All categories

2 years ago

If

a^{2}+bx^{2} =13 " align="absmiddle" class="latex-formula">, and ab=6, find the value of
a) $(a+b)^{2}$
b) $(a-b)^{2}$

Mathematics

1 answer:

Mkey [24]2 years ago

7 0

$a^2-b^2=13;\ ab=6$

$a)\\(a+b)^2=a^2+2ab+b^2=(a^2+b^2)+2(ab)=13+2\cdot6=25\\\\b)\\(a-b)^2=a^2-2ab+b^2=(a^2+b^2)-2(ab)=13-2\cdot6=1$

You might be interested in

The number of girls in Mrs. Manning’s classes was 12 less than twice the number of boys. She had a total of 108 students in her

FromTheMoon [43]

40 boys and 68 girls

let's start with variables and an equation.

boys: x

girls: 2x - 12

and we know that boys and girls make up the class. so let's add the two expressions.

x + 2x - 12 = 108

3x - 12 = 108

+ 12 + 12

3x = 120

x = 40 boys

BUT x is only the number of BOYS in the class. so we have to find girls now. let's plug in our value of x into the girls' equation.

2x - 12 = # of girls

2(40) -12 = # of girls

80 - 12 = # of girls

68 girls

let's check our answer!

68 + 40 does in fact add to 108, therefore our answer is correct.

4 0

2 years ago

im sci-fi gurl and i nedd your guys help by the end of tommorow for those who go to connexus academy know this what are all 15 a

Crazy boy [7]

Answer:

what do you mean your not giving any questions about what you need help on

3 0

2 years ago

The volume V of an ice cream cone is given by V = 2 3 πR3 + 1 3 πR2h where R is the common radius of the spherical cap and the c

Nuetrik [128]

Answer:

The change in volume is estimated to be 17.20 $\rm{in^3}$

Step-by-step explanation:

The linearization or linear approximation of a function $f(x)$ is given by:

$f(x_0+dx) \approx f(x_0) + df(x)|_{x_0}$ where $df$ is the total differential of the function evaluated in the given point.

For the given function, the linearization is:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh$

Taking $R_0=1.5$ inches and $h=3$ inches and evaluating the partial derivatives we obtain:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh\\V(R, h) = V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh$

substituting the values and taking $dx=0.1$ and $dh=0.3$ inches we have:

$V(R_0+dR, h_0+dh) =V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh\\V(1.5+0.1, 3+0.3) =V(1.5, 3) + (\frac{2 \cdot 3 \pi \cdot 1.5}{3} + 2 \pi 1.5^2)\cdot 0.1 + (\frac{\pi 1.5^2}{3} )\cdot 0.3\\V(1.5+0.1, 3+0.3) = 17.2002\\\boxed{V(1.5+0.1, 3+0.3) \approx 17.20}$

Therefore the change in volume is estimated to be 17.20 $\rm{in^3}$

4 0

2 years ago

Im in summer school and i need to pass this please help me

andreev551 [17]

g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.

<h3>Which statement compares the graph of the two functions?</h3>

First, a vertical shift of N units is written as:

g(x) = f(x) + N

if N > 0 the shift is upwards.
If N < 0 the shift is downwards.

A horizontal shift of N units is written as:

g(x) = f(x + N).

if N < 0, the shift is to the right.
If N > 0, the shift is to the left.

In this case, we have:

g(x) = f(x + 8) + 4

So g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.

If you want to learn more about translations:

brainly.com/question/24850937

#SPJ1

8 0

1 year ago

If using the method of completing the square to solve the quadratic equation

oee [108]

The answer would be 361/4 added to each side of the formula

7 0

2 years ago