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1 year ago

What is the common ratio between successive terms in the sequence 2 - 4 8 -16 32 -64

Mathematics

1 answer:

Dmitriy789 [7]1 year ago

3 0

Answer:

The common ratio of the sequence is -2.

Step-by-step explanation:

To find the common ratio of a sequence, we divide each term by it's predecessor.

-4/2 = 8/-4 = -16/8 = ... = -2

The common ratio of the sequence is -2.

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What is the y-intercept of the function f(x)=4 - 5x? (Hint: use the commutative property)

Tom [10]

Answer:

Therefore the y-intercept of the function is 4.

Step-by-step explanation:

Intercepts:

The line which intersect on x-axis and y-axis are called intercepts.

y-intercept: The line or function which intersect at y-axis. So when the line intersect at y-axis, X coordinate is zero.

So in the given Function Put x = 0 we will get the y-intercept

$f(x)= 4-5x$

Put x =0

$f(0)= 4-5\times 0$

$f(0)= 4-0=4$

Therefore the y-intercept of the function is 4.

7 0

3 years ago

Consider f and c below. f(x, y) = (3 + 4xy2)i + 4x2yj, c is the arc of the hyperbola y = 1/x from (1, 1) to 3, 1 3 (a) find a fu

irga5000 [103]

We want to find a scalar function $f(x,y)$ such that $\nabla f(x,y)=\mathbf f(x,y)=\dfrac{\partial f}{\partial x}\,\mathbf i+\dfrac{\partial f}{\partial y}\,\mathbf j$ .
So we need to have
$\dfrac{\partial f}{\partial x}=3+4xy^2$
Integrating both sides with respect to $x$ gives
$f(x,y)=3x+2x^2y^2+g(y)$
Differentiating with respect to $y$ gives
$\dfrac{\partial f}{\partial y}=4x^2y+\dfrac{\mathrm dg}{\mathrm dy}=4x^2y$ $\implies\dfrac{\mathrm dg}{\mathrm dy}=0$ $\implies g(y)=C$
So we find that
$f(x,y)=3x+2x^2y^2+C$
By the fundamental theorem of calculus, we then know the line integral depends only on the values of $f(x,y)$ at the endpoints of the path. Therefore

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(3,\frac13\right)-f(1,1)=11-5=6$

4 0

3 years ago

A billboard is 27 feet high and casts a 36-foot shadow at noon. At the same time, a fir tree next to the billboard casts a 48-fo

Archy [21]

Proportion can be used to find the height = 0.75

Step-by-step explanation:

A billboard is 27 feet high and casts a 36-foot shadow at noon.

Height of billboard = 27 feet

Height of shadow of billboard = 36 feet

$\frac{\texttt{Height of billboard}}{\texttt{Height of shadow of billboard}}=\frac{27}{36}\\\\\frac{\texttt{Height of billboard}}{\texttt{Height of shadow of billboard}}=\frac{3}{4}=0.75$