A rectangular garden has a perimeter of 174 feet. The length is 9 feet more than twice the width. Find the length and the width.

Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture

ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

x^2 = 1

x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

f(-1) = (-1)^3 = -1

So, using the points (1,1) and (-1,-1) in our parallel line, we have:

first line using (1,1) : 1 = 3*1 + b

b = -2

second line using (-1,-1) : -1 = -3*1 + b

b = 2

The value of b is the y-intercept of the line, so the line with smaller y-intercept is y = 3x - 2, and the line with larger y-intercept is y = 3x + 2

8 0

3 years ago

Please help meeeeeeee

slavikrds [6]

D no Solution would be the answer

7 0

2 years ago

Which of the statements are true about the function f given by f(x) = 100-e? Select all that apply.

tatiyna

From the above function, it is clear that the value of f is never 0. Hence the statement that is true is (Option E), See explanation of same below.

<h3>What is the explanation for the above function?</h3>

Note that the function is related to Euler's number which is depicted as:
e ≈ 2.7182. The function is given as:

f(x) = 100 * $e^{-x}$

Assuming x = -2, we'd have:

100 * 2.7182 $^{-2}$

= 271.82 $^{-2}$

= 0.00001353354

Hence, even when x tends < 0 the function f(x) thus, is never 0. See the attached graph for confirmation.

Learn more about functions at:

brainly.com/question/25638609

#SPJ1

6 0

2 years ago

0.6(6.5x10^5) simplify

EleoNora [17]

Exact form : 3.9*10^5
decimal form : 390000

4 0

3 years ago

What is the first step in solving the equation x2 – 16/25 = 0?

Keith_Richards [23]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-(16/25)=0

Step by step solution :Step 1 : 16 Simplify —— 25 Equation at the end of step 1 : 16 (x2) - —— = 0 25 Step 2 :Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 25 as the denominator :

x2 x2 • 25 x2 = —— = ——————— 1 25

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x2 • 25 - (16) 25x2 - 16 —————————————— = ————————— 25 25 Trying to factor as a Difference of Squares :

2.3 Factoring: 25x2 - 16

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5
Check : 16 is the square of 4
Check : x2 is the square of x1 

Factorization is : (5x + 4) • (5x - 4)

Equation at the end of step 2 : (5x + 4) • (5x - 4) ——————————————————— = 0 25 Step 3 :When a fraction equals zero : 3.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

(5x+4)•(5x-4) ————————————— • 25 = 0 • 25 25

Now, on the left hand side, the 25 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
(5x+4) • (5x-4) = 0

Theory - Roots of a product :

3.2 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.3 Solve : 5x+4 = 0

Subtract 4 from both sides of the equation :
 5x = -4
Divide both sides of the equation by 5:
 x = -4/5 = -0.800

Solving a Single Variable Equation :

3.4 Solve : 5x-4 = 0

Add 4 to both sides of the equation :
 5x = 4
Divide both sides of the equation by 5:
 x = 4/5 = 0.800

x = 4/5 = 0.800
 x = -4/5 = -0.800

3 0

3 years ago

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