long calls, but they are no so common. There are a lot of "regular" calls that might last for 60 seconds.

Also, in this case, we are taking into account all the calls from people in the school in one day (yesterday), so, may be 1.000 calls? The actual number really doesn't matter, but the fact that the number is very big. Because of the big number, we can expect a symmetric distribution.

The number of pounds in 32 kg would be 70.5479.

A pound is an imperial unit used to measure bulk or weight. A kilogram is a metric measuring unit. The letters lb and lbm stand for pounds. Kilo or kg are used to denote kilograms. 0.4535 kilograms make up one pound.

In both the British imperial system and the United States' customary system, weight is measured in pounds. Measuring a person's weight is one common application of pounds.

The weight of a kilogram is 2.2046 pounds. We convert kilograms (kg) to pounds (lb) using the formula 1 kg = 2.2 lb. By multiplying by 2.2, we may convert a kilogram to a pound. We divide by 2.2 to change a pound into a kilogram.

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Answer:

Step-by-step explanation:

Solve:

(a+b+c) (a+b-c)=

(a²+ab-ac+ab+b²-bc+ac+bc-c²)=

a²+ab-ac+ab+b²-bc+ac+bc-c²=

a²+2ab+0ac+b²+0bc-c²=

a²+2ab+b²-c²

Answer:

The answer is a² + 2ab + b² - c²

Step-by-step explanation:

(a + b + c) × (a + b - c)

a² + ab - ac + ba + b² - bc + ca + cb - c²

a² + ab + ba - ac + ca + b² - bc + cb - c²

a² + 2ab + b² - c²

Thus, The answer is a² + 2ab + b² - c²

-TheUnknownScientist 72

Answer:

The first 2 are the answers.

Answer:

a) -6

b) 3

c) Y = -6x + 3

Step-by-step explanation:

Pick two points and find rise/run = slope

rise y1 - y2 = 9 - 3 = 6

run x1 - x2 = -1 - 0 = -1

slope = 6 / -1 = -6

The y intercept is where x = 0 which is given in the table (0,3) so

y intercept = 3

Point slope form is y = mx + b , so

y = -6x + 3

To calculate the energy of the resulting explosion when a 10,000 kg UFO made of antimatter crashes with a 40,000 kg plane made of matter, we can use Einstein's famous equation, E=mc², which relates energy (E) to mass (m) and the speed of light (c).

In this case, we'll need to calculate the total mass of matter and antimatter involved in the collision and then use the equation to find the energy released. The equation E=mc² states that energy is equal to the mass multiplied by the square of the speed of light (c). In this scenario, we have a collision between a UFO made of antimatter and a plane made of matter. Antimatter and matter annihilate each other when they come into contact, resulting in a release of energy.

To calculate the energy of the resulting explosion, we need to determine the total mass involved in the collision. The total mass can be calculated by adding the masses of the UFO and the plane together. In this case, the UFO has a mass of 10,000 kg and the plane has a mass of 40,000 kg, so the total mass is 50,000 kg.

Next, we can use the equation E=mc² to calculate the energy. The speed of light (c) is a constant value, approximately 3 x 10^8 meters per second. Plugging in the values, we have E = (50,000 kg) x (3 x 10^8 m/s)². Simplifying the equation, we have E = 50,000 kg x 9 x 10^16 m²/s².Multiplying the numbers, we get E = 4.5 x 10^21 joules. Therefore, the energy of the resulting explosion when the UFO and plane collide is approximately 4.5 x 10^21 joules.

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