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3 years ago

Suppose f is a one-to-one function with f(2)=8 and f’(2)=4. What is the value of (f^-1)’(8)?

Mathematics

1 answer:

yuradex [85]3 years ago

5 0

Answer:

1/4

Step-by-step explanation:

The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.

The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...

(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4

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forty-seven marbles are shared between some children. each child receives six marbles and there are five marbles left over. how

Nadya [2.5K]

The total number of children can be calculated using linear equation in one variable. The marbles are shared among 7children.

<u>Solution</u>

Total number of marbles = 47

The number of marbles received by each child = 6

Let the number of children be x

Then according to the question'

Total number of marbles received by all children + 5 = Total number of marbles

6x + 5 = 47

6x = 47- 5

6x = 42

x = 7

now, the number of children is 7.

<h3>What is linear equation in one variable?</h3>

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
Here, the variables x and y, the coefficients A and B, and the constant C are all present.
A linear equation's graph will always be a straight line.
One-variable linear equations are fairly simple to solve. To determine the value of the unknown variable, the variables are divided and placed on one side of the equation, and the constants are combined and placed on the other side.

Know more about linear equation brainly.com/question/12974594

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6 0

2 years ago

In circle S, angle QTR is an inscribed angle.<br><br><br> What is the measure of angle QRS?

docker41 [41]

<h2>Answer:</h2>

angle QRS = 51°

<h2>Step-by-step explanation:</h2>

The diagram for the question has been attached to this response.

From the diagram, some circle theorems can be applied.

<em><u>Circle theorem:</u></em>

The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any other point on the remaining part of the circle.

From the diagram, QR is the arc and therefore:

∠QSR = 2 x ∠ QTR

<em>Since ∠QTR = 39°</em>

=> ∠QSR = 2 x 39°

=> ∠QSR = 78°

<u><em>Other theorem:</em></u>

(i)The base angles of an isosceles triangle are equal.

Triangle QSR is an isosceles triangle, therefore, angles SQR and QRS are equal. i.e

∠SQR = ∠QRS

(ii) The sum of angles of a triangle is 180°. i.e

∠SQR + ∠QRS + ∠QSR = 180°

<em>Since ∠SQR = ∠QRS and ∠QSR = 78°</em>

=> ∠QRS + ∠QRS + 78° = 180°

=> 2(∠QRS) = 180° - 78°

=> 2(∠QRS) = 102°

<em>Divide both sides by 2</em>

=> ∠QRS = 51°

Therefore, angle QRS = 51°

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3 years ago

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umka21 [38]

Part 1. 9
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4 0

3 years ago

Someone please help me!!

Elenna [48]

This problem looks really scary am I right? Well, actually it isn't too bad.

Let me explain something really quick.
When two like terms are over each other they equal 1. For instance 3/3. In the case of two numbers with powers they can also cancel out if they are the same number to a power. Here is why:

3² / 3² = (3*3) / (3*3) = 9/9 = 1

What if the powers are unequal?

3²/3 = (3*3) / 3 = 9 / 3 = 3

In the case where the powers are unequal (in the case of the example we have a power of 2 and a power of 1) we simply SUBTRACT the powers. In the case where the bottom is bigger you'll have the following problem:

3²/3³ = (3*3) / (3*3*3) = 9 / 27 = 1/3

If you have trouble understanding the subtraction simply write out the multiplication. Then if you see numbers which are equal on the top on the bottom cross them out till there are no equal terms on the top or bottom. In the case above you can cross out the 2 threes at the top and are left with 1 three at the bottom.

For our problem: (Note the ^ symbol is the same as saying being brought to the power of... so it's equivalent to the problem you see on your screen!)

5^4 / 5^6 = (5*5*5*5) / (5*5*5*5*5*5) = 1 / (5*5) = 1 / 25

Our answer is:
1/25

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3 years ago

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In one year angelica's height went from 60 inches to 64 inches.what was the percent of increase in angelica's height?

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4 years ago