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3 years ago

If LM=41-2x and NP=7x+5, find LM

Mathematics

1 answer:

Tatiana [17]3 years ago

8 0

Answer:
LM = 33 units

Explanation:
From the drawing:
LM = NP
41 - 2x = 7x + 5
41 - 5 = 7x + 2x
36 = 9x
x = 9

This means that:
LM = 41 - 2x
LM = 41 - 2(4)
LM = 33 units

Hope this helps :)

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Find the average value of f over the region D. f(x, y) = 3xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 9)

MakcuM [25]

The average value of f over the region D is 243/4

To answer the question, we need to know what the average value of a function is

<h3>What is the average value of a function?</h3>

The average value of a function f(x) over an interval [a,b] is given by

$\frac{1}{b - a} \int\limits^b_a {f(x)} \, dx$

Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).

x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9

So, $\frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ = \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0} \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\= \frac{81}{2} X3 X \frac{1}{2} \\= \frac{243}{4}$

So, the average value of f over the region D is 243/4

Learn more about average value of a function here:

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8 0

1 year ago

HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4

Natalka [10]

Answer:

Option A is correct.

Value of $S_{22} = 15.4$

Step-by-step explanation:

Given: $a_{12} = 2.4$ and common difference(d) = 3.4

A sequence of numbers is arithmetic i.e, it increases or decreases by a constant amount each term.

The sum of the nth term of a arithmetic sequence is given by;

$S_n =\frac{n}{2}(2a+(n-1)d)$ , where n is the number of terms, a is the first term and d is the common difference.

We also know the nth tern sequence formula which is given by ;

$a_n = a+(n-1)d$ ......[2]

First find a.

it is given that $a_{12} = 2.4$

Put n =12 and d=3.4 in equation [2] we have;

$a_{12} = a+(12-1)(3.4)$

$a_{12} = a+(11)(3.4)$

2.4 = a + 37.4

Simplify:

a = - 35

Now, to calculate $S_{22}$

we use equation [1];

here, n =2 , a =-35 and d=3.4

$S_{22} = \frac{22}{2}(2(-35)+(22-1)(3.4))$

$S_{22} = (11)(-70+21(3.4))$

$S_{22} = (11)(-70+71.4)$

$S_{22} = (11)(1.4)$

Simplify:

$S_{22} = 15.4$

Therefore, the sum of sequence of 22nd term i.e, $S_{22} = 15.4$

8 0

3 years ago

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Mashcka [7]

Your answer would be 4c + 6 - 3c - 4

This is because when you simplify, you get 4c - 3c = c, and 6 - 4 = 2, so combining the two terms gives you c + 2.

I hope this helps!

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3 years ago

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harina [27]

I’m thinking it would be c sorry if it’s incorrect .

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2 years ago

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1/6 because __|__|__|__|__|__|
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