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3 years ago

If the product of x^2a-1/y^3b+4 and x^7b-4/y^10-a is x^24/y^19 find the value of a and b

Mathematics

1 answer:

lidiya [134]3 years ago

6 0

Answer:

a = 4; b = 3

Step-by-step explanation:

For the question to make any sense, we need to add parentheses.

... x^(2a-1)/y^(3b+4) × x^(7b-4)/y^(10-a) = x^24/y^19

Equating exponents, we have ...

... (2a-1) + (7b-4) = 24 . . . . exponent of x in the product

... (3b+4) + (10 -a) = 19 . . . exponent of y in the product

Simplifying these two equations, we get

... 2a +7b = 29

... a -3b = -5

By Cramer's rule, ...

... a = (7·(-5) -(-3·29)/(7·1 -(-3·2)) = 52/13 = 4

... b = (29·1 -(-5·2))/13 = 39/13 = 3

_____

More about Cramer's Rule

If you have the linear equations ...

ax +by = c
dx +ey = f

The solutions for the variables x and y can be found directly from the equation coefficients as ...

... x = (bf -ec)/(bd -ea)

... y = (cd -fa)/(bd -ea) . . . . same denominator as for the first equation

Once you recognize the pattern in the products, the formula is not difficult to remember.

___

This is actually the Vedic math version of Cramer's rule. It differs from the usual presentation of Cramer's rule in that both numerator and denominator are negated. This makes the pattern of products easier to remember and gives exactly the same result.

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20 POINTS PLZ HELP!!!

Alexandra [31]

Both triangles that are given (with right angles) lie in plane m, proving that AC is perpendicular to plane m. As angle acd is from a triangle that shares the common perpendicular, it too is a right angle

4 0

3 years ago

Between the time Iko woke up and lunchtime,the temperature rose by 11.Then by the time he went to bed,the temperature dropped by

dimaraw [331]

Answer:

11 + ( - 14)

Explanation:

The complete question is:

Between the time iko woke up and lunchtime, the temperature rose by 11º. Then by the time he went to bed, the temperature dropped by 14º.

Write an addition expression for the temperature relative to when iko woke up.

<h2>Solution</h2>

It is said that between the time Iko woke up and lunchtime, the temperature rose by 11 degrees. A rise means the temperature increased and you must add 11º.

Then, relative to when Iko woke up the temperature is:

+ 11º

Then, by the time Iko went to bed, the temperature dropped by 14º. A drop means that the change is negative. This means that you must add a negative number, and the additive expression is:

+ 11º + (- 14º).

If you want the overall change in temperature you do the operation:

11 + (-14) = 11 - 14 = - 3. A net decrease of 3º.

But the answer to this question is the additive expression:

11 + ( - 14) ← answer

4 0

3 years ago

what is the polynomial function of lowest degree with leading coefficient of 1 and roots 2 and 1 + square root2

Marta_Voda [28]

If the roots to such a polynomial are 2 and $1+\sqrt2$ , then we can write it as

$(x-2)(x-(1+\sqrt2))$

courtesy of the fundamental theorem of algebra. Now expanding yields

$(x-2)(x-1-\sqrt2)=x^2-2x-(1+\sqrt2)x+2(1+\sqrt2)=x^2-(3+\sqrt2)x+2+2\sqrt2$

which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.

So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use $1-\sqrt2$ as a root. In this case, that would make our polynomial

$(x-2)(x-(1+\sqrt2))(x-(1-\sqrt2))=x^3-4x^2+3x+2$

so that the answer is (probably) the third choice.

Whoever originally wrote this question should reevaluate their word choice...

5 0

3 years ago

Which of the following expressions represents “the quotient of nine times a number and seven ?

blsea [12.9K]

Answer:

9n÷7

Step-by-step explanation:

A quotient means a ratio or one quantity being divided by another, or in algebraic terms (a/b). In this case, the first quantity is "nine times a number" represented in terms of n as (n). The other quantity is just the number 7.

Dividing the 9 times n by 9 gives us the following:

9n÷7

Hope this helps :>

7 0

3 years ago

A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has d

Alinara [238K]

Answer:

Read step by step explanation

Step-by-step explanation:

The owner already knows that the limit for the average time delivered pizzas is 38 minutes. So we conclude

1.-The resulting mean from sample data ( x ) ( 27 customers) need to be smaller than 38 minutes, any value of sample above 38 minutes means more time for the delivery action and will indicate a failure for the future project

2.-As sample size is smaller than 30 the test has to be t-student one tail test to the left

Test hypothesis

Null hypothesis H₀ x = 38

Alternative hypothesis Hₐ x < 38

We should test at a significance level α = 0,05 (α = 5%)

If the result of the test is to accept H₀ delivery project won´t be implemented, if on the other hand, H₀ is rejected then in the condition of the alternative hypothesis we accept Hₐ the sample indicates that we have a smaller average time than 38 minutes.

4 0

3 years ago