What is the area of a circle 3.102 cm in diameter? (note: the units will be cm2, you only need to enter the number)?

Answer:  5

Step-by-step explanation:

In the given picture we have a table representing two columns as x and y.

We know that the slope of the function is given by :-

[tex]k=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using points (0,4) and (2,14) from the table , we get the slope of the function will be :-

[tex]k=\dfrac{14-4}{2-0}\\\\\\=\dfrac{10}{2}=5[/tex]

Therefore, the slope of the given function in the table = 5

The area of the region is [tex]\(\frac{64}{3}\)[/tex] square units.

To find the area of the region bounded by the parabola \(y = x^2\), the tangent line at the point (2, 4), and the x-axis, we'll first determine the points of intersection.

The tangent line at (2, 4) has the same slope as the derivative of the parabola at x = 2. The derivative of [tex]\(y = x^2\)[/tex] is [tex]\(2x\)[/tex], so at x = 2, the slope is [tex]\(2 \times 2 = 4\)[/tex]. Thus, the equation of the tangent line is [tex]\(y - 4 = 4(x - 2)\)[/tex].

Now, let's find the points of intersection between the parabola and the tangent line:

[tex]\[x^2 = 4(x - 2) + 4\][/tex]

Solving for x, we get [tex]\(x^2 - 4x = 0\)[/tex], which factors to [tex]\(x(x - 4) = 0\)[/tex]. So, [tex]\(x = 0\)[/tex] and [tex]\(x = 4\)[/tex].

Now, integrate the absolute difference of the functions from 0 to 4 to find the area:

[tex]\[A = \int_0^4 |x^2 - (4x - 4)| \,dx.\][/tex]

Evaluate the integral:

[tex]\[A = \int_0^4 (x^2 - 4x + 4) \,dx = \frac{1}{3}x^3 - 2x^2 + 4x \Big|_0^4 = \frac{64}{3}.\][/tex]

Therefore, the area of the region is [tex]\(\frac{64}{3}\)[/tex] square units.

The answer is: [tex]\frac{8}{3}[/tex].

The area of the region bounded by the parabola [tex]\( y = x^2 \)[/tex], the tangent line to this parabola at the point (2, 4), and the x-axis is given by the integral of the difference between the parabola and the tangent line from [tex]\( x = 0 \) to \( x = 2 \)[/tex].

First, we need to find the equation of the tangent line to the parabola at the point (2, 4). The slope of the tangent line is the derivative of the parabola's equation at \( x = 2 \). The derivative of [tex]\( y = x^2 \)[/tex] is [tex]\( y' = 2x \).[/tex] At[tex]\( x = 2 \)[/tex], the slope is [tex]\( 2 \cdot 2 = 4 \)[/tex].

Using the point-slope form of a line,[tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is a point on the line, we get the equation of the tangent line as follows:

[tex]\[ y - 4 = 4(x - 2) \][/tex]

[tex]\[ y = 4x - 8 + 4 \][/tex]

[tex]\[ y = 4x - 4 \][/tex]

Now, we will find the area under the parabola and above the tangent line from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. The integral of [tex]\( x^2 \)[/tex] from 0 to 2 is:

[tex]\[ \int_{0}^{2} x^2 \, dx = \left[ \frac{x^3}{3} \right]_{0}^{2} = \frac{2^3}{3} - \frac{0^3}{3} = \frac{8}{3} \][/tex]

The integral of the tangent line \( y = 4x - 4 \) from 0 to 2 is:

[tex]\[ \int_{0}^{2} (4x - 4) \, dx = \left[ 2x^2 - 4x \right]_{0}^{2} = (2 \cdot 2^2 - 4 \cdot 2) - (2 \cdot 0^2 - 4 \cdot 0) = (8 - 8) - (0 - 0) = 0 \][/tex]

The area between the parabola and the tangent line is the difference between these two integrals:

[tex]\[ \text{Area} = \int_{0}^{2} x^2 \, dx - \int_{0}^{2} (4x - 4) \, dx \][/tex]

[tex]\[ \text{Area} = \frac{8}{3} - 0 \][/tex]

[tex]\[ \text{Area} = \frac{8}{3} \][/tex]

Therefore, the area of the region bounded by the parabola [tex]\( y = x^2 \)[/tex], the tangent line at the point (2, 4), and the x-axis is [tex]\( \boxed{\frac{8}{3}} \)[/tex] square units.

A. f(-5) = -(-5)^2-4(-5)+4 = -1

  f(5) = -(5)^2-4(5)+4 = -41

-1 + -41 = -42

B. -1 - -41 = 40

48/12 = 4 feet

24/2 = 2 feet

 4 *2 = 8 square feet

Answer:

                     8 feet squared

The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ

Here,

The expression is [tex]16 - x^{2}[/tex]

We have to find the value of expression after substitute 4 sinθ for x.

What is substitution method?

Substitution method is algebraic method to solve the linear equations.



Now,

The expression is [tex]16 - x^{2}[/tex]

By putting x = 4 sinθ in above equation, we get;

[tex]16 - x^{2}[/tex]  = 16 - ( 4 sinθ)^2

            = 16 - 16 sin^2θ

            = 16 ( 1 - sin^2θ )

            = 16 cos^2θ

Since,  1 - sin^2θ = cos^2θ

Hence, The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ

Learn more about the substitution method visit:

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To simplify the expression 16 - x² after substituting 4 sin θ for x, you end up with 16 cos² θ, using the Pythagorean trigonometric identity.

To simplify the expression 16 - x² after substituting 4 sin θ for x, where 0° < θ < 90°, we follow these steps:

The substitution gives us 16 - (4 sin θ)².

To further simplify:

The question asked is related to probability, which is a topic in Mathematics. After calculating the probability of selecting a good quart of milk four times in a row (considering that the quantity decreases each time a good quart is selected), the probability equates approximately to 0.3 or 30%.

The given question is a statistical problem related to probability and involves the concept of independent events. In this case, each quart of milk being good or spoiled is an independent event, meaning the outcome of one event doesn't affect the other.

In the cooler, there are 20 quarts of milk in total, 15 of which are good (20 - 5 spoilt quarts equals 15 good ones). Hence, the probability of selecting a good quart of milk at first is 15/20, or 0.75.

After removing one good quart, there are now 14 good quarts out of 19. Hence, the probability of drawing a second good quart is 14/19. We can calculate the probabilities for the third and fourth quarts in the same way, resulting in 13/18 and 12/17 respectively.

Since these are independent events, the probability of all these events happening is the product of their individual probabilities. Therefore, the answer is 0.75* (14/19)* (13/18)* (12/17), which is approximately 0.3 or 30%.

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Answer:

D. $455.80

Step-by-step explanation:

True Balance = Bank Statement - Outstanding Checks

= $592.53 - ($49.80 + $86.93)

= $455.80

Answer:

I just had to do this problem and,

B is (10, -4) and D is (58/9, -2)

Step-by-step explanation:

Final answer:

To find the expression with a quotient greater than 1, we convert the mixed numbers into improper fractions and perform the division for each expression. The expression that gives a quotient greater than 1 is 5 3/4 divided by 7 3/8.

Explanation:

To find the expression that has a quotient greater than 1, we need to divide the given fractions. Let's examine each expression:

4 2/3 divided by 5 1/4: To divide mixed numbers, we convert them into improper fractions and then perform the division. In this case, the quotient is less than 1.

3 1/8 divided by 2 2/5: Similar to the first expression, we convert the mixed numbers into improper fractions and divide. The quotient is also less than 1.

1 6/7 divided by 2 1/3: Again, convert the mixed numbers into improper fractions and perform the division. The quotient is less than 1.

5 3/4 divided by 7 3/8: Convert the mixed numbers into improper fractions and divide. The quotient is greater than 1, so this is the expression we're looking for.

Therefore, the expression with a quotient greater than 1 is 5 3/4 divided by 7 3/8.

The numerator of the equivalent fraction with denominator 12 for 1/2 is 6. This comes from multiplying both the numerator and denominator of 1/2 by the same number (6).

To find the numerator of the equivalent fraction with denominator 12 for 1/2, we simply multiply both parts of the fraction by the same number such that the denominator becomes 12. We know that 2 * 6 equals 12, so we multiply the numerator 1 by 6 as well, which gives us the numerator 6.

Therefore, the fraction 1/2 is equivalent to 6/12.

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