The diagram shows a cubeAh=11.3cn correct to the nearest millimetre calculate the lower bound for the length of an edge of the cub you must show all your working
Answers
Answer:
Lower bound for the length of the edge = 42.5 cm
Step-by-step explanation:
From the picture attached,
FH is the diagonal of square EFGH.
Therefore, length of diagonal FH = [tex]\sqrt{FG^2+HG^2}[/tex]
(By applying Pythagoras theorem)
In triangle AFH,
AH² = AF² + FH²
= AF² + [tex](\sqrt{FG^2+HG^2})^2[/tex]
= AF² + FG² + HG²
AH² = 3HG²
(11.3)² = 3(HG²)
HG = [tex]\sqrt{\frac{127.69}{3}}[/tex]
HG = 42.563 cm
For distance correct to the nearest mm, lower bound for the length of the edge = 42.5 cm
And upper bound for the length of the edge = 43.6 cm
The side lengths of a cu be are congruent, so the edge length of the cu be is 65 mm
The length of diagonal A H is given as:
[tex]\mathbf{AH = 11.3cm}[/tex]
Considering triangle A FH, we have:
[tex]\mathbf{AH^2 = A\ F^2 + FH^2}[/tex]
So, we have:
[tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]
Considering triangle HE F, we have:
[tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex]
Substitute [tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex] in [tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]
[tex]\mathbf{11.3^2 = A\ F^2 + EF^2 + EH^2}[/tex]
The side lengths of a cu be are congruent.
This means that: A F = EF = EH
So, we have:
[tex]\mathbf{11.3^2 = A\ F^2 + A\ F^2 + A\ F^2}[/tex]
Evaluate like terms
[tex]\mathbf{11.3^2 = 3A\ F^2}[/tex]
Evaluate squares
[tex]\mathbf{127.69 = 3A\ F^2}[/tex]
Divide both sides by 3
[tex]\mathbf{42.563= A\ F^2}[/tex]
Take square roots
[tex]\mathbf{6.52= A\ F}[/tex]
Rewrite as:
[tex]\mathbf{A\ F = 6.52cm}[/tex]
Convert to m m
[tex]\mathbf{A\ F = 6.52 \times 10mm}[/tex]
[tex]\mathbf{A\ F = 65.2\ mm}[/tex]
Approximate
[tex]\mathbf{A\ F = 65\ mm}[/tex]
Hence, the edge length is 65 mm
Read more about cu bes at:
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Answer:
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Answers
The value of b for which the quadratic equation x² - bx + 16 = 0 have exactly two different integer solutions is b > 8
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
A quadratic equation is in the form:
y = ax² + bx + c
Where a, b and c are constants.
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The value of b for which the quadratic equation x² - bx + 16 = 0 have exactly two different integer solutions is b > 8
Find out more on equation at: https://brainly.com/question/2972832
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Step-by-step explanation:
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Answers
Answer:
y= -2/8x + 3
Step-by-step explanation:
Step-by-step explanation:
The slope-intercept form of the equation is :
y = mx+b
The given equation is :
-2x-8y= 24
Taking x term to RHS.
-8y = 24 +2x
Dividing both sides by -8
[tex]\dfrac{-8y}{-8} = \dfrac{24}{-8} +\dfrac{2x}{-8}\\\\y=-3-\dfrac{x}{4}\\\\or\\\\y=\dfrac{-1}{4}x+(-3)[/tex]
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Answer:
6/9=2/3
hope this helps
have a good day :)
Step-by-step explanation:
Answer: 6/9
Step-by-step explanation:
btw can you please help me with my latest question in my profile? Would really appreciate it!
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Answer:
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Step-by-step explanation:
your answer is correct
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Answer:
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Step-by-step explanation:
1.5/.4=3.75
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Answers
Answer:
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Step-by-step explanation:
Given:
Number of blue marble = 5
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Probability[Choosing red and blue consecutive]
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Will mark brainliest!
Answers
Answer:
n = 245
Step-by-step explanation:
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We know that, the nth term of an AP is given by :
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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~Help please and ty~ ✨Brainilist✨
Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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put it in its correct order
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Show your work
Answers
9514 1404 393
Answer:
x = 2 1/3
Step-by-step explanation:
We can examine the equations to see where the solution lies.
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In the first quadrant, the graph of h(x) is farther from the origin and steeper than the graph of f(x). The lines must cross in the 4th quadrant at some value of x that is greater than 3/2. The fraction in the definition of f(x) suggests that the solution will be a multiple of 1/3.
The attached table shows a couple of guesses at values of x that would make f(x) = h(x). We find that x = 7/3 is the solution we're looking for.
_____
Additional comment
Repetitive function evaluations are done conveniently and with fewer errors by a calculator or spreadsheet that can work with tables of values. Here, we have used a graphing calculator. These tools are readily available for free on almost any phone, tablet, or desktop computer platform.
in a study of 225 adults the average heart rate was 72 beats per minute assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute what does a margin of error of 1.1 for the 90% confidence interval of the average beats per minute mean
Answers
Answer:
There Is A 90% Chance That The Population Mean Is Between 70.9 And 73.1 Beats Per Minute. There Is A 90% Chance That The Population Mean Is Between 62 And 82 Beats Per Minute. There Is A 10% Chance That The Population Mean Is Less Than 72 Beats Per Minute
Hope it helps
PLEASE HELP ASAP!!!!
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Answer:
yes the answer is 456
Step-by-step explanation:
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Answer:
the scale factor of RSTU to R'S'T'U' is 1/3
Step-by-step explanation:
look at the graph and count how many squares are needed for the line RS (3) and how many for the line R'S' (9).
this is 1:3 or 1/3
all other sides follow the same ratio.
the point P is diagonally one square down from S and 3 squares down from S'.
Find the area of The Polygon. 12 points.
will give * branliest *
Answers
Answer:
A = 1/2 × b × h
A = 1/2 × 60 × 30
A = 1/2 x 900
A = 450
--------
A = 1/2 x 6 x 18
A= 1/2 x 54
A = 27
----------
27 + 450 = 477
=477
Step-by-step explanation:
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and d are integers.
1. x2 - 6x + 8 = (ax + b)(cx + d)
2.3x3 - 6x2 - 24x = 3x(ax + b)(cx + d)
3. 2x2 - 2x - 24 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
Answers
9514 1404 393
Answer:
(a, b, c, d) = (1, -4, 1, -2)(a, b, c, d) = (1, -4, 1, 2)(a, b, c, d) = (1, -4, 2, 6)Step-by-step explanation:
Once you remove the common factor from the terms, you are looking for factors of the remaining constant term that have a sum equal to the coefficient of the linear term. These factors are the constants in the binomial factors.
__
1. 8 = (-4)(-2) ⇒ x^2 -6x +8 = (x -4)(x -2)
(a, b, c, d) = (1, -4, 1, -2)
__
2. -8 = (-4)(+2) ⇒ 3x^3 -6x^2 -24x = 3x(x -4)(x +2)
(a, b, c, d) = (1, -4, 1, 2)
__
3. -12 = (-4)(3) ⇒ 2x^2 -2x -24 = 2(x -4)(x +3) = (x -4)(2x +6)
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I need help asap thanks
Answers
Answer:
Square root of 0.028
Step-by-step explanation:
17% = 0.17
1/7 = 0.142
1/8 = 0.125 so it isnt in the inequality
1.7 is outside of the inequality
0.091 is out of the inequality
Square root of 0.028 = 0.167 (So it's in the inequality)
Feel free to mark it as brainliest :D
-21. A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately normally distributed and has a standard deviation of 20 mm. The company wishes to test mm versus mm, using the results of n 10 samples. (a) Find the P-value
Answers
Answer:
0.057
Step-by-step explanation:
To obtain the p value, we need to obtain the test statistic :
For a one sample test :
Test statistic is given by :
(xbar - μ) ÷ (σ/√(n))
(185 - 175) ÷ (20/√(10))
10 ÷ 6.3245553
Test statistic = 1.581
Qe used the Z distribution because we are working with the population standard deviation.
Using the Pvalue from test statistic calculator :
Pvalue obtained using the Pvalue from Z statistic calculator, we obtain ;
Pvalue = 0.0569