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vredina [299]
2 years ago
11

a manufacturer of bicycle parts requires that a bicycle chain have a width of 0.3 inch with an absolute deviation of at most 0.0

003 inch. write and solve an absolute value inequality that represents the acceptable widths.
Mathematics
1 answer:
quester [9]2 years ago
3 0

Answer:

|w-0.3| \leq 0.0003

And solving we got:

-0.0003 \leq w-0.3 \leq 0.0003

0.3-0.0003 \leq w \leq 0.3+0.0003

0.2997 \leq w \leq 0.3003

Step-by-step explanation:

For this case we can define the following notation:

W represent the width

And we want a maximum error of 0.0003 so we can set up the following equation:

|w-0.3| \leq 0.0003

And solving we got:

-0.0003 \leq w-0.3 \leq 0.0003

0.3-0.0003 \leq w \leq 0.3+0.0003

0.2997 \leq w \leq 0.3003

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In right ABC, AN is the altitude to the hypotenuse. FindBN, AN, and AC,if AB =2 5 in, and NC= 1 in.
Rama09 [41]

From the statement of the problem, we have:

• a right triangle △ABC,

,

• the altitude to the hypotenuse is denoted AN,

,

• AB = 2√5 in,

,

• NC = 1 in.

Using the data above, we draw the following diagram:

We must compute BN, AN and AC.

To solve this problem, we will use Pitagoras Theorem, which states that:

h^2=a^2+b^2\text{.}

Where h is the hypotenuse, a and b the sides of a right triangle.

(I) From the picture, we see that we have two sub right triangles:

1) △ANC with sides:

• h = AC,

,

• a = ,NC = 1,,

,

• b = NA.

2) △ANB with sides:

• h = ,AB = 2√5,,

,

• a = BN,

,

• b = NA,

Replacing the data of the triangles in Pitagoras, Theorem, we get the following equations:

\begin{cases}AC^2=1^2+NA^2, \\ (2\sqrt[]{5})^2=BN^2+NA^2\text{.}\end{cases}\Rightarrow\begin{cases}NA^2=AC^2-1, \\ NA^2=20-BN^2\text{.}\end{cases}

Equalling the last two equations, we have:

\begin{gathered} AC^2-1=20-BN^2.^{} \\ AC^2=21-BN^2\text{.} \end{gathered}

(II) To find the values of AC and BN we need another equation. We find that equation applying the Pigatoras Theorem to the sides of the bigger right triangle:

3) △ABC has sides:

• h = BC = ,BN + 1,,

,

• a = AC,

,

• b = ,AB = 2√5,,

Replacing these data in Pitagoras Theorem, we have:

\begin{gathered} \mleft(BN+1\mright)^2=(2\sqrt[]{5})^2+AC^2 \\ (BN+1)^2=20+AC^2, \\ AC^2=(BN+1)^2-20. \end{gathered}

Equalling the last equation to the one from (I), we have:

\begin{gathered} 21-BN^2=(BN+1)^2-20, \\ 21-BN^2=BN^2+2BN+1-20 \\ 2BN^2+2BN-40=0, \\ BN^2+BN-20=0. \end{gathered}

(III) Solving for BN the last quadratic equation, we get two values:

\begin{gathered} BN=4, \\ BN=-5. \end{gathered}

Because BN is a length, we must discard the negative value. So we have:

BN=4.

Replacing this value in the equation for AC, we get:

\begin{gathered} AC^2=21-4^2, \\ AC^2=5, \\ AC=\sqrt[]{5}. \end{gathered}

Finally, replacing the value of AC in the equation of NA, we get:

\begin{gathered} NA^2=(\sqrt[]{5})^2-1, \\ NA^2=5-1, \\ NA=\sqrt[]{4}, \\ AN=NA=2. \end{gathered}

Answers

The lengths of the sides are:

• BN = 4 in,

,

• AN = 2 in,

,

• AC = √5 in.

7 0
1 year ago
2s+4+4s+2+3 what do you have to do to get this answer
VikaD [51]
Combine like terms... 2s and 4s are like terms so that's 6s 4,2,3 are like terms add that up its 9. So it would look like this 6s+9
5 0
3 years ago
What’s the slope of the line?
yulyashka [42]

Answer:

the slope is 1

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Help Me | It says: Multiply by the ones. Regroup if needed. Then It says: 2x6 ones = ? Ones or ? Ten and ? Ones | 2x4 tens = ? T
Marianna [84]
2×6 ones= 12 ones
2× 4 tens(40)=80(8 tens)
tens(10)+1 ten=20(2 tens)
2×3 hundreds(300)=600(6 hundreds)
3 0
3 years ago
Read 2 more answers
M,H, and G have written more than a combined total of 22 articles. H has written 1/4 as many as M. G has written 3/2 as M. Write
Natalka [10]

Missing part of the question:

Write an inequality to determine the number of articles, M could have written for the school newspaper.

Answer:

The inequality: 11M > 88

The solution: M > 8

Step-by-step explanation:

Given

From the question, we have the following parameters:

M + H + G > 22

H = \frac{1}{4}M

G = \frac{3}{2}M

Required

Determine the inequality to solve for M

Substitute the values for H and G in the inequality:

M + H + G > 22

M + \frac{1}{4}M + \frac{3}{2}M > 22

Multiply through by 4

4(M + \frac{1}{4}M + \frac{3}{2}M) > 22*4

4M + M + 6M > 88

11M > 88

Divide both sides by 11

M > 8

4 0
3 years ago
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