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2 years ago

Kate is constructing an equilateral triangle. She has already used her straightedge to construct the line segment shown.

1 answer:

7 0

The correct Answer is B. Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass. I just took the quiz and got it right.

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Which graph represents the function f(x) = -|x+3|?

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The last one is correct

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2 years ago

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How to I solve this please help!!! I will give Brainliest.

worty [1.4K]

Answer:

x is 35

Step-by-step explanation:

First do 180 -40 and get 140. Then add 3x plus x to get 4x because they are the same value/ Do 140/ 4x and get 35. X equals 35.

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2 years ago

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water will be both added to and drained from a bathtub at the same time for 5 minutes. the total amount of water added to the ba

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There would be 12 litres in the tub after 4 minutes

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2 years ago

An engineering student answered 81 questons correctly on a 90 question test. What percent of the question did she answer correct

anyanavicka [17]

Answer:

90% of the questions she answered correctly

Step-by-step explanation:

%age = 81/90 * 100= 90 % correctness

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2 years ago

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At x = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at x = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at x = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

4 0

2 years ago