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2 years ago

Graph the line with slope -1/3 passing through the point (2, 1).

Mathematics

1 answer:

bogdanovich [222]2 years ago

5 0

Answer:

Step-by-step explanation:

y = mx + b

y = -x/3 + b

1 = -2/3 + b

b = 5/3

y = -x/3 + 5/3

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Identify each expression that represents the slope of a tangent to the curve y=1/x+1 at any point (x,y) .

tankabanditka [31]

Answer:

Slope of a tangent to the curve = $f'(x) = \frac{-1 }{(x+1)^{2} }$

Step-by-step explanation:

Given - y = 1/x+1

To find - Identify each expression that represents the slope of a tangent to the curve y=1/x+1 at any point (x,y) .

Proof -

We know that,

Slope of tangent line = f'(x) = $\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

We have,

f(x) = y = $\frac{1}{x+1}$

So,

f(x+h) = $\frac{1}{x+h+1}$

Now,

Slope = f'(x)

And

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \\= \lim_{h \to 0} \frac{\frac{1}{x+h+1} - \frac{1}{x+1} }{h}\\= \lim_{h \to 0} \frac{x+1 - (x+h+1) }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{x +1 - x-h-1 }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-h }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-1 }{(x+1)(x+h+1)}\\= \frac{-1 }{(x+1)(x+0+1)}\\= \frac{-1 }{(x+1)(x+1)}\\= \frac{-1 }{(x+1)^{2} }$

∴ we get

Slope of a tangent to the curve = $f'(x) = \frac{-1 }{(x+1)^{2} }$

6 0

3 years ago

Solve the missing elements for each problem. Use 3.14 for π. Area π r² ; C = π D

nalin [4]

<h3>Answer and Solution</h3>

1. Radius = 32/2 = 16 inches

Diameter = 32 inches

Circumference = 3.14 × 32 = 100.48 inches

Area = 3.14 × 256 = 803.84 inches

2. Radius :- 40 / 2 = 20 inches

Diameter = 40 inches

Circumference = 3.14 × 40 = 125.6 inches

Area = 3.14 × 20 × 20 = 1256 inches

3. Radius = 28 / 2 = 14 inches

Diameter = 28 inches

Circumference = 3.14 × 28 = 87.92 inches

Area = 3.14 × 14 × 14 = 615.44 inches

4. Radius = 18/2 = 9 inches

Diameter = 18 inches

Circumference = 3.14 × 18 = 56.52 inches

Area = 3.14 × 9 × 9 = 254.34 inches

5. Radius = 5 inches

Diameter = 5 × 2 = 10 inches

Circumference = 3.14 × 10 = 31.4 inches

Area = 3.14 × 5 × 5 = 78.5 inches

6. Radius = 2 inches

Diameter = 2 × 2 = 4 inches

Circumference = 3.14 × 4 = 12.56 inches

Area = 3.14 × 2 × 2 = 12.56 inches

8 0

3 years ago

Rectangle A, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0), B(6, 0), C(6,

Alenkinab [10]

The dimensions of the rectangle would be (6-2) x (7-0) = 4 x 7

That makes the area (4)(7) = 28.

That makes the perimeter (7+4)(2) = 22

That makes the diagonal sqrt((7^2)+(4^2)) = sqrt(49+16) = sqrt(65)

3 0

3 years ago

Rewrite the fraction as a decimal 15/4

Orlov [11]

Answer:

3.75

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find three consecutive integers have a sum of -36 what is the largest integer

Inessa [10]

3 consecutive integers : x, x + 1, x + 2

x + (x + 1) + (x + 2) = - 36...combine like terms
3x + 3 = -36...subtract 3 from both sides
3x = -36 - 3
3x = - 39....divide both sides by 3
x = -39/3
x = - 13

x + 1 = -13 + 1 = -12
x + 2 = -13 + 2 = -11

the largest integer would be -11

7 0

3 years ago