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3 years ago

The graph of an exponential function has

Mathematics

2 answers:

Anton [14]3 years ago

4 0

Answer:

I need answer to this also

Gre4nikov [31]3 years ago

3 0

Answer:

The “J” line.

Step-by-step explanation:

The graph passes through the point (0,1).

The domain is all real numbers.

The range is y>0.

The graph is continuous.

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If an arithmetic sequence

goblinko [34]

Answer:

a₄ = 12

Step-by-step explanation:

To obtain the terms in the sequence add 2 to the previous term, that is

a₂ = a₁ + 2 = 6 + 2 = 8

a₃ = a₂ + 2 = 8 + 2 = 10

a₄ = a₃ + 2 = 10 + 2 = 12

5 0

2 years ago

Determining Sine and Cosine Values

marysya [2.9K]

Is there an attachment?

6 0

3 years ago

What value does f(x,y) = (x + 2y)/(x -2y) approach as (x,y) approaches (0,0) along the x-axis?

WARRIOR [948]

Answer:

B. f(x,y) has no limit and does not approach infinity or minus infinity as (x,y) approaches (0,0) along the x-axis.

Step-by-step explanation:

Given the function

f(x,y) = (x + 2y)/(x -2y)

We can apply

y = mx

then

lim (x,y) → (0, 0) f(x,y) = lim (x,mx) → (0, 0) f(x, mx)

⇒ lim (x → 0) (x + 2mx)/(x -2mx) = lim (x → 0) x(1+2m)/(x*(1-2m)) = (1+2m)/(1-2m)

y = x²

then

lim (x,y) → (0, 0) f(x,y) = lim (x → 0) f(x)

⇒ lim (x → 0) (x + 2x²)/(x -2x²) = (1 + 4(0))/(1 - 4(0)) = 1

y = x³

then

lim (x,y) → (0, 0) f(x,y) = lim (x → 0) f(x)

⇒ lim (x → 0) (x + 2x³)/(x -2x³) = (1 + 6(0)²)/(1 - 6(0)²) = 1

We applied L'Hopital's rule to solve the limits.

Then, we can say that f(x,y) has no limit since the limits obtained are different.

4 0

3 years ago

A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m². The surface area of the image is 315 m². T

Westkost [7]

The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

<h3>How does dilation affect length, area, and volume of an object?</h3>

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly,

Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that;

Surface area of pre-image = 35 m²
Surface area of dilated image = 315 m²
Height of pre-image = 5.8 m
Height of dilated image.

Let the scale fator of dilation be k.

Then:

So area of pre-image = k² × area of dilated image

Thus, we get:

$35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3$

(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)

Thus, we get:

Height of pre-image = (1/3) × Height of dilated image (say h)

$5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m$

Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

Learn more about dilation here:

brainly.com/question/3266920

4 0

2 years ago

Read 2 more answers

"let v = r 2 with the usual addition and scalar multiplication defined by k(u1, u2) = (ku1, 0). determine which of the five axio

expeople1 [14]

Let $\mathbf u\in\mathbb R^2$ , where

$\mathbf u=(u_1,u_2)$

and let $k\in\mathbb R$ be any real constant.

Given this definition of scalar multiplication, we can see right away that there is no identity element $e$ such that

$e\mathbf u=\mathbf u$

because

$e\mathbf u=e(u_1,u_2)=(eu_1,0)\neq(u_1,u_2)=\mathbf u$

5 0

3 years ago