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2 years ago

5y+4x=10.51 8y+3x=10.39

Mathematics

1 answer:

Phoenix [80]2 years ago

7 0

Answer:

(x, y) = (1.89, 0.59)

Step-by-step explanation:

Written in general form, the equations are ...

4x +5y -10.51 = 0

3x +8y -10.39 = 0

These can be solved using the cross-multiplication method to find ...

∆1 = (4)(8) -(3)(5) = 17

∆2 = (5)(-10.39) -(8)(-10.51) = 32.13

∆3 = (-10.51)(3) -(-10.39)(4) = 10.03

Then the values of the variables are ...

x = ∆2/∆1 = 32.13/17 = 1.89

y = ∆3/∆1 = 10.03/17 = 0.59

The solution is (x, y) = (1.89, 0.59).

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Given that the measure of X is 57° and the measure of y is 51° find the measure of z

avanturin [10]

9514 1404 393

Answer:

132°

Step-by-step explanation:

Name the vertex of each angle the same as the angle letter. Name the intersection of the "horizontal" and "vertical lines" point Q.

Angle ZXQ is vertical to ∠x, so is the same measure.

Angle YQX is the value that makes the sum of angles in triangle XYQ be 180°. That is ...

∠YQX = 180° -51° -57° = 72°

This is also the measure of its vertical angle in the other triangle. Angle z is the sum of that vertical angle and 60°, so we have ...

∠z = 72° +60°

∠z = 132°

_____

<em>Additional comment</em>

The relations we used are ...

vertical angles are congruent
sum of angles in a triangle is 180°
an exterior angle is equal to the sum of the remote interior angles

8 0

2 years ago

Find the maclaurin series for f(x) using the definition of a maclaurin series. [assume that f has a power series expansion. do n

Nady [450]

The equation of $f(x) = e^{-6x}$ by maclaurin series is $f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}$ .

The maclaurin series for f(x) is defined by the following formula:

$f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}$ --------------(1)

Where $f^{i}$ is the i - th derivative of the function

If f(x) = $e^{-6x}$ , then the formula of the i - th derivative of the function is:

$f^{i} =(-6)^{i} .e^{-6x}$ ----------------------(2)

Then,

$f^{i}(0) = (-6)^{i}$

Lastly, the equation of the trascendental function by Maclaurin series is: $f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i} }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}$ ---------------(3)

Hence,

The equation of $f(x) = e^{-6x}$ by maclaurin series is $f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}$ .

Find out more information about maclaurin series here

brainly.com/question/24179531

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4 0

1 year ago

Consider the three restrictions (i), (ii), and (iii) placed on the sets in Cantor’s Theorem. (a) Find a sequence of sets that sa

murzikaleks [220]

Answer:

check the explanation

Step-by-step explanation:

When it comes to the field of elementary set theory, Cantor's theorem is a basic result which affirms that, for whichever set, the set of the entire subsets will have a strictly bigger cardinality than itself. For the finite sets, Cantor's theorem can be affirmed to be true by plain enumerating the number that are in the subsets.

The full step by step explanation is in the attached image below