All categories

4 years ago

Given:

Mathematics

1 answer:

Anuta_ua [19.1K]4 years ago

7 0

Answer:

84 square units.

Step-by-step explanation:

If LM - KN = 4, then denote KN = x and LM = x+4.

1. Consider right triangle KLM. By the Pythagorean theorem,

$KL^2 =ML^2+MK^2,\\ \\15^2=(x+4)^2+MK^2.$

2. Consider right triangle KMN. By the Pythagorean theorem,

$MN^2 =NK^2+MK^2,\\ \\13^2=x^2+MK^2.$

Subtract these two equations:

$15^2-13^2=(x+4)^2-x^2,\\ \\225-169=x^2+8x+16-x^2,\\ \\56=8x+16,\\ \\8x=56-16,\\ \\8x=40,\\ \\x=5\ un.$

Then

$13^2=5^2+MK^2,\\ \\MK^2=169-25,\\ \\MK^2=144,\\ \\MK=12\ un.$

The area of KLMN is

$A_{KLMN}=\dfrac{LM+KN}{2}\cdot MK=\dfrac{5+9}{2}\cdot 12=14\cdot 6=84\ un^2.$

You might be interested in

How do we round 8.465 nearest hundredths

kiruha [24]

The second number after the decimal is the hundredths place. To round to that place, you look at the number after it. In this case 6 is the hundredths place and 5 is the number after it. If the number after it is 5 or higher, the hundredths place number increases by 1, if it is less than 5 the hundredths place number doesn't change. So the answer is 8.47.

8 0

4 years ago

Read 2 more answers

Scott and Letitia are brother and sister. After dinner, they have to do the dishes, with one washing and the other drying. They

ehidna [41]

Answer:

The probability that Scott will wash is 2.5

Step-by-step explanation:

Given

Let the events be: P = Purple and G = Green

$P = 2$

$G = 3$

Required

The probability of Scott washing the dishes

If Scott washes the dishes, then it means he picks two spoons of the same color handle.

So, we have to calculate the probability of picking the same handle. i.e.

$P(Same) = P(G_1\ and\ G_2) + P(P_1\ and\ P_2)$

This gives:

$P(G_1\ and\ G_2) = P(G_1) * P(G_2)$

$P(G_1\ and\ G_2) = \frac{n(G)}{Total} * \frac{n(G)-1}{Total - 1}$

$P(G_1\ and\ G_2) = \frac{3}{5} * \frac{3-1}{5- 1}$

$P(G_1\ and\ G_2) = \frac{3}{5} * \frac{2}{4}$

$P(G_1\ and\ G_2) = \frac{3}{10}$

$P(P_1\ and\ P_2) = P(P_1) * P(P_2)$

$P(P_1\ and\ P_2) = \frac{n(P)}{Total} * \frac{n(P)-1}{Total - 1}$

$P(P_1\ and\ P_2) = \frac{2}{5} * \frac{2-1}{5- 1}$

$P(P_1\ and\ P_2) = \frac{2}{5} * \frac{1}{4}$

$P(P_1\ and\ P_2) = \frac{1}{10}$

<em>Note that: 1 is subtracted because it is a probability without replacement</em>

So, we have:

$P(Same) = P(G_1\ and\ G_2) + P(P_1\ and\ P_2)$

$P(Same) = \frac{3}{10} + \frac{1}{10}$

$P(Same) = \frac{3+1}{10}$

$P(Same) = \frac{4}{10}$

$P(Same) = \frac{2}{5}$

8 0

3 years ago

SOMEONE PLEASE ANSWER WITH WORK I WILL GOVE BRAINLIEST

Ira Lisetskai [31]

Answer: what grade are you in

<h3 />

Step-by-step explanation:

5 0

3 years ago

in a class book order, 2/3 of the books are fantasy and 1/4 of the books are biography. if the order contains 60 books, how many

Finger [1]

So we know that 2/3=fantasy
1/4=bio
so bio+fantasy=2/3+1/4
2/3 times 4/4=8/12
1/4 times 3/3=3/12
2/3+1/4=8/12+3/12=11/12

11/12 of 60 are bio or fantassy
mltiply
11/12 times 60=660/12=55

answer is 55

8 0

3 years ago

Read 2 more answers

Calculate the probability that a particle in a one-dimensional box of length aa is found between 0.29a0.29a and 0.34a0.34a when

Helga [31]

Answer:

P(0.29a < X < 0.34a) = -(4a/π) [(cos 0.34πa²) - (cos 0.29πa²)]

Assuming the box is of unit length, a = 1,

0.29a = 0.29 and 0.34a = 0.34

P(0.29 < X < 0.34) = (-4/π) [(cos 0.34π) - (cos 0.29π)] = 0.167 = 0.17 to 2 s.f

Step-by-step explanation:

ψ(x) = 2a(√sin(πxa)

The probability of finding a particle in a specific position for a given energy level in a one-dimensional box is related to the square of the wavefunction

The probability of finding a particle between two points 0.29a and 0.34a is given mathematically as

P(0.29a < X < 0.34a) = ∫⁰•³⁴ᵃ₀.₂₉ₐ ψ²(x) dx

That is, integrating from 0.29a to 0.34a

ψ²(x) = [2a(√sin(πxa)]² = 4a² sin(πxa)

∫⁰•³⁴ᵃ₀.₂₉ₐ ψ²(x) dx = ∫⁰•³⁴ᵃ₀.₂₉ₐ (4a² sin(πxa)) dx

∫⁰•³⁴ᵃ₀.₂₉ₐ (4a² sin(πxa))

= - [(4a²/πa)cos(πxa)]⁰•³⁴ᵃ₀.₂₉ₐ

- [(4a/π)cos(πxa)]⁰•³⁴ᵃ₀.₂₉ₐ = -(4a/π) [(cos 0.34πa²) - (cos 0.29πa²)]

P(0.29a < X < 0.34a) = -(4a/π) [(cos 0.34πa²) - (cos 0.29πa²)]

Assuming the box is of unit length, a = 1

P(0.29 < X < 0.34) = (-4/π) [(cos 0.34π) - (cos 0.29π)] = (-1.273) [0.482 - 0.613] = 0.167.

7 0

4 years ago