If 5x^2 + y^4 = −9 then evaluate d^2y/dx^2 when x = 2 and y = 1. Round your answer to two decimal places.

When [tex]\( a \)[/tex] is negative in the equation [tex]\( y = ax^2 \)[/tex], the parabola opens downwards. So, the answer is (a).

To determine the direction in which the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens, we need to understand the properties of the quadratic function. Let's analyze this step by step:

1. Identify the general form of the equation:

  The given equation is [tex]\( y = ax^2 \)[/tex].

2. Determine the effect of the coefficient [tex]\( a \)[/tex] on the parabola:

  - If [tex]\( a \)[/tex] is positive, the parabola opens upwards.

  - If [tex]\( a \)[/tex] is negative, the parabola opens downwards.

3. Evaluate the given condition:

  The problem states that [tex]\( a \)[/tex] is negative.

4. Apply the condition to the quadratic equation:

  Since [tex]\( a \)[/tex] is negative, the coefficient of [tex]\( x^2 \)[/tex] in the equation [tex]\( y = ax^2 \)[/tex] is negative.

5. Conclusion:

  When [tex]\( a \)[/tex] is negative, the parabola opens downwards.

Therefore, the correct answer is:

a. down

Answer-

[tex]\boxed{\boxed{L=\dfrac{g}{4\pi^2 f^2}}}[/tex]

Solution-

The equation for time period of a simple pendulum is given by,

[tex]T=2\pi \sqrt{\dfrac{L}{g}}[/tex]

Where,

T = Time period,

L = Length of the rod,

g = Acceleration due to gravity.

Frequency (f) of the pendulum is the reciprocal of its period, i.e

[tex]f=\dfrac{1}{T}\ \Rightarrow T=\dfrac{1}{f}[/tex]

Putting the values,

[tex]\Rightarrow \dfrac{1}{f}=2\pi \sqrt{\dfrac{L}{g}}[/tex]

[tex]\Rightarrow (\dfrac{1}{f})^2=(2\pi \sqrt{\dfrac{L}{g}})^2[/tex]

[tex]\Rightarrow \dfrac{1}{f^2}=4\pi^2 \dfrac{L}{g}[/tex]

[tex]\Rightarrow L=\dfrac{g}{4\pi^2 f^2}[/tex]

A = Layer 4..................................................

The correct decimal that represents eighteen and eight hundredths is 18.08, with the '8' in the hundredths place following the whole number 18.

The decimal that shows eighteen and eight hundredths is 18.08. This is because the number 18 represents the whole part, and the decimal part .08 represents the hundredths place. To express this, we place a decimal point after the whole number 18, followed by two digits: the first digit after the decimal point for tenths (which is 0 in this case), and the second digit for hundredths, which is 8. Thus, the correct decimal representation would be 18.08, as opposed to 18.80 which shows eighty hundredths, or .1808 which implies a number less than one with eight hundredths and eight ten-thousandths.

To calculate the time necessary for an investment to accrue a specific amount of interest, use the simple interest formula. For this question, it would take 6 years for a $1525 investment to earn $237.90 at a 2.6% interest rate.

To find the amount of time (t) needed for an investment to earn a certain amount of interest (I), we can use the simple interest formula: Interest = Principal x rate x time. Given that Interest ($237.90), Principal ($1525), and the annual nominal interest rate (2.6% or 0.026 as a decimal) are known, we can isolate time (t) and solve for it.

The formula with the given values is: $237.90 = $1525 x 0.026 x t.

To isolate t, we divide both sides by the product of the principal and the rate:

t = $237.90 / ($1525 x 0.026)

t = $237.90 / $39.65

t = 6 years

Therefore, it would take 6 years for the investment to earn $237.90 in interest at an annual rate of 2.6%.

The piecewise function representing Tracy's cell phone charges is C(m) = {29 if m ≤ 250, 29 + (0.35)(m - 250) if m > 250.}.

Based on Tracy's cell phone plan, we want to create a piecewise function that represents the charges based on her usage. She is offered 250 free minutes at a flat rate, and any additional minutes are billed at an additional rate per minute. This piecewise function will have two parts: one for when Tracy's usage is at or below 250 minutes, and another for when her usage exceeds 250 minutes.

The first part of the function accounts for the flat rate up to 250 minutes:

If m ≤ 250, then C(m) = 29.

The second part of the function accounts for additional charges past 250 minutes:

If m > 250, then C(m) = 29 + (m - 250) * 0.35.

Therefore, the piecewise function that represents Tracy's cell phone charges based on the minutes used (m) is:

C(m) = {
 29 if m ≤ 250,
 29 + (0.35)(m - 250) if m > 250.
}

You can infer from this problem that for every 100 m that John was able to run, it takes him 9.93 seconds. To get how much time is needed for 26 – mile marathon, you need to divide 26 miles by 100 meters. But first, you need to convert 26 miles to meters first.

1 mile = 1,609.34 meters

26 miles = 41,842.84 meters

41,824.84 meters / 100 meters = 418.43 x 9.93 seconds = 4,155 seconds or 69.25 minutes

The correct equation for the relationship between the measures of the segments, angles, and arcs is [tex]PR^2[/tex] = PS * PT. The last option is the right choice.

Power of a Tangent: We know that the power of a point from an external point P to a circle is equal to the product of the lengths of the two tangents drawn from P to the circle (PQ * PR = PS * PT).

Identify the Tangents and Secant: In the given diagram, PR is the secant intersecting the circle at points T and S, and PQ and PS are the tangents drawn from P to points Q and S, respectively.

Apply the Power of a Tangent Theorem: Since PS and PT are tangents from P, we can apply the power of a tangent theorem to get:

PS * PT = PQ * PR.

Substitute PQ with PR: Since PQ and PR are both tangents drawn from the same point P, they have the same length (PQ = PR). Substituting PQ with PR in the equation, we get:

PS * PT = PR * PR.

Simplify the Equation: Simplifying the equation PR * PR = PS * PT, we get the final equation:

[tex]PR^2[/tex] = PS * PT.

Therefore, the equation [tex]PR^2[/tex] = PS * PT correctly represents the relationship between the measures of the segments, angles, and arcs in the given diagram.

The last option is the right choice.

The coefficient of the x-term in the slope-intercept equation of a line represents the slope. The slope indicates how the y-value changes with each one-unit increase of the x-value. The constant term 'b' is the y-intercept, the point where the line crosses the y-axis.

In the slope-intercept equation of a line, typically written as y = mx + b, the coefficient of the x-term gives the slope of the line. The slope, represented by the letter 'm', defines the steepness of the line, or how much the y-value changes for every one-unit increase in x. The y-intercept is given by the constant term 'b', which indicates the point where the line crosses the y-axis, occurring when x equals zero.

Slope is especially important in fields like economics as it measures the relationship between two variables. A positive slope means that as x increases, y also increases, and vice versa for a negative slope. Therefore, knowing the slope allows us to predict how one variable will change in response to the other.

Answer:

150

Step-by-step explanation:

C. (–7x + 4)(4 – 7x)

Answer:

the answer is point S

~batmans wife dun dun dun...aka ~serenitybella

Answer:

Step-by-step explanation:

What is the measure of the central angle?

Answer : 140°

What ratio represents the measure of the central angle compared to the measure of the entire circle?

Answer7/18

If s = , what is the length of minor arc AB?

Answer : 14π

[tex] 4*e^{2x} -3 = 12 [/tex]

Step 1:

Here we have -3 in subtraction on the left side, so when we take it to the right we apply opposite operation of subtraction that is addition.

[tex] 4*e^{2x} = 12+3 [/tex]

[tex] 4*e^{2x} = 15 [/tex]

Step 2:

Next we have 4 in multiplication on left side, so dividing right side by 4,

[tex] e^{2x} = 15/4 [/tex]

[tex] e^{2x} = 3.75 [/tex]

Step 3:

taking log on both sides

[tex] ln ( e^{2x}) = ln(3.75) [/tex]

[tex] {2x} =ln 3.75 [/tex]

Step 4:

Dividing right side by 2,

x= ln (3.75) /2 = 0.66088

Answer : x = 0.66088..

Answer:1/4c+5

Step-by-step explanation: