carla looks from the top of a diving board, and lines up a ball floating on the surface of the water with the bottom of the opposite corner of the pool. calculate the total distance across the surface of the pool. explain your reasoning

The question is about finding the first and second derivatives of y with respect to x. The first derivative dy/dx is found to be (1+t)e^-2t, and the second derivative d2y/dx2 is found to be -2e^-2t.

The derivatives are found by differentiating each function with respect to t first, using the product and chain rules, respectively: the derivatives dy/dt and dx/dt are dy/dt = e^-t - te^-t and dx/dt = e^t. Then, dy/dx can be found as (dy/dt)/(dx/dt), and the second derivative d2y/dx2 can be obtained by differentiating dy/dx with respect to x, which will utilize the quotient rule. Specifically, dy/dx = (e^-t(1+t))/(e^t) which simplifies to (1+t)e^-2t, and after a relatively complex differentiation for d2y/dx2, we get -2e^-2t.

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The number 9 can be expressed as a power of 3 by finding the appropriate exponent that, when raised to the base 3, equals 9. This exponent is 2, making 9 written as a power of 3 to be 3².

To write the number 9 as a power of the base 3, we look for an exponent that can be raised to the base 3 to result in the number 9. This is achieved by recognizing that 3 squared (3²) equals 9. So, 9 expressed as a power of 3 is 3².

When raising a number to a power, such as generating the cubing of exponentials, you cube the digit term normally and multiply the exponent by 3. However, in this case of 9 as a power of 3, we are not cubing but rather finding which power results in the number 9 when using the base 3. The process involves simple experimentation or recollection that 3¹ = 3, 3² = 9, and so on.

In mathematics, writing numbers in exponential form is essential, as it simplifies operations and understanding of scale. It's a useful concept, not only for integer powers but also when dealing with decimal or negative exponents.

Answer:

∠ NLO ≅ ∠ NPM Corresponding Parts of Congruent Triangles Are Congruent

Step-by-step explanation:

It's on my chart on the test this is 100% right

Final answer:

Hector used the Angle-Angle-Side Postulate to show congruency between two triangles. Therefore, the corresponding angles are congruent with the CPCTC principle. Thus, option 3 is correct.

Explanation:

Hector claims that ΔLNO ≅ ΔPNM is based on the Angle-Angle-Side Postulate.

Since the triangles are congruent, their corresponding parts must also be congruent.

Therefore, the statement that ∠NLO ≅ ∠NPM is supported by the principle that Corresponding Parts of Congruent Triangles Are Congruent (CPCTC).

Robin's basket is heavier than Ted's basket by 2 ounces.

To determine whose basket is heavier, we need to find the total weight of each basket.

Ted's basket contains 5 apples, each weighing 8 ounces. Therefore, the total weight of Ted's basket is 5 * 8 = 40 ounces.

Robin's basket contains 6 apples, each weighing 7 ounces. Therefore, the total weight of Robin's basket is 6 * 7 = 42 ounces.

Since Robin's basket weighs 42 ounces and Ted's basket weighs 40 ounces, Robin's basket is heavier by 2 ounces.

Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

Here, given that,

Olivia must earn 475 points out of 550 to receive a b in math.

so far she had earned 240 test points

85 quiz point

and 40 homework points.

Solution: 240 + 85 + 40 = 365

Now, we get,

475 - 365 = 110

Hence, Answer: Olivia needs 110 points on her final exam in order to earn at least a B in Math.

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Out of 400 students in school, 200 students would want sandwich in school.

The question is asking to predict how many students would want sandwiches for lunch in a school of 400 based on a sample of 24 students where 12 wanted a sandwich.

Calculate the proportion of students in the sample wanting a sandwich: 12/24 = 0.5

Apply the proportion to the larger school: 0.5 x 400 = 200 students.

we know that

a) A box of ground nutmeg weighs [tex]1 1/3[/tex] ounces

b) There are [tex]20[/tex] teaspoons of nutmeg in the box

Step 1

Convert mixed number to an improper fraction

[tex]1\frac{1}{3} \ ounces= \frac{1*3+1}{3}= \frac{4}{3}\ ounces[/tex]

Step 2

By proportion

Find the weight of one teaspoon

[tex]\frac{(4/3)}{20} \frac{ounces}{teaspoons} =\frac{x}{1} \frac{ounces}{teaspoon} \\ \\x= \frac{4}{20*3}\\ \\x= \frac{4}{60}\ ounces\\\\x=\frac{1}{15}\ ounces[/tex]

therefore

the answer is the option

[tex]\frac{1}{15}\ ounces[/tex]

Answer:

C. 14

Step-by-step explanation:

I just answered it correct

Answer: [tex]y = 2x + 6[/tex]

Step-by-step explanation:

Let x represents the number of days .

Given : There are 6 quarters in a jar.

Jill adds 2 quarters to the jar every day.

Then, the number of quarters added in x days = 2x

Now, the total number of quarters in the jar after x days = 2x+6

Hence, the linear equation represents the total amount of quarters in the jar after x days will be:-

[tex]y = 2x + 6[/tex]

Answer:

its A if you are taking the unit test

Step-by-step explanation:

Final answer:

The total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.

Explanation:

To find the total interest, we need to use the formula:

Interest = Principal × Rate × Time

Given that the principal is $32,000, the interest rate is 6.1%, and the time is 10 years, we can substitute these values into the formula to calculate the total interest:

Principal: $32,000

Rate: 6.1%

Time: 10 years

Interest = $32,000 × 0.061 × 10 = $19,520

Therefore, the total interest on a ten-year, 6.1% loan with a principal of $32,000 is $19,520.

The slope intercept form of the given equation of a line is y= -3/2 x -15.

The given equation of the line is -3x-2y=30.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Now,

-3x-2y=30

⇒ -2y=3x+30

⇒ y= -3/2 x -15

Therefore, the slope intercept form of the given equation of a line is y= -3/2 x -15.

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Answer:$352.16

Im in a rush so cant add explaination

By the definition of the functions of trigonometry, the sine of  is equal to the -coordinate of the point with polar coordinates , giving . Similarly, , since it is the -coordinate of this point. Filling out the rest trigonometric functions then gives