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3 years ago

HELP ME PLEASE I'M CRYING! PLEASE!

Mathematics

1 answer:

inna [77]3 years ago

6 0

Answer:

1. 15*4= 60cm^2

2. 3.14*2*10.5 = 65.94‬= 66cm

3. r=C /2π r=4cm

Step-by-step explanation:

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Ezpress 3x + 11/x² + 6x + 9<br>as partial fractions,

andreev551 [17]

Answer:

$\frac{3}{x + 3} + \frac{2}{(x+3)^2}$

Step-by-step explanation:

Given

$\frac{3x + 11}{x^2 +6x + 9}$

Required

Express as partial fraction

$\frac{3x + 11}{x^2 +6x + 9}$

Expand the numerator

$\frac{3x + 11}{x^2 +3x +3x+ 9}$

Factorize

$\frac{3x + 11}{x(x +3) +3(x+ 3)}$

Factor out x + 3

$\frac{3x + 11}{(x +3)(x+ 3)}$

$\frac{3x + 11}{(x +3)^2}$

As a partial fraction, we have:

$\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}$

Take LCM

$\frac{3x + 11}{(x +3)^2} = \frac{A(x+3) + B}{(x + 3)^2}$

Cancel out (x + 3)^2 on both sides

$3x + 11 = A(x+3) + B$

Open bracket

$3x + 11 = Ax+3A + B$

By comparison, we have:

$Ax = 3x$ ===> $A = 3$

$3A + B = 11$

Substitute 3 for A

$3*3 + B = 11$

$9 + B = 11$

Solve for B

$B = 11-9$

$B =2$

Substitute: $A = 3$ and $B =2$ in

$\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}$

$\frac{3x + 11}{(x +3)^2} = \frac{3}{x + 3} + \frac{2}{(x+3)^2}$

Hence, the partial fraction is:

$\frac{3}{x + 3} + \frac{2}{(x+3)^2}$

7 0

2 years ago

How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Nina [5.8K]

<h3>Explanation:</h3>

For a system of 2 equations in 2 unknowns, there are 3 cases:

slopes are different — one solution
slopes are the same and y-intercepts are different — no solutions
slopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at <em>one</em> point, the <em>solution</em>.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence <em>no solutions</em>. If the lines are the same line, they intersect at all points, so there are <em>infinitely many solutions</em>.

7 0

3 years ago

Find the value of sin E rounded to the nearest hundredth, if necessary.

Oduvanchick [21]

Answer:

Step-by-step explanation:

using sin formula

$\frac{sin~E}{15} =\frac{sin ~90}{39} \\sin ~E=15 \times ~\frac{1}{39} =\frac{5}{13}$