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3 years ago

Which is the correct label of the parallel lines?

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

6 0

the answer is a || b, or the first option

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Cube roots of 1 are +1 and -1 (true and false)

mario62 [17]

False cube root of 1 is plus 1 only.

7 0

3 years ago

15. The equation below defines z as a differentiable function of x and y. Find the value of dz/dy at the point (1, 1, 1).

MariettaO [177]

Isolate the term with $z^2$ .

$x^2 - 5y^2 + xyz^2 = y - 4 \implies xyz^2 = -x^2 + 5y^2 + y - 4$

Differentiate both sides with respect to $y$ .

$\dfrac{\partial(xyz^2)}{\partial y} = \dfrac{\partial(-x^2 + 5y^2 + y - 4)}{\partial y}$

By the product and chain rules,

$xz^2 + 2xyz \dfrac{\partial z}{\partial y} = 10y + 1$

Solve for the partial derivative, then evaluate at $(x,y,z) = (1,1,1)$ .

$\dfrac{\partial z}{\partial y} = \dfrac{10y + 1 - xz^2}{2xyz}$

$\dfrac{\partial z}{\partial y} \bigg|_{x=1,y=1,z=1} = \dfrac{10 + 1 - 1}{2} = \boxed{5}$

4 0

2 years ago

What is 3/4−(−2/3), expressed as an improper fraction?

Mariana [72]

Step-by-step explanation:

make them common denominators then the two negatives cancel out one so then subtract.

4 0

3 years ago

Read 2 more answers

If all the dimensions of a cube are are multipied by 5 the surface area of the cube will change by a factor of ten. True or fals

marta [7]

SA=6edge^2
if each edge is ultipied by 5

SA=6(5edge)^2
SA=(6)25edge^2
the sureface area will be multiplied by 25

5 0

3 years ago

A triangle has a perimeter of 10a + 3b +12 and has sides of length 3a+8 and 5+b, what is the length of the third side?

makvit [3.9K]

Answer:

The third side of the triangle is (7a + 2b -1).

Step-by-step explanation:

The length of the first side = (3a +8)

The length of the second side = (5 +b)

Let us assume the third side = m

The perimeter of the triangle = SUM OF ALL 3 SIDES

⇒ (10a + 3b +12) = (3a +8) + (5 +b) + m

or, (10a + 3b +12) = 3a + b + 13 + m

or, m = (10a + 3b +12) -(3a + b + 13)

= 10 a + 3b + 12 - 3a - b - 13

= 7a + 2b -1 = ( 10 - 3a) + (3b -b) + 12 -13

or, m = (7a + 2b -1)

Hence, the third side of the triangle is (7a + 2b -1).

6 0

3 years ago