Please check the image for directions, Five stars, and like. Thank you

Step-by-step explanation:

the volume of container B is Travers from A to B.

so, the volume of the empty space in A is exactly the volume of container B.

the volume of a cylinder is

base area × height = pi×r² × height.

the reside is as always half of the diameter.

r = 8/2 = 4 ft

the volume of the empty space in A = the volume of container B =

= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈

≈ 1,005.3 ft³

Answer:

its reflection

Step-by-step explanation:

a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Answer:

It is Reflection. Check if it is in the list.

The area of this triangle is 30 m².

Area is a surface measure, that is, it is the amount of space that a geometric figure occupies on a flat surface.

To calculate the area of a triangle, we can use the formula:

Area = (base x height) / 2

In the case of the given triangle, we can choose the measure of 5m as the base and the measure of 12m as the height, since the height forms a right angle with the base and is perpendicular to it.

So, we have:

Area = (b*h)/2

Area = (5m * 12m) / 2

Area = 30m²

The balance of the account after the seventh deposit can be calculated using the formula below:

A = P (1 + r/n)ⁿ

where:

A = the balance of the account

P = The initial deposit of $800

r = the interest rate of 5%

n = the number of times the interest is compounded annually

n = 1

Therefore, the balance of the account after the seventh deposit is:

A = 800 (1 + 0.05/1)⁷

A = 800 (1.05)⁷

A = 800 (1.4176875)

A = 1128.54

Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.

Answer:

-8: (-4, -3]

-7: (-3, -1]

(-5, -1]: (-5, -1]

(-4, -1]: (-4, -1]

[-3, 1]: [-3, 1]

(2, 1): (1, 2]

Step-by-step explanation:

See Venn diagram below

The fig's right side of total surface = 42yds.

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

According to our question-

(17+17+8)yds

42yds

learn more about surface area click here:

https://brainly.com/question/16519513

#SPJ1

The derivative of f(x) is

[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].

The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.

In this case, the function f(x) is a polynomial, which means it is a combination of terms of the form [tex]ax^b[/tex], where a and b are constants. The derivative of f(x) can be calculated by taking the derivative of each term in the function and then combining them together.

The derivative of a term [tex]ax^b[/tex] is [tex]abx^(b-1)[/tex]. For the first term of f(x),[tex]-5x^pi[/tex], the derivative is [tex]-5pi x^(pi-1)[/tex]. For the second term, [tex]6.1x^5.1[/tex] the derivative is[tex]6.1 * 5.1x^(5.1-1)[/tex]. For the third term, [tex]pi^5.1[/tex], the derivative is [tex]5.1pi^(5.1-1)[/tex].

Combining these terms together, the derivative of f(x) is

[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].

This answer is the derivative of the given function. This is how the function changes as its input changes.

For more questions related to function

https://brainly.com/question/24748644

#SPJ1

The derivative of f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is  [tex]-5\pi x^{\pi -1}[/tex]+  [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex] which can be calculated with the power rule.

The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.

The derivative of the given function f(x) = [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] can be calculated with the power rule, which states that the derivative of xⁿ is nx⁽ⁿ⁻¹⁾

To calculate the derivative of the given function, we begin by applying the power rule to each term.

The first term is [tex]-5^{\pi }[/tex] which has a derivative of [tex]-5\pi x^{\pi -1}[/tex].

The second term is [tex]6.1x^{5.1}[/tex] which has a derivative of [tex]6.1*5.1x^{5.1-1}[/tex].

The third term is [tex]\pi^{5.1}[/tex], which has a derivative of 5.1[tex]\pi^{5.1-1}[/tex].

Therefore, the derivative of the given function

f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is  [tex]-5\pi x^{\pi -1}[/tex]+  [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex].

For more questions related to function

https://brainly.com/question/24748644

#SPJ1

Question:

Compute the derivative of the given function.

f(x) = - [tex]5x^{\pi }[/tex]+[tex]6.1x^{5.1}[/tex]+[tex]\pi^{5.1}[/tex]

​

The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.

To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.

To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.

To know more on perpendicular bisectors

https://brainly.com/question/24753075

#SPJ4

--The question is incomplete, answering to the question below--

"find the midpoint of a line and arc using straight edge-compass-construction method"

Step-by-step explanation:

For RIGHT triangles, using S-O-H-C-A-H-T-O-A

A sinA= cosB         yes   12/13 = 12/13

B. sinA=tanB          no      12 /13   not equal to  5/12

C. sinB= tanA         no       5/13   not equal to  12/5

D. sinB= cosB         no        5/13   not equal to 12/13

A) sinA= cοsB statement is true. Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A.

A triangle is a twο-dimensiοnal geοmetric shape that cοnsists οf three straight line segments, called sides, that cοnnect three nοn-cοllinear pοints, called vertices.

Based οn the given image, the fοllοwing statements are true:

1. The triangle is a right triangle, which means that οne οf the angles is a right angle (90 degrees).

2. The side οppοsite the right angle is called the hypοtenuse, which is the lοngest side οf the triangle. In this case, it is the side that is labeled "c".

3. The οther twο sides οf the triangle are called legs. In this case, they are labelled "a" and "b".

4. The Pythagοrean theοrem applies tο this triangle, which states that the sum οf the squares οf the lengths οf the legs is equal tο the square οf the length οf the hypοtenuse. In οther wοrds,  [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].

Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A

A sinA= cοsB         yes     12/13 = 12/13

B. sinA=tanB          nο       12 /13   nοt equal tο  5/12

C. sinB= tanA         nο       5/13   nοt equal tο  12/5

D. sinB= cοsB         nο       5/13   nοt equal tο 12/13.

To learn more about triangle from given link:

https://brainly.com/question/2773823

#SPJ1

Complete Question:

In  Δ ABC , angle C is right Angle

Which Statement must be True?

A sinA= cosB

B. sinA=tanB

C. sinB= tanA

D. sinB= cosB

The value of the constant c that makes the following function are c = 0.

Constant is a term used to describe a value that remains unchanged or fixed throughout a program or process. It can be a numeric value, a character value, a string, or a Boolean (true/false) value. Common examples of constants include physical constants, mathematical constants, and programming-language keywords.A constant is a value that does not change, regardless of the conditions or context in which it is used. Common examples of constants include mathematical values such as pi (3.14159), physical constants such as the speed of light (299,792,458 m/s), and other constants such as the universal gravitational constant (6.67408 × 10−11 m3 kg−1 s−2).

To learn more about constant

https://brainly.com/question/27598477

#SPJ1

Therefore, c must equal 0 in order for the two sides of the function to be equal. and The one with the greater absolute value is b = 10.

A function is a block of code that performs a specific task. It is a subprogram or a set of instructions that can be used multiple times in a program.

27. For the function to be continuous at x = 7, the limit of the function as x approaches 7 from the left must equal the limit of the function as x approaches 7 from the right.
This means that the value of y as x approaches 7 must be the same on both the left and right sides of the point.
Since the left side of the function is y = c*y + 3, the right side of the function must also be equal to y = c*y + 3.
Therefore, c must equal 0 in order for the two sides of the function to be equal.

28. In order for the function to be continuous at x = 5, the value of y at x = 5 must be the same on both the left and right sides of the point.
Since the left side of the function is y = b - 2x, the right side of the function must also be equal to y = b - 2x.
Therefore, b must equal 10 in order for the two sides of the function to be equal.

To learn more about function

https://brainly.com/question/11624077

#SPJ1

Complete Question:

Alberto's statement is flawed because all squares can be called rectangles, but not vice versa

Alberto's reasoning is flawed because all squares can be called rectangles, but not all rectangles are squares.

While it is true that squares meet the definition of rectangles, not all rectangles meet the definition of squares.

A square is a special type of rectangle with all sides equal in length.

Therefore, Alberto's argument violates the logical concept of implication, where the truth of one proposition (squares can be called rectangles) does not necessarily imply the truth of the converse (all rectangles must be called squares).

Read more about rectangles at

https://brainly.com/question/25292087

#SPJ1

To obtain the required equation we divide the equation by sin²Ø.

The first six functions are trigonometric, with the domain value being the angle of a right triangle and the range being a number. The angle, expressed in degrees or radians, serves as the domain and the range of the trigonometric function (sometimes known as the "trig function") of f(x) = sin. Like with all other functions, we have the domain and range. In calculus, geometry, and algebra, trigonometric functions are often utilised.

The given equation is:

sin²Ø+cos²Ø=1

To obtain the required equation we divide the equation with sin²Ø:

sin²Ø/sin²Ø +cos²Ø/ sin²Ø = 1/sin²Ø

1 + cot²Ø = csc²Ø

Hence, to obtain the required equation we divide the equation by sin²Ø.

Learn more about trigonometric functions here:

https://brainly.com/question/6904750

#SPJ1

Answer:

Acquired resources

Step-by-step explanation:

Acquired resources

Answer:

y=9/x  => proportional

y = x - 12 ==> non-proportional

h = 3d ==> proportional

f = 1/3 e = proportional

Step-by-step explanation:

A proportional equation is of the general form

y = kx (directly proportional) or

y = k/x  (inversely proportional)

k is known as the constant of proportionality

y = 9/x ==> k = 9  proportional
y = x - 12  cannot be expressed as y = kx or y = k/x

h = 3d ==> k = 3  proportional

f = 1/3 e ==> k = 1/3   proportional

(a) Therefore after t = 1.75 seconds the diver will hit the water.

(b) The velocity the diver hit the water is 56 ft/s.

From the given condition we have d(t) = 16t²

and the height is 49ft

(a) Now when the diver hit the water the equation become

16t² = 49

t² = 49/16

t = ±7/4

t = ±1.75

since time can not be negative so t = 1.75

Therefore after t = 1.75 seconds the diver will hit the water.

(b)

Now differentiating d(t) with respect to t we get

d'(t) = 32t

now putting t=7/4 we get

the velocity d'(7/4) = 32*7/4

d'(7/4) = 56ft/s

Therefore the velocity the diver hit the water is 56 ft/s.

To learn more about differentiation link is here:

brainly.com/question/14496325

#SPJ4

The complete question is :

A cliff diver plunges from a height of 49ft above the water surface. The distance the diver falls in t seconds is given by the function d(t)=16t²ft

(a) After how many seconds will the diver hit the water?

(b) With what velocity (in ft/s ) does the diver hit the water?

The value of error term E(x,y) = 8x^2 - 8x - 56.

The definition of differentiability states that a function f(x,y) is differentiable at a point (a,b) if there exists a linear function L(x,y) such that:

f(x,y) - f(a,b) = L(x,y) + E(x,y)

where E(x,y) is an error term that approaches 0 as (x,y) approaches (a,b).

In the case of the function f(x,y) = 8x^2 - 8y, we want to find E(x,y) at the point (-1,-7).

First, we need to calculate f(-1,-7):

f(-1,-7) = 8(-1)^2 - 8(-7) = 56

Next, we need to find the linear function L(x,y) that approximates f(x,y) near (-1,-7). To do this, we can use the gradient of f(x,y) at (-1,-7):

∇f(-1,-7) = (16,-8)

The linear function L(x,y) is given by:

L(x,y) = f(-1,-7) + ∇f(-1,-7) · (x+1, y+7)

where · denotes the dot product.

Substituting the values, we get:

L(x,y) = 56 + (16,-8) · (x+1, y+7)

= 56 + 16(x+1) - 8(y+7)

= 8x - 8y

Finally, we can calculate the error term E(x,y) as:

E(x,y) = f(x,y) - L(x,y) - f(-1,-7)

= 8x^2 - 8y - (8x - 8y) - 56

= 8x^2 - 8x - 56

Therefore, the error term E(x,y) for the function f(x,y) = 8x^2 - 8y at the point (-1,-7) is E(x,y) = 8x^2 - 8x - 56.

To know more about differentiable:

https://brainly.com/question/29894954

#SPJ4

Step-by-step explanation:

Set it up as a ratio:

14 is to (14 +6)   as   21 is to  ?

14/20 = 21/?

? = 21 * 20 / 14 = 30 units

We can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams for standard deviation of 0.13 gram.

A normal distribution is a symmetric, bell-shaped continuous probability distribution that is defined by its mean and standard deviation. The majority of the data in a normal distribution is located close to the mean, and the number of data points decreases as you deviate from the mean in either direction. Because many real-world events, like human height or test scores, have a tendency to follow a normal distribution, the normal distribution is frequently utilised in statistics. A helpful technique for determining the range of values within a normal distribution based on the mean and standard deviation is the empirical rule, commonly known as the 68-95-99.7 rule.

Given that, the mean of 3.30 grams and standard deviation of 0.13 gram.

Using the empirical formula the range that falls in 95% is associated to two standard deviations.

Mean + 2 standard deviations = 3.30 + 2(0.13) = 3.56 grams

Mean - 2 standard deviations = 3.30 - 2(0.13) = 3.04 grams

Hence, we can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams.

Learn more about normal distribution here:

https://brainly.com/question/12421652

#SPJ1

The result of the cross breeding between the heterozygous and homozygous pea plant is  the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.

In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).

When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).

The possible combinations of alleles that the offspring can inherit from their parents are:

Gg x gg

Therefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.

Learn more on crossbreeding here;

https://brainly.com/question/8588470

#SPJ1

If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}

The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.

Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:

P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)

By the principle of inclusion-exclusion, we can write:

P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}

where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.

This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.

In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.

To learn more about probabilities click on,

https://brainly.com/question/14289336

#SPJ4

The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.

Martin features a spinner with four compartments marked A, B, C, and D.

To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.

Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

know more about the sample space

https://brainly.com/question/2117233

#SPJ1

Rhiannon arrived home approximately 17 minutes earlier than Alexander.

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

To solve this problem, we can use the formula:

time = distance / speed

a) The time it took Alexander to get home is:

time_Alexander = 14 km / 20 km/h = 0.7 hours

The time it took Rhiannon to get home is:

time_Rhiannon = 10 km / 24 km/h = 0.41667 hours

Since Rhiannon's time is smaller than Alexander's, Rhiannon arrived home earlier.

b) The time difference between their arrivals is:

time_difference = time_Alexander - time_Rhiannon = 0.7 hours - 0.41667 hours = 0.28333 hours

To convert this to minutes, we can multiply by 60:

time_difference_in_minutes = 0.28333 hours x 60 minutes/hour ≈ 17 minutes

Therefore, Rhiannon arrived home approximately 17 minutes earlier than Alexander.

To learn more about the average visit:

https://brainly.com/question/20118982

#SPJ1

Answer:

Step-by-step explanation:

Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.

We set up synthetic division as follows:

-1 | 1 -3 16 20

| -1 4 -20

|_____________

1 -4 20 0

The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:

x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))

= (4 ± sqrt(-64)) / 2

= 2 ± 2i√2

Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.

Answer:

the question is incomplete, so I looked for similar questions:

There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.

the answer = 3 x 4 x 2 = 24 possible combinations

Explanation:

for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich

since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24

If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.

For this question's answer, there are 2 x 5 = 10 lunch specials are possible.

The number of lunch specials possible are 10.

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total of

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]

This is called permutation of k items chosen out of m items (all distinct).

We are given that;

Number of sandwiches=2

Number of drinks=5

Now,

To find the total number of lunch specials, we need to multiply the number of choices for sandwiches by the number of choices for drinks.

Number of sandwich choices = 2

Number of drink choices = 5

Total number of lunch specials = 2 x 5 = 10

Therefore, by combinations and permutations there are 10 possible lunch specials.

Learn more about combinations and permutations here:

https://brainly.com/question/16107928

#SPJ2

Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:

A = B + 0.2B

Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:

A = 1.2B

Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:

(B lebih kecil dari A) / A x 100%

Substitusikan nilai A = 1.2B dan kita dapatkan:

(B lebih kecil dari 1.2B) / 1.2B x 100%

Maka:

0.2B / 1.2B x 100%

= 0.1667 x 100%

= 16.67%

Jadi, B adalah 16.67% lebih kecil dari A.

Untuk Konsultasi: 0813-7200-6413

Answer:

center: (0, -2)

radius: 6

Step-by-step explanation:

You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.

see image.

a) As per the given budget, the amount of interval that would be better for the city is 95% confidence interval.

b) The interval that be worse for the planners is depends on sample size

c) They achieve an interval estimate that would better serve their planning needs is depends on margin of error

d) The number of days worth of data should they collect to have confidence of estimating the true mean to 30 days

To obtain a better estimate, the city can create a confidence interval, which is a range of values that is likely to contain the true population mean with a certain degree of confidence.

However, there are also some disadvantages to using a confidence interval. The interval estimate may be wider than a point estimate, which means that the budget planners may have to allocate a larger budget to account for the uncertainty in the estimate.

To achieve a better interval estimate, the city could increase the sample size or reduce the variability of the data. Increasing the sample size reduces the margin of error and increases the precision of the estimate.

Finally, to determine how many days' worth of data the city should collect to estimate the true mean with a certain degree of confidence, the city would need to consider the desired level of precision, the variability of the data, and the desired level of confidence.

Typically, a larger sample size will provide a more accurate estimate, but this also depends on the variability of the data. In general, a sample size of at least 30 is recommended for a reasonably accurate estimate.

To know more about budget here

https://brainly.com/question/15683430

#SPJ4

The value of PF1 + PF2 equals to 10 for any point P on curve ellipse of equation 16x^2 + 25y^2 = 400. So, the correct answer is B).

We can start by finding the coordinates of the point P on curve of the ellipse. We can write the equation of the ellipse as:

16x^2 + 25y^2 = 400

Dividing both sides by 400, we get:

x^2/25 + y^2/16 = 1

So, the center of the ellipse is at the origin (0,0) and the semi-axes are a=5 and b=4.

Let the coordinates of point P be (x,y). Then, we can use the distance formula to find the distances PF1 and PF2:

PF1 = sqrt((x-3)^2 + y^2)

PF2 = sqrt((x+3)^2 + y^2)

Therefore, PF1 + PF2 = sqrt((x-3)^2 + y^2) + sqrt((x+3)^2 + y^2)

We can use the property that the sum of the distances from any point on an ellipse to its two foci is constant, and is equal to 2a, where a is the semi-major axis. So, we have:

PF1 + PF2 = 2a = 2(5) = 10

Therefore, PF1 + PF2 equals to 10 for any point P on the ellipse 16x^2 + 25y^2 = 400. So, the correct option is B).

To know more about Point on Curve:

https://brainly.com/question/22562758

#SPJ4

Using differentiation, the area of the triangle is decreasing at the given time.

The formula for the area of a triangle is:

A = (1/2)bh

where b is the base and h is the height.

Differentiating both sides of the equation with respect to time t, we get:

[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]

Substituting the given values, we get:

[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]

Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.

Learn more on area of a triangle here;

https://brainly.com/question/29255326

#SPJ1