Find the distance BF for the points B(1, –1) and F(

Can someone help me on these problems and show work

Salsk061 [2.6K]

The simplified expression are as follows;

6mn³ - mn² + 3mn³ + 15mn² = 9mn³ + 14mn²

a⁴b³ + 8a⁴b³ = 9a⁴b³

<h3>How to simplify an expression?</h3>

A simplified expression is express to its lowest term.

Therefore,

6mn³ - mn² + 3mn³ + 15mn²

combine like terms

6mn³ + 3mn³ - mn² + 15mn²

9mn³ + 14mn²

a⁴b³ + 8a⁴b³ = 9a⁴b³

learn more on simplification here: brainly.com/question/403991

#SPJ1

3 0

1 year ago

Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1

hichkok12 [17]

Answer:

$\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}$

Step-by-step explanation:

Given that:

The surface area (S.A) $z = x^2 +y^2$

Hence the S.A is of form z = f(x,y)

Then the S.A can be represented with the equation

$A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA$

where :

D = cylinder $x^2 +y^2 =1$

In polar co-ordinates:

D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)

Similarly, $\dfrac{\partial z}{\partial x} = 2x$ and $\dfrac{\partial z}{\partial y} = 2y$

Therefore;

$S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA$

$= \iint_D \sqrt{1+4(x^2+y^2)} \ dA$

$= \int^{2 \pi}_{0} \int^{1}_{0} \sqrt{1+4r^2} \ r \ dr \d \theta$

$= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0$

$= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1]$

$\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}$

6 0

2 years ago

Jimmy set his score for his math test. After the math teacher returnee his paper to him, he realized that if he increased his ta

mixer [17]

When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful.
So, if we let:
a = test score
b = target score
then, using the information given:
a = 1.1b + 1
a = 1.15b - 3
and we get simultaneous equations.
'1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the simultaneous equations, we can just solve them now:
There are a number of ways to do this but I will use my preferred method:
Rearrange to express in terms of b:
a = 1.1b + 1
then b = (a - 1)/1.1
a = 1.15b - 3
then b = (a + 3)/1.15
Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a:
(a - 1)/1.1 = (a + 3)/1.15
1.15 * (a - 1) = 1.1 * (a + 3)
1.15a - 1.15 = 1.1a + 3.3
0.05a = 4.45
a = 89

8 0

2 years ago

ill give brainliest n a recent survey, 3 out of every 5 students said Math is their favorite class.If 200 students were surveyed

anyanavicka [17]

Answer: D. 120 students

Step-by-step explanation:

This is an easy solution

Take 300 and divide it by 5

300/5

This will result in 40

Now Multiply 40 by 3

Like so: 40x3

This will result in 120

6 0

1 year ago

Read 2 more answers

Use the figure to name a plane containing point L.

luda_lava [24]

Put a picture pleasee

5 0

2 years ago

Find the distance BF for the points B(1, –1) and F(–3, 5).