if f(x) = f(g(x)), where f(−2) = 2, f '(−2) = 2, f '(0) = 2, g(0) = −2, and g'(0) = 3, find f '(0). f '(0) =

Answers

Answer 1

Using the chain rule, Therefore, f'(0) = 2.

Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) to obtain :

f'(x) = f'(g(x)) * g'(x)

substitute x = 0, we get:

f'(0) = f'(g(0)) * g'(0)

We are given that g(0) = -2 and g'(0) = 3. Therefore, we need to find g(0) and g'(0) in order to determine f'(0).

To do this, we can use the fact that f(x) = f(g(x)). Substituting x = 0 into this equation, we get:

f(0) = f(g(0))

Since f(-2) = 2, we have:

f(g(0)) = f(-2)

Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) with respect to x to obtain:

f'(x) = f'(g(x)) * g'(x)

substitute x = -2, we get:

f'(-2) = f'(g(-2)) * g'(-2)

We are given that f'(-2) = 2 and g'(-2) = 3. Therefore, we can solve for f'(g(-2)):

f'(g(-2)) = f'(-2) / g'(-2) = 2/3

Since f'(x) = f'(g(x)) * g'(x), we can substitute g(0) = -2 and f'(g(-2)) = 2/3 into the equation f'(0) = f'(g(0)) * g'(0) to obtain:

f'(0) = f'(g(0)) * g'(0) = f'(g(-2)) * g'(0) = (2/3) * 3 = 2

Therefore, f'(0) = 2.

To learn more about  chain rule:

https://brainly.com/question/28972262

#SPJ4


Related Questions

please help I domt understand​

please help I domt understand

Answers

Standard form of an equation is Ax + By = C
So here, y = 2/5 * x - 3
y = (2x - 15) / 5
5y = 2x - 15
2x - 5y = 15

PLS HELP!! right answer = gets

PLS HELP!! right answer = gets

Answers

The awnswer is (1,-3) (if I'm not right try typing it it an app called math away it can solve that no problems)

Solve the equation : 12/x+2

Solve the equation : 12/x+2

Answers

Answer:

the third answer x= 18 only is correct

Felipe bought a collection of 525 old sports cards at a
garage sale. He decided to sort them into piles of baseball
players, football players, soccer players, basketball players
and hockey players . He was surprised to find that each
pile of cards had an equal amount. How many of each type
of card was in his collection?

Answers

Answer:

105 in each pile of cards .5 types of card in his collection

Solve for a? Please help

Solve for a? Please help

Answers

we can answer it as follow

The red one show the GCF factor form it is -7 then you you ommit negative of numinator by negative of denominator . then you multiply both side by 4/7

the you simplify and solve a .

Solve for a? Please help

PLS HELP WRITE EACH EXPRESSION AS A SINGLE POWER DO NOT EVALUATE

PLS HELP WRITE EACH EXPRESSION AS A SINGLE POWER DO NOT EVALUATE

Answers

Answer:

1.  3³

2.  (-5)⁴

3.  3¹⁰

4.  4⁰

Step-by-step explanation:

When multiplying exponents with the same base, you add the exponents.  When dividing exponents with the same base, you subtract the exponents.  When raising a number with an exponent to another power, multiply the exponents.

1.  \(\frac{3^4*3^6}{3^2*3^5} =\frac{3^{10}}{3^7}=3^3\)

2.  \(\frac{(-5)^{12}}{(-5)^3*(-5)^5} =\frac{(-5)^{12}}{(-5)^8}=(-5)^4\)

3.  \((3^2)^5=3^{10}\)

4.  \(\frac{4^0*4^4}{4^1 * 4^3} =\frac{4^4}{4^4}=4^0\)

Explain how to modify the graphs F(x) and g(x) to graph the solution to set the following system of inequalities. How can the solution set be identified? Y>x^2-1
Y<-x^2+4

Explain how to modify the graphs F(x) and g(x) to graph the solution to set the following system of inequalities.

Answers

The following rigid transformations are applied:

Reflection around the line y = -1.Translation 5 units in the +y direction.

The solution set is found by the fact that the domain of quadratic functions is the entire real domain.

How to apply rigid transformations to understand the differences between two given functions

According to the Euclidean geometry, rigid transformations are those transformations applied on geometrical loci such that Euclidean distances are conserved in every point of the loci. Reflections and translations are sound examples of rigid transformations.

In this question we must derive all needed rigid transformations to turn f(x) into g(x), both quadratic functions. After a careful analysis we conclude that the following rigid transformations are applied:

Reflection around the line y = -1.Translation 5 units in the +y direction.

The solution set is represent by all x-values such that the function exists. According to real algebra we remember that the domain of quadratic functions is the real domain. Thus, the solution sets of f(x) and g(x) are the real domain.

To learn more on rigid transformations, we kindly invite to check this verified question: https://brainly.com/question/1761538

The Anderson family is preparing for a family reunion they think they will need 18 juice boxes for every six children who attend how many juice boxes will they need if they are expecting 28 children

Answers

The answer will be 84 juice boxes.

If you divide 18 juice boxes by 6 children, that’s 3 juice boxes per child. Since they are expecting 28 children, you multiply the rate of 3 juice boxes by 28 to get 84.

Answer:

84

Step-by-step explanation:

If it's 18 juice boxes for 6 children then the ration is 6:18. Since both numbers are divisible by 3, do that. You then get a ratio of 2:6, both of those are divisible by 2, do that and get 1:3. So there's 3 juice boxes per kid, so multiply 28x3 and get 84.

according to your text, which of the following is the primary source of primate endangerment today? habitat destruction human diseases social stress and dislocation use of primates for pets

Answers

Based on the text, the primary source of primate endangerment today is habitat destruction.

Habitat destruction is considered the primary source of primate endangerment based on various factors mentioned in the text. Primates, like many other species, heavily rely on their natural habitats for survival, including food, shelter, and breeding. However, human activities such as deforestation, urbanization, and land conversion for agriculture or infrastructure development have significantly reduced and fragmented primate habitats.

Habitat destruction leads to the loss of critical resources and disrupts the ecological balance necessary for primate populations to thrive. As their habitats shrink, primates face increased competition for limited resources, reduced access to food and water sources, and decreased opportunities for successful reproduction and rearing of offspring. This loss of habitat also exposes primates to increased vulnerability to predation, disease transmission, and human-wildlife conflicts.

To know more about primate,

https://brainly.com/question/30667610

#SPJ11

If a student picked is 10 years old, what
are the chances that they skip breakfast?

If a student picked is 10 years old, whatare the chances that they skip breakfast?

Answers

Answer:

There are 29% chance that they will skip their breakfast

Step-by-step explanation:

40 / 14 x 10 = the percentage of the kid skipping his breakfast

40 / 14 x 10 = 28.5%

28.5 = (rounded off) = 29%

The kid has a 29% chance of skipping the breakfast

Does anyone know the last two? Match the correct property to the equation showing that property.

Does anyone know the last two? Match the correct property to the equation showing that property.

Answers

Explanation: The 4th one is the distributive property because it shows an     equal sign and the 5th one is the inverse property of addition because it uses more than addition.

Answer: 4th one is distributive property 5th one is inverse property of addition

P.S. I am sure 95% sure that I am correct.

a rectangular prism has a length of 8 in., a width of 4 in., and a height of 214 in.the prism is filled with cubes that have edge lengths of 14 in.how many cubes are needed to fill the rectangular prism?

Answers

To fill the rectangular prism we need 1 cube.

To find the number of cubes needed to fill the rectangular prism, we can calculate the volume of the prism and divide it by the volume of a single cube.

The volume of the rectangular prism is given by the formula:

Volume = Length × Width × Height

Substituting the given values:

Volume = 8 in. × 4 in. × 21 in.

Volume = 672 in³

The volume of a cube is given by the formula:

Volume = Edge Length³

Substituting the given edge length:

Volume of a cube = (14 in.)³

Volume of a cube = 2744 in³

Now, we can divide the volume of the prism by the volume of a single cube to find the number of cubes needed:

Number of cubes = Volume of prism / Volume of a single cube

Number of cubes = 672 in³ / 2744 in³

Calculating this division gives:

Number of cubes ≈ 0.245

Since we cannot have a fraction of a cube, we need to round up to the nearest whole number. Therefore, we would need 1 cube to fill the rectangular prism.

Learn more about cube at https://brainly.com/question/14973490

#SPJ11

4 3/7 + 6 1/5 = ?
Please EXPLAIN!!!
I'm too lazy and when I lazy I not so smart ;)

Answers

Answer:

Welp here is the answer to your question, 372/35 in exact form. in mixed number form it is 10 22/35

Find the difference of (t−8)−(t+15)

Answers

Answer:

Step-by-step explanation:

(t-8)-(t+15)

t-8-t-15

t-t-8-15

-23

The value of the expression after subtraction will be;

⇒ - 23

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (t - 8) - (t + 15)

Now,

Subtract the expression as;

⇒ (t - 8) - (t + 15)

⇒ t - 8 - t - 15

⇒ t - t - 8 - 15

⇒ - 23

Thus, The value of the expression after subtraction will be;

⇒ - 23

Learn more about the subtraction visit:

https://brainly.com/question/28467694

#SPJ2

which of the following equations represent a line that is parallel y=5x-4 ad passes through the point (3,4)

Answers

The equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.

How to write the point-slope form equation?

We are given that

The slope of given line = 5And passed through point (3, 4)

Slope of parallel lines is the same, so slope of the line parallel to the given line will be m = 5

We have the slope and a point, using the point-slope form we can write the equation of the line:

\(\rightarrow\text{y} - 4 =5 \ (\text{x} - 3)\)

\(\rightarrow\text{y} = 5\text{x} - 15 + 4\)

\(\rightarrow\bold{y = 5x - 11}\)

Hence, the equation that represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4) is y = 5x - 11.

To know more about point-slope form, visit:

https://brainly.com/question/28895991

Your question is incomplete. The complete question is-

Which of the following equations represents a line that is parallel to y = 5x - 4 and passes through the point (3, 4)?

A. y = 5x - 7

B. y = 5x + 19

C. y = -1/5x -4

D. y = 5x - 11

what is 32z-48 factored with gcf

Answers

Answer:

We found the factors and prime factorization of 32 and 48. The biggest common factor number is the GCF number. So the greatest common factor 32 and 48 is 16.

Step-by-step explanation:

What is the GCF of 32and 48?

16

Greatest common factor (GCF) of 32 and 48 is 16.

i if (x == null) return alreadyreversed; node y = x.next; x.next = alreadyreversed; return reverse (y, x);

Answers

The code snippet is a recursive function to reverse a singly linked list.

When the current node (x) is null, it returns the already reversed list. Otherwise, it reverses the remaining list and returns the result.

The code is a part of a recursive function that aims to reverse a singly linked list. It starts by checking if the current node (x) is null, meaning that the end of the list has been reached. If true, it returns the already reversed part (alreadyreversed).

If the current node is not null, it proceeds to the next step by assigning the next node (y) as x.next. Then, it changes the next pointer of the current node (x) to point to the already reversed part (x.next = alreadyreversed).

Finally, it calls the same function again with the updated parameters (reverse(y, x)) to continue reversing the remaining list. This process continues until the base case (x == null) is encountered, and the fully reversed list is returned.

To know more about recursive function click on below link:

https://brainly.com/question/30027987#

#SPJ11

3. true or false? (ln n) 2 is big-o of n. justify your answer

Answers

False.

To determine whether (ln n)^2 is big-O of n, we need to examine the growth rates of both functions as n approaches infinity.

The function (ln n)^2 grows much slower than the function n. Taking the logarithm of n twice results in a logarithmic growth rate, which is significantly slower than the linear growth rate of n.

In the big-O notation, we are concerned with the worst-case behavior of a function. For (ln n)^2 to be big-O of n, there must exist constants c and n0 such that (ln n)^2 ≤ c * n for all n ≥ n0.

However, no matter what constants c and n0 we choose, there will always be an n large enough where (ln n)^2 exceeds c * n. Therefore, (ln n)^2 is not big-O of n.

Hence, the statement is false.

To know more about  functions refer here

https://brainly.com/question/21145944#

#SPJ11

The latest online craze is a new game,khan on seven. You get 100 points for playing the game. In addition,you get 50 points for each seven-letter word you make with the ten letter you receive.sal wants to break the record,and he needs 18,000 or more points to do so

Answers

Answer:

how do I get started here

help meeeeeeeeeeeeeee pleaseeeeeee

help meeeeeeeeeeeeeee pleaseeeeeee

Answers

Answer: Width = 5.7 feet, Length = 10.5 feet

Step-by-step explanation:

Let the width be w. Then, the length is 2w-0.9.

\(w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5\)

A standard pair of six-sided dice is rolled. what is the probability of rolling a sum less than 8? express your answer as a fraction or a decimal number rounded to four

Answers

The answer is 0.5833 using probability.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

When two dice are rolled sample space is of 36 elements.

The elements which give sum less than 8 are given as follow

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5)

(3,1),(3,2),(3,3),(3,4)

(4,1),(4,2),(4,3)

(5,1),(5,2)

(6,1)

Here the total number of elements that satisfy conditions is 21

Hence probability is given by (21/36)

Probability=0.5833

Learn more about probability, by the following link.

https://brainly.com/question/24756209

#SPJ4

Which of this is NOT a family of antiderivative of 2(3x + 2) ? a. 3 2(3x + 2)4 - +C 12 (3x + 2)4 - -C 6 b. 4(3x + 2)4 12 + K (3x + 2) 6 + K

Answers

4(3x + 2)4 12 + K (3x + 2) 6 + K is NOT a family of antiderivative of 2(3x + 2). The correct answer is Option b.


To find the antiderivative of 2(3x + 2), follow these steps:

1. Notice the function is 2(3x + 2).
2. Apply the power rule of integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1.
3. In this case, n = 1, so the antiderivative is (2(3x + 2)^2)/(2) + C.
4. Simplify to obtain (3x + 2)^2 + C.

Option b doesn't match this result, so it is NOT a family of antiderivatives of 2(3x + 2).

Learn more about antiderivative:

https://brainly.com/question/12956882

#SPJ11

there are 15 different colored marbles in a bag and you have one six-sided die. if you roll the die and choose a marble, how many possible combinations of marble color and die number are possible?

Answers

There are 90 possible combinations of marble color and die number that are possible from a bag of 15 different colored marbles and rolling one six-sided die.

This can be determined using the multiplication principle of counting.

The multiplication principle of counting can be used to find the number of ways two or more tasks can be performed together. The principle states that if there are m ways to perform task A and n ways to perform task B, then there are m × n ways to perform both tasks A and B.

To apply the multiplication principle of counting to this problem, we need to determine the number of ways the die can land and the number of ways a marble can be chosen. There are six possible outcomes of rolling a six-sided die, and there are 15 different colored marbles to choose from. Thus, the number of possible combinations of marble color and die number is: 15 different colored marbles × 6 possible die numbers= 90 possible combinations.

To know more about possible combinations: https://brainly.com/question/29089154

#SPJ11

A rectangle has an area of 36 square centimeters. The width of the rectangle is 4 centimeters.
What is the length of the rectangle?

Answers

A=lw
A/w=l
36/4=l
9=l
The length of the rectangle is 9cm

Compute the range for a distribution where the highest score is 89 and the lowest score is 27.

Answers

Answer:

The range of the distribution is 62

Step-by-step explanation:

Here in this question, we are interested in computing the value for the range.

Mathematically;

range = Highest value - lowest value

from the question, highest valve = 89 while lowest value = 27

Plugging the values into the range equation, we have;

Range = 89-27 = 62

Nadya deposited $1,000 into a savings account that pays 3. 5% simple interest per year. Which expression represents the value of her investment after 8 years?

Answers

The expression that represents the value of Nandy's investment after 8 years is A = 1000 (1 + 3.5(8)).

What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

So, the expression that can represent the above situation is:

The total money Nadya deposited is $1000.

Interest is 3.15%.

Total years are 8.

Simple interest formula: A = P (1 + rt)

Where a is the final amount, p is the principal amount, r is the interest return and t is the time in years.

Then, we have:

A = 1000 (1 + 3.5(8))

A = 1000(29)

A = 29,000

Therefore, the expression that represents the value of Nandy's investment after 8 years is A = 1000 (1 + 3.5(8)).

Know more about expressions here:

https://brainly.com/question/28934492

#SPJ4

Find the area of each figure. Round to the nearest hundredth where necessary. Only 1 and 5 please!

Find the area of each figure. Round to the nearest hundredth where necessary. Only 1 and 5 please!

Answers

Answer:

See below

Step-by-step explanation:

To begin, it is volume, not area

1. 8 x 12 x 17 = 1632 in ^3

5. 9 x 9 x 13.5 = 1093.5 in^3

If you want to find SURFACE AREA:

1. 2(8 x 12) + 2(8 x 17) + 2(17 x 12) = 872 in^2

5. 2(9 x 9) + 4(9 x 17) = 774 in^2

for the function f whose graph is given below, list the following quantities in increasing order, from smallest to largest. a: ∫80f(x)dxb: ∫30f(x)dxc: ∫85f(x)dxd: ∫50f(x)dx

Answers

Therefore, we can order the integrals as follows, from smallest to largest:

a: ∫80f(x)dx (interval [3, 0], negative values, short length)

b: ∫30f(x)dx (interval [0, 5], positive values, longer length)

d: ∫50f(x)dx (interval [0, 5] and part of [5, 8], positive values, longest length)

c: ∫85f(x)dx (interval [5, 8], positive values, short length)

However, we can compare the given intervals in terms of their length and the position of the function on those intervals to determine the order of the integrals. From left to right, the intervals and their approximate lengths are:

Interval [3, 0]: length 3

Interval [0, 5]: length 5

Interval [5, 8]: length 3

Now we need to examine the position of the function on each interval. From the graph, we can see that the function is negative on the interval [3, 0] and positive on the intervals [0, 5] and [5, 8].

To know more about integrals,

https://brainly.com/question/29208679

#SPJ11

Complete question:

For the function f whose graph is given below, list the following quantities in increasing order, from smallest to largest.

a: ∫80f(x)dx

b: ∫30f(x)dx

c: ∫85f(x)dxd: ∫50f(x)dx

i need help with this question, thx to anyone who helps! :)

i need help with this question, thx to anyone who helps! :)

Answers

Answer:

Golf balls

Step-by-step explanation:

There is a much higher chance of her picking an even number in the golf ball tank because there are way more golf balls with even numbers. (2, 4, 6, 8, etc.)

How do you find the inverse of a matrix in Matlab?

Answers

In Matlab, you can find the inverse of a matrix using the "inv" function. This will calculate the inverse of matrix A and store the result in matrix B. If A is invertible, then B will contain the inverse of A. If A is not invertible, Matlab will return an error.

Suppose you have a matrix "A", and you want to find its inverse. You can do this by typing:

B = inv(A);

This will calculate the inverse of matrix A and store the result in matrix B. If A is invertible, then B will contain the inverse of A. If A is not invertible, Matlab will return an error.

Note that calculating the inverse of a matrix can be computationally expensive and should be avoided if possible. In some cases, it may be more efficient to use other methods, such as solving a system of linear equations using the backslash operator.

Learn more about matrix :

https://brainly.com/question/28180105

#SPJ4

Other Questions
Consider a search engine Sen for news documents.Sen is supported by a crawler Chad.Chad downloads documents from a web of authenticated source-databases producing verified news. The databases are frequently assessed and rated by each other as well by readers of news. Ratings by readers who read a large number of documents from a variety of sources weigh more than ratings by readers who read very little or read only from a limited set of sources. Ratings by sources that are rated high weigh more than ratings by sources that are not rated high. Sen is also supportedby an indexing system, Ida. Ida filters documents downloaded by Chad for content free of violence, orders them based on chronology as well asthe ratings assigned to the sources (i.e. the databases), and stores them in an inverted index. Explain which of the ranking models - amongPopularity, Quality, Relevance, Suitability, and Timeliness - are used and how by Sen? Find the value of log1/1000 Could someone tell me if they are right???? I need help please what does it mean by the term self demagnetization. Use the Law of Sines to find all triangles if a = 50", a =25, b = 26. While working, keep at least 4 decimal places. Round all final answers to 2 decimal places. Based on the audio, Paulina and her friend ________. van a la playa van al centro comercial van al parque van a la piscina Hi! This assignment is due soon! Can someone help me with transversals of parallel lines: solve for x. Thank you! EXPLAIN why volcanoes are more likely to be found along the Ring of Fire. (3 points)Include these words in your explanation: friction, lithospheric plates, magma CAN SOMEONE PLEASE GIVE ME EXPLANATION g Determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration. Group of answer choices 13 3 26 4 75 On March 27 2021, Bank of Canada Governor Stephen Poloz unveiled a plan to buy a minimum of $5 billion a week in Government of Canada bonds. When the Bank of Canada finances Canada's debt directly by buying Government bonds, some people say that it is effectively "printing money" in the sense that it provides the Government with an interest-free loan. Technically, the Government does pay an interest on the loan from the Bank of Canada, but those interests will in the most part be returned to the Government as dividend because the Government owns the central bank. QUESTION: In the context of 2021, why was this monetary policy more likely to expand the money supply than the usual policy of lowering interest rates? Select ALL relevant answers, if any. Because in 2021, the interest rate was already very close to zero and could hardly be lowered any more. Because in a time of economic uncertainty, people may be reluctant to borrow even if the interest rates are lowered. Because the trilemma of exchange rate does not allow to conduct monetary policy for domestic purposes while having a fixed exchange rate. Because "printing money" creates inflation If ammonium phosphate reacts with sodium chloride in aqueous solution, what are the products? What is 2/3n plus 3/2n equals negative 13/4 The work done when a force moves a body through a distance of 15m is 1800j. What is the value of the force applied Which is the graph of x298.6? ?95 6 97 98 9 100 101 102 10305 96 97 8 9 100 01 102 103||||-+95 6 7 8 9 100 100 10 103|||| + ++ +++95 6 7 8 9 100 101 102 103 A student is planning to produce and sell music DVDs for $5.50 each. A computer with a DVD burner costs $800, and eachblank DVD costs $1.50. Let x represent the number of DVDs he makes. Express the cost C as a function of x From what country did the term cowboy originate, which influenced the American cowboy?A. MexicoB. EnglandC. CanadaD. Brazil the nurse is caring for a client who is receiving amikacin for the treatment of a serious staphylococcus aureus infection. what assessment should the nurse prioritize? A pinhole camera has a small circular aperture of diameter D. Light from distant objects passes through the aperture into an otherwise dark box, falling on a screen at the other end of the box. The aperture in a pinhole camera has diameter D=0.600mm. Two point sources of light of wavelength 550nm are at a distance L from the hole. The separation between the sources is 2.80cm, and they are just resolved by the camera. What is L? 3. A drone takes off from the base of a mountain at a height of 27 ft below sea level. The dronethen flies up 642 ft before landing at the top of the mountain. How tall is the mountain? (I WILL MARK BRAINLIEST) After reading the excerpt, describe what happened in 1977 and 1984 as it relates to competitive advantage."In 1977, there was a severe drought on Daphne Major. All the vegetation on the island was affected. Most of the finches died. The birds quickly ate all the small, soft seeds. In time, only the large, tough seeds remained. During this drought, when food was scarce, the small finches with smaller beaks died. The finches with larger, stronger beaks that could eat the harder seeds survived. The Grants found that the offspring of the birds that survived the 1977 drought tended to be larger and have bigger beaks. Now, in 1984 1985, the Grants studied the birds during a season with heavy rainfall. They found that during the year with heavy rainfall, the birds that were best able to consume the small, soft seeds survived and reproduced, while the birds that could only eat the heavier seeds died. Those birds then produced offspring that had beaks that were suitable for eating small, soft seeds. The birds that had the beaks that were most useful for consuming the type of seed that was most abundant in any given season had competitive advantage over other birds. Species with a competitive advantage in a given environment have a greater chance of surviving and reproducing. The Grants found that adaptations can occur within a few generations."