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AysviL [449]
2 years ago
14

A bolt falls off an airplane at an altitude of 500 m. How long will it take the bolt to reach

Mathematics
1 answer:
Rudik [331]2 years ago
8 0

Answer:

t = sqrt(500/4.9) =~ 10.1 seconds/ Answer: 10.1015 seconds (this is approximate)

Step-by-step explanation:

Use 4.9t^2 + v0t = s

a) A bolt falls off an airplane at an altitude of 500 m. Approximately how long does it take the bolt to reach the ground?

s = 4.9t^2 + v0t = 500

4.9t^2 = 500

t = sqrt(500/4.9) =~ 10.1 seconds

Part A)

v = initial velocity = 0

s = 500 = vertical distance the object travels (from plane to ground)  

Plug in the given values and solve for t

4.9t^2 + v*t = s

4.9t^2 + 0*t = 500

4.9t^2 + 0 = 500

4.9t^2 = 500

t^2 = 500/4.9

t^2 = 102.04081632653

t = sqrt(102.04081632653)

t = 10.101525445522

t = 10.1015

Answer: 10.1015 seconds (this is approximate)

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PLEASE HELP 8th GRADE MATH QUESTION OVER HERE!!!
patriot [66]

The side AB measures option 2. \sqrt{20}} units long.

Step-by-step explanation:

Step 1:

The coordinates of the given triangle ABC are A (4, 5), B (2, 1), and C (4, 1).

The sides of the triangle are AB, BC, and CA. We need to determine the length of AB.

To calculate the distance between two points, we use the formula d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}.

where (x_{1},y_{1}) are the coordinates of the first point and (x_{2},y_{2}) are the coordinates of the second point.

Step 2:

For A (4, 5) and B (2, 1), (x_{1},y_{1}) = (4, 5) and (x_{2},y_{2}) = (2, 1). Substituting these values in the distance formula, we get

d=\sqrt{\left(2-4\right)^{2}+\left(1-5}\right)^{2}} = \sqrt{\left(2\right)^{2}+\left(4}\right)^{2}}=\sqrt{20}}.

So the side AB measures \sqrt{20}} units long which is the second option.

6 0
2 years ago
Kianna started her homework at 4:30 pm. She finished at 5:05 pm. How many SECONDS did it take her to finish her homework? *
lozanna [386]

Answer:

2100 second

Step-by-step explanation:

4:30 pm to minutes

4 × 60 + 30 = 240 + 30

= 270 minutes

5:05 to minutes

5 × 60 + 5 = 300 + 5

= 305

4:30 to 5:05

305 - 270

= 35 minutes

35 minutes to second

35 × 60

= 2100 second

6 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
Solve the following equations;-<br><br> x - 9 /√x + 3 =1
fgiga [73]

Answer:

13 , 6.

Step-by-step explanation:

A equation is given to us and we need to find out the value of x . The given equation to us is ,

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Cross multiply ,

\sf\implies x - 9 =\sqrt{ x +3}

Squaring both sides ,

\sf\implies (x - 9)^2 = x + 3

Simplify the whole square ,

\sf\implies x^2+9^2-2.9.x = x +3 \\

\sf\implies x^2+81 - 18x = x -3

Add 3 and subtract x on both sides ,

\sf\implies x^2 -18x-x +81-3=0

Simplify ,

\sf\implies x^2 -19x +78=0

Split the middle term of the quadratic equation,

\sf\implies x^2-13x-6x+78=0

Take out common ,

\sf\implies x( x -13)-6(x-13)=0

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Equate both factors to 0 ,

\sf\implies \boxed{\pink{\sf x = 13,6}}

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2 years ago
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW?
snow_lady [41]

Answer:

1. D. 1

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3. A. y=1/x

Step-by-step explanation:

too long to give te explanations but they're there in the attachments

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