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3 years ago

Find the gradient of the line passing through (6,8) and (4,10)

Mathematics

1 answer:

Mariulka [41]3 years ago

7 0

Question:

Find the gradient of the line passing through (6,8) and (4,10).

Answer:

-1 is the right answer.

Step-by-step explanation:

Slope of the line = The gradient of the line

Gradient of the line is known as change in the value of y-axis by change in the value of x-axis

Gradient = ∆y\∆x

$Gradient = \frac{y_ 2 - y_1}{x_2 - x_1} = \frac{(10 - 8)}{(4 - 6)} = \frac{(2)}{(- 2)} =\boxed{- 1}\\$

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Evaluate the function at the given numbers( correct to six decimal places). Use the results to guess the value of the limit or e

netineya [11]

Answer:

Value of the limit is 0.5.

Step-by-step explanation:

Given,

$F(x)=\frac{e^x-1-x}{x^2}$

When,

$x=1,F(1)=frac{e^1-1-1}{1}=e-2=0.718281$

$x=0.5, F(0.5)=\frac{e^0.5-1-0.5}{(0.5)^2}=0.594885$

$x=0.1, F(0.1)=\frac{e^0.1-1-0.1}{(0.1)^2}=0.517091$

$x=0.05, F(0.05)=\frac{e^0.05-1-0.05}{(0.05)^2}=0.508438$

$x=0.01, F(0.01)=\frac{e^0.01-1-0.01}{(0.01)^2}=0.501670 \hfill (1)$

Correct upto six decimal places.

Now,

$\lim_{x\to 0}F(x)=\lim_{x\to 0}\frac{e^x-1-x}{x^2}$ $(\frac{0}{0})$ form, applying L-Hospital rule that is differentiating numerator and denominator we get,

$\lim_{x\to 0}F(x)$

$=\lim_{x\to 0}\frac{e^x-1}{2x}$ $(\frac{0}{0})$ form.

$=\lim_{x\to 0}\frac{e^x}{2}=\frac{1}{2}=0.5\hfill (2)$

Limit exist and is 0.5. That is according to (1) we can see as the value of x lesser than 1 and tending to near 0, value of the function decreases respectively. And from (2) it shows ultimately it decreases and reach at 0.5, consider as limit point of F(x).

8 0

3 years ago

What area is this composite figure??

klemol [59]

This composite figure consists of a right triangle and semicircle

The area of a triangle is: 1/2(bh)

The area of a semicircle is 1/2(pi)(r²)

Plug in the values:

1/2( 12)(8)

=48

1/2(3.14)(4²)

=25.12

25.12+48=73.12

Hope this helped :)

3 0

3 years ago

If u=(0,3), what is the magnitude of 3u

Rina8888 [55]

Answer:

<em>9.</em>

Step-by-step explanation:

3 * √)0^2 + 3^2)

= 3*3

= 9.

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3 years ago

Question and answer in picture

Andrews [41]

Answer:

i think the answer is B but don't take my word for it

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3 years ago

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Simplify the sum. Answers in the attachment. Will award brainliest.

pychu [463]

Answer:

your answer is C.

Step-by-step explanation:

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3 years ago