1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Free_Kalibri [48]
2 years ago
12

Evaluate x-7;x=23 expression for the given value(s)of the variable(s).

Mathematics
1 answer:
Arada [10]2 years ago
5 0
x-7 \ for \ x=23 \\
23-7=16 \\ \\
\boxed{x-7=16 \ for \ x=23}
You might be interested in
Sean is comparing dog food prices.At pet foods store,the total weight of a bag of dog food varies directly with the number of ba
12345 [234]

Answer:

Step-by-step explained :

7 0
3 years ago
What is 3 divided by 11/12
Lena [83]

Answer:

0.02272

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tab
Leona [35]

Answer:

a. 5 b. y = -\frac{3}{4}x + \frac{1}{2} c. 148.5 d. 1/7

Step-by-step explanation:

Here is the complete question

Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f() is a real number Let f be an increasing function with f(0) = 2. The derivative of f is given by f'(x) = sin(πx) + x² +3. (a) Find f" (-2) (b) Write an equation for the line tangent to the graph of y = 1/f(x) at x = 0. (c) Let I be the function defined by g(x) = f (√(3x² + 4). Find g(2). (d) Let h be the inverse function of f. Find h' (2). Please respond on separate paper, following directions from your teacher.

Solution

a. f"(2)

f"(x) = df'(x)/dx = d(sin(πx) + x² +3)/dx = cos(πx) + 2x

f"(2) = cos(π × 2) + 2 × 2

f"(2) = cos(2π) + 4

f"(2) = 1 + 4

f"(2) = 5

b. Equation for the line tangent to the graph of y = 1/f(x) at x = 0

We first find f(x) by integrating f'(x)

f(x) = ∫f'(x)dx = ∫(sin(πx) + x² +3)dx = -cos(πx)/π + x³/3 +3x + C

f(0) = 2 so,

2 = -cos(π × 0)/π + 0³/3 +3 × 0 + C

2 = -cos(0)/π + 0 + 0 + C

2 = -1/π + C

C = 2 + 1/π

f(x) = -cos(πx)/π + x³/3 +3x + 2 + 1/π

f(x) = [1-cos(πx)]/π + x³/3 +3x + 2

y = 1/f(x) = 1/([1-cos(πx)]/π + x³/3 +3x + 2)

The tangent to y is thus dy/dx

dy/dx = d1/([1-cos(πx)]/π + x³/3 +3x + 2)/dx

dy/dx = -([1-cos(πx)]/π + x³/3 +3x + 2)⁻²(sin(πx) + x² +3)

at x = 0,

dy/dx = -([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)⁻²(sin(π × 0) + 0² +3)

dy/dx = -([1-cos(0)]/π + 0 + 0 + 2)⁻²(sin(0) + 0 +3)

dy/dx = -([1 - 1]/π + 0 + 0 + 2)⁻²(0 + 0 +3)

dy/dx = -(0/π + 2)⁻²(3)

dy/dx = -(0 + 2)⁻²(3)

dy/dx = -(2)⁻²(3)

dy/dx = -3/4

At x = 0,

y = 1/([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)

y = 1/([1-cos(0)]/π + 0 + 0 + 2)

y = 1/([1 - 1]/π + 2)

y = 1/(0/π + 2)

y = 1/(0 + 2)

y = 1/2

So, the equation of the tangent at (0, 1/2) is

\frac{y - \frac{1}{2} }{x - 0} = -\frac{3}{4}  \\y - \frac{1}{2} = -\frac{3}{4}x\\y = -\frac{3}{4}x + \frac{1}{2}

c. If g(x) = f (√(3x² + 4). Find g'(2)

g(x) = f (√(3x² + 4) = [1-cos(π√(3x² + 4)]/π + √(3x² + 4)³/3 +3√(3x² + 4) + 2

g'(x) = [3xsinπ√(3x² + 4) + 18x(3x² + 4) + 9x]/√(3x² + 4)

g'(2) = [3(2)sinπ√(3(2)² + 4) + 18(2)(3(2)² + 4) + 9(2)]/√(3(2)² + 4)

g'(2) = [6sinπ√(12 + 4) + 36(12 + 4) + 18]/√12 + 4)

g'(2) = [6sinπ√(16) + 36(16) + 18]/√16)

g'(2) = [6sin4π + 576 + 18]/4)

g'(2) = [6 × 0 + 576 + 18]/4)

g'(2) = [0 + 576 + 18]/4)

g'(2) = 594/4

g'(2) = 148.5

d. If h be the inverse function of f. Find h' (2)

If h(x) = f⁻¹(x)

then h'(x) = 1/f'(x)

h'(x) = 1/(sin(πx) + x² +3)

h'(2) = 1/(sin(π2) + 2² +3)

h'(2) = 1/(sin(2π) + 4 +3)

h'(2) = 1/(0 + 4 +3)

h'(2) = 1/7

7 0
3 years ago
The dual bar chart shows the hair colour of boys and girls in a year group. What fraction of the red haired students are boys? G
Step2247 [10]

Answer:

\frac{3}{4}

Step-by-step explanation:

Total red haired students = 15+5 = 20

Boys = 15

<u><em>Fraction:</em></u>

=> \frac{15}{20}

<u><em>In simplest form:</em></u>

=> \frac{3}{4}

3 0
3 years ago
Bill works for the Stuff It Mailing Service. He receives 25 cents for each document he puts together and prepares for
KATRIN_1 [288]

Answer:

(a)Bill's Total piecework pay =$500

(b)Amount owed by his boss=$26

Step-by-step explanation:

Let the number of documents put together and prepared for mailing by Bill =x

Bill receives 25 Cents=$0.25 for every document

Therefore for x documents, Bill should receive: $0.25x

If Bill prepared 2000 documents for mailing

x=2000

The amount he should receive = $0.25 X 2000 =$500

(a)Bill's Total piecework pay =$500

(b)Amount owed by his boss

=500-474

=$26

3 0
3 years ago
Other questions:
  • The volume of a prism is 8000 mm3. What is the volume of this prism, measured in cm3?
    9·1 answer
  • Find the median of the following data:<br> 9, 15, 17, 18, 6, 20, 8, 5, 18, 18, 10, 5, 14, 12, 10, 7
    9·2 answers
  • You have 6 donuts and you want to give 2/3 of them to a friend and keep 1/3 for yourself. How much of the whole pan of brownies
    8·2 answers
  • Find the slope of a line given the following two points: (-1, 3) and (5,-2).
    13·1 answer
  • Which of the following best represents the average rate at which a person can quickly walk? (2 points)
    14·1 answer
  • There are 24 kids in Miss Finns class 15 are boys how many are girls
    13·2 answers
  • The telephone company charges $1.35 fir the first 3 minutes of a phone call and $0.35 for each additional minute. i talk on the
    7·1 answer
  • Exercise 2
    15·1 answer
  • 2x + 4y = 12
    12·1 answer
  • "HOT PIZZA" is offering a 20% discount on all its pizza
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!