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Setler [38]
2 years ago
6

Solve the following problems using Pythagoras. Include a diagram . a. How long must a ladder be to reach 12 ft up the wall, if t

hefoot of the ladder is placed 2.5 ft away from the wall
Mathematics
2 answers:
RideAnS [48]2 years ago
7 0

Answer:

sqrt(601)/2 ft

Step-by-step explanation:

The legs of the right triangle are 12 and 2.5. by the Pythagorean Theorem, the length of the ladder is sqrt(12^2 + 2.5^2) = sqrt(150.25). Simplified is sqrt(601)/2 ft.

RUDIKE [14]2 years ago
6 0

The length of ladder used is 12.25 ft.

<h3>What is Pythagoras theorem?</h3>

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

example:

The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.

Solution:

Given : Hypotenuse = 16 units

Let us consider the given side of a triangle as the perpendicular height = 8 units

On substituting the given dimensions to the Pythagoras theorem formula

Hypotenuse^2 = Base^2 + Height^2

16^2 = B^2 + 8^2

B^2 = 256 - 64

B = √192 = 13.856 units

Therefore, the measure of the third side of a triangle is 13.856 units.

given:

base=  2.5 ft,  

perpendicular= 12 ft

Using Pythagoras theorem,

H² =  B² + P²

H² = 2.5² + 12²

H² = 6.25+ 144

H= 12.25 ft

Learn more about Pythagoras theorem here:  brainly.com/question/343682

#SPJ2

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Answer:

\frac{dy}{dx} = - \frac{3}{2x^{\frac{3}{2} } }

Step-by-step explanation:

Differentiate using the power rule

\frac{d}{dx} (ax^{n} ) = nax^{n-1}

Given

y = \frac{3}{\sqrt{x} } = 3x^{-\frac{1}{2} } , then

\frac{dy}{dx} = - \frac{3}{2} x^{-\frac{3}{2} } = - \frac{3}{2x^{\frac{3}{2} } }

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3 years ago
Divide.<br><br> 26−6<br><br> Enter your answer as a mixed number, in simplified form,
matrenka [14]

Answer:

20

Step-by-step explanation:

20-6=20

5 0
2 years ago
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telo118 [61]
The answer to this question is true

8 0
3 years ago
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In 2016, the mean number of wins for teams in Major League Baseball was 81 wins with a standard deviation of 10.7 wins. (a) The
Kay [80]

Answer:

(a) The Chicago Cubs broke the Curse of the Billy Goat by winning the World Series in 2016. Find and interpret the z-score for the Chicago Cubs, who had 103 wins in 2016.

Z score = 2.05607

Interpreting the z score, since the z score is positive, this means, the data point is to the right of the mean.

(b) The Chicago White Sox had a z-score of 20.28. Find the number of wins for the Chicago White Sox for 2016.

= 298 wins

Step-by-step explanation:

In 2016, the mean number of wins for teams in Major League Baseball was 81 wins with a standard deviation of 10.7 wins.

(a) The Chicago Cubs broke the Curse of the Billy Goat by winning the World Series in 2016. Find and interpret the z-score for the Chicago Cubs, who had 103 wins in 2016.

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

x = 103 wins, μ = 81 wins, σ = 10.7

z = 103 - 81/10.7

z = 2.05607

Interpreting the z score, since the z score is positive, this means, the data point is to the right of the mean.

(b) The Chicago White Sox had a z-score of 20.28. Find the number of wins for the Chicago White Sox for 2016.

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the above question, we are asked to find the number of wins, this means we should find the raw score = x

z = 20.28, x = ? μ = 81 , σ = 10.7

Hence,

20.28 = x - 81/10.7

Cross Multiply

20.28 × 10.7 = x - 81

216.996 = x - 81

x = 216.996 + 81

x = 297.996

x is approximately 298 wins

Therefore, the number of wins for the Chicago White Sox for 2016 is approximately 298 wins

4 0
3 years ago
At a local preschool, there is a ratio of 3 boys to every 4 girls. If there are 245 total preschoolers enrolled, then how many a
Reika [66]

Set up the equation by writing the number of students in the ratio as a fraction:

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3x= 980-4x Add 4x on both sides:

7x= 980 Divide both sides by 7:

x= 140 this is how many girls there are. And:

245-140= 105= boys

5 0
2 years ago
Read 2 more answers
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