Find the equation for the tangent plane and the normal line at the point P0(1,2,3) on the surface 3x^2 +y^2+z^2=20

To solve this youd have to do 72-15 which equals out to be 68 feet.

Your answer is The submarine descended 68 feet.

Answer:

\(x=-2, \frac{21}{5}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define equation

5m² - 11m - 42 = 0

Step 2: Define variables

a = 5

b = -11

c = -42

Step 3: Find roots

The fraction \(\dfrac{10}{2}\) is equal to 5.

Important information:

The given number can be written as:

\(5=\dfrac{5}{1}\)

Now, multiply the numerator and denominator by the same natural number which is greater than 1, to get a fraction.

Multiply the numerator and denominator by 2.

\(\dfrac{5\times 2}{1\times 2}=\dfrac{10}{2}\)

Therefore, the fraction \(\dfrac{10}{2}\) is equal to 5.

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The fraction 5/1 is equal to 5, 25/5, and 30/6.

We have,

When we write a whole number as a fraction, we can express it by placing the number over the denominator of 1.

This is because any number divided by 1 is equal to itself.

In the case of the number 5,

We can write it as a fraction by placing it over 1:

5/1

This fraction represents the whole number 5, where the numerator (5) indicates the quantity or value, and the denominator (1) represents a single unit.

Or,

25/5 can also be written as 5// = 5

30/6 can also be written as 5/1 = 5

Thus,

The fraction 5/1 is equal to 5, 25/5, and 30/6.

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Answer:

C

Step-by-step explanation:

this is the answer since it involves a minus sign

Answer:

y = 2/5x - 2

Step-by-step explanation:

y inter =  -2

slope is rise / run = 2/5

Answer:

y=2/5x-2

Step-by-step explanation:

y=mx+b

b=-2 is where the line crosses the y axis and that is what the y intercept is

m=2/5 which is the slope to calculate the slope do x1-x2 over y1-y2

See attachment for math work and answer.

We can use the equation of tangent as a structure.

\(y - f(a) = f'(a)(x - a)\)

Our f(a) is y-point and Our a is x-point..

Looking back at the equation, our f(a) would be 3 and a would be - 4

Therefore the answer is (-4,3)

Answer:

Vertical angles are both the same angle measure while a linear pair is 2 sets of points creating a line.

Step-by-step explanation:

Answer:

a. The area of the square is 25 feet x 25 feet = 625 square feet.

b. To find the percent of points that landed in the pond, we divide the number of points that landed in the pond by the total number of points generated and multiply by 100.

3,200 points / 5,000 points = 0.64

0.64 x 100 = 64%

so 64% of the points landed in the pond.

c. To find the area of the pond, we multiply the proportion of points that landed in the pond by the area of the square.

64% of the points landed in the pond = 0.64

Area of the pond = 0.64 x 625 square feet = 400 square feet. So, the area of the pond, to the nearest square foot, is 400 square feet.

Step-by-step explanation:

Answer:514 grams  of rice is in each of the 10 containers

Step-by-step explanation:

Amount of rice bought  =6 kilograms of rice.

6 kilograms =6000grams

Amount of rice reaming after filling 10 containers =860g

Amount used to fill up the containers ==6000grams-860grams =5140 grams

To get the amount filled inside the 10 containers since same amount is in each, we divide by 10

5140 grams/10=514 grams

The Variance Inflation Factor (VIF) measures the degree of correlation or the collinearity of the explanatory variables.

VIF quantifies how much each explanatory variable is correlated with a linear combination of the other variables in a multiple regression model. This can help identify variables that are redundant, irrelevant, or harmful to the model's accuracy. The VIF is calculated for each explanatory variable by dividing the variance of the regression coefficient estimates by the variance of the regression coefficient estimates when that variable is excluded from the model.

If the VIF is greater than 1, it indicates that the variance of the regression coefficient estimate for that variable is inflated by the presence of the other variables, which reduces the model's accuracy. Therefore, a VIF greater than 1 is considered to be an indication of collinearity or multicollinearity in the explanatory variables. The VIF measures the degree of correlation or the collinearity of the explanatory variables, and it can identify variables that are redundant, irrelevant, or harmful to the model's accuracy.

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Answer:

is it 4.2626

Step-by-step explanation:

let me know if it right

Answer:

44 litres

Step-by-step explanation:

We subtract the remainders from the amounts.

447 - 7 = 440

577 - 5 = 572

669 - 9 = 660

Now we need the GCF of 440, 572, 660

440 = 2³ × 5 × 11

572 = 2² × 11 × 13

660 = 2² × 3 × 5 × 11

GCF = 2² × 11 = 44

The greatest common factor is 44.

Answer: 44

Check:

447/44 = 10 reminder 7

577/44 = 13 remainder 5

669/44 = 15 remainder 9

Answer:

the width is 8 inches

Step-by-step explanation:

area=length x width

88=11(w)

w=8

Answer:

8

Step-by-step explanation:

A flyer is the shape of a rectangle ad its area uses the formula A = l*w. Since the area is 88 and the length is 11 inches, then 88 = 11*w. Solve for w.

88/11 = 11w/11

8=w

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Answer:It should be 49.365

Step-by-step explanation:

Answer:

the answer is 49.365

Step-by-step explanation:

because if you line the decimals up and just add normal

hope this helped

Answer:

its 90 bro whenever you see that square on a corner its always 90 degrees

Step-by-step explanation:

Answer:

The answer is 90 degrees.

Whenever you see a square in the corner, it means it's 90 degrees.

It's also red, meaning that that is what you're trying to find.

Answer:

25%

Step-by-step explanation:

As the given situation the parameters are below:-

Cost of each box = 3 pounds

Amount of cereal in each box = 160 g

now,

160 g of cereal = 100%

and

25% of 1 box of cereal = 25% of 160 g which is

\(= \frac{25}{100} \times 160 g= 40 g\)

As per the question,  it is mention that Jane need her idea to give the equal value of amount as Tim's idea, provided

160 g of cereal costs 3 pounds

and

1 g of cereal will cost

=  \(\frac{3}{60}\ pounds\)

40 g of cereal will cost \(40\times \frac{3}{160} = \frac{3}{4}\ pounds\)

So, the percentage of \(\frac{3}{4}\) the pound is of 3 pounds is 3 ÷ 4 ÷ 3 × 100

= 25%

Therefore as the situation, Jane need to decline the amount by 25% for the same amount as Tim's idea.

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression. To do this, we need to assign a variable to the unknown number and then use multiplication and subtraction to represent the given information.

Let x be the unknown number. The product of three and x is 3x. Twelve less than 3x is 3x - 12. Therefore, the algebraic expression for "twelve less than the product of three and a number" is 3x - 12. This expression represents a value that is 12 less than three times the number x.

For instance, if we know that a number is 7, we can use this expression to find the value of "twelve less than the product of three and 7."3x - 12 = 3(7) - 12= 21 - 12= 9Therefore, the value of "twelve less than the product of three and 7" is 9. We can also use this expression to write an equation and solve for x. For example, if we know that the value of "twelve less than the product of three and a number" is 33, we can write an equation:3x - 12 = 33Then, we can solve for x:3x = 33 + 123x = 45x = 15. Therefore, the unknown number is 15.

To summarize, the phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

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x=4

Step-by-step explanation:

Distrubutive property: 5x-50=30-15x

get x on one side: 5x-50+15x=30

combine like terms: 20x-50=30

subtract on both sides: 20x=30+50

20x=80

simplify: 20/20=80/20

x=4

In parallelogram, The rug is too long to fit in the room. Even though the rug is narrower than the room, its length is greater than the height of the room, so it would not fit in the space.

Use the formula for the area of a parallelogram: A = base x height. We are given that the area of Lanie's room is 108 square feet, so we can write:

108 = base x height

We are also given that the rug is 6 feet wide and 10 feet long, so its area is:

A_rug = 6 x 10 = 60 square feet

Now we need to compare the dimensions to see if the rug will fit on the floor of Lanie's room. Let's start with the height of the parallelogram. We are given that the base is 9 feet, but we need to find the height. We can rearrange the formula for area to solve for height:

height = A / base

Plugging in the values we know, we get:

height = 108 / 9 = 12 feet

So the height of the parallelogram is 12 feet.

Now we can compare the dimensions:

- Compare the length of the rug to the height of the parallelogram: 10 feet > 12 feet (the rug is longer than the height of the room)
- Compare the widths of the rug and the room: 6 feet < 9 feet (the rug is narrower than the room)

Based on these comparisons, we can see that the rug is too long to fit in the room. Even though the rug is narrower than the room, its length is greater than the height of the room, so it would not fit in the space.

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Answer:

A = 8,820.24 yd²

Step-by-step explanation:

\(A = \pi r^{2}\)

r = diameter ÷ 2

r = 106 ÷ 2 = 53

A = (3.14)(53)²

A = (3.14)(2809)

A = 8,820.24 yd²

Answer:

8,820.26 yd²

Step-by-step explanation:

(see attached for reference)

Given:

Diameter, D = 106 yd

π = 3.14

Area of circle

= (1/4) π D²

= (1/4) (3.14) (106)²

= 8,820.26 yd²

Answer:

11,000

Step-by-step explanation:

Hey there! I'm happy to help!

This symbol is an absolute value symbol. It means that we are looking for that number's distance from 0. There is no such thing as a negative distance; the distances are all positive, so both ∣9∣ and ∣-9∣ have a value of 9.

Have a wonderful day and keep on learning! :D

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

To find the maximum and minimum values of the blood pressure function p(t), we need to examine the behavior of the sinusoidal term, -40sin(3t), within the given time interval. The function is a sine wave with an amplitude of 40 and a period of 2π/3. This means that the maximum value occurs at the peak of the sine wave (amplitude + offset), and the minimum value occurs at the trough (amplitude - offset).

The maximum blood pressure corresponds to the peak of the sine wave, which is 40 + 160 = 200 mmHg. To find the time at which this occurs, we set the argument of the sine function, 3t, equal to π/2 (since the peak of the sine wave is π/2 radians). Solving for t gives t = (π/2) / 3 = π/6 ≈ 0.524 seconds.

Similarly, the minimum blood pressure corresponds to the trough of the sine wave, which is -40 + 160 = 120 mmHg. Setting the argument of the sine function equal to 3π/2 (the trough of the sine wave), we find t = (3π/2) / 3 = π/2 ≈ 1.571 seconds.

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

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Answer:

Equation is the second one, term is the first one, expression is the third one, inequality is the last one

Step-by-step explanation:

Answer: equation is the one with the =, expression is 4x+(-2), inequality is the one with the greater than sign, and the term is -9

The range for the strength of the concrete samples provided is 1110 psi, and the sample standard deviation is 456.7 psi.

In the given set of concrete strength values, the range is calculated by subtracting the lowest value from the highest value. In this case, the lowest value is 2950 psi and the highest value is 4060 psi. Thus, the range is obtained by subtracting 2950 from 4060, resulting in a range of 1110 psi.

To compute the sample standard deviation, we follow a two-step process. First, we calculate the mean (average) of the data set, which is found by summing up all the values and dividing by the total number of values. In this case, the mean is (3980 + 4060 + 3200 + 3100 + 2950 + 3830 + 4060 + 4060) / 8 = 3695 psi.

Next, we find the difference between each data point and the mean, square each difference, sum up the squared differences, divide by (n-1), and take the square root. Performing these calculations for the given data set, we obtain a sample standard deviation of approximately 456.7 psi.

In summary, the range for the concrete strength is 1110 psi, indicating the difference between the highest and lowest values. The sample standard deviation of 456.7 psi reflects the dispersion of the data points around the mean, providing a measure of the variability in concrete strength samples.

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Given the expression:

We will rewrite the expression to be as the form (x - a)² = b

So, we need to make a complete square

The coefficient of x = -2

Half the coefficient = -1

Square it will give 1

So, add (1) to both sides of the equation

Factor the left side of the equation, it is a complete square

Compare the result to the given form.

So, the answer will be: