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
sergij07 [2.7K]
3 years ago
13

Emily started at 16 on a

Mathematics
2 answers:
Vikki [24]3 years ago
7 0
It is 50 numbers long
valkas [14]3 years ago
5 0
50 numbers in total :))))
You might be interested in
Which is the equation of the line that contains points (0, 5) and (5, 8)
AURORKA [14]
<span>Points: (0, 5) and (5, 8)Slope: 3/5 Equation: y = 3/5x+5 in slope intercept form.</span>
7 0
3 years ago
Read 2 more answers
I need help on these two problems
sattari [20]
50. since n_1/4<1 the equation is not true. it has no solution.
48. same thing since 45 <= z the equation is not true.
6 0
3 years ago
How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3?
ahrayia [7]

Answer:

4. Infinitely many

Step-by-step explanation:

5x + 3(x − 1) = 10x − 2x − 3

5x+3x-3=8x-3

5x+3x-8x=3-3

0=0

x∈R

6 0
3 years ago
Writing a geometry proof seems to take a very specific kind of skill along with a specialized vocabulary. Yet you have also seen
ANTONII [103]

In geometry proofs, we commonly use step-by-step logic to figure out the proof. This is commonly used in Computer Science for understanding how computers work, process, and store information(I speak from personal experience). This is also commonly used in Law. You use this in Law as a lawyer to deduce information using step-by-step logical processes and logic, otherwise it's just wishful thinking. So, Law also uses the same reasoning skills used in Geometry proofs.

3 0
2 years ago
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
Other questions:
  • Toxic Pollution: In the first year of a study, health officials discovered toxic pollutants in the soil surrounding a factory. T
    12·1 answer
  • The cost of renting a car is $26.60 plus $10 per day. Sales tax is 6%. Which 2 expressions represent the cost of renting a car f
    6·1 answer
  • The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed.
    7·1 answer
  • What is 3000000 5000 20 6 in standard form
    6·1 answer
  • Last year, a baseball team paid $10 per bat and $6 per glove, spending a total of $520. This year, the prices went up to $15 per
    14·1 answer
  • A right triangular prism is for meters long and 5 m wide with a high of 8 m what is the volume
    15·2 answers
  • What is the scale factor? Is it a reduction or an enlargement? ​
    12·2 answers
  • Pls help. (Use answers below)
    14·2 answers
  • I need help bad plz.
    15·2 answers
  • Samir also picks pumpkins from his garden. He picked 6 7/10 kg, but 2.6 of pumpkins were spoiled and could not be used for decor
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!