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3 years ago

True or False? If a number rounds DOWN when rounded to the nearest

Mathematics

1 answer:

DedPeter [7]3 years ago

3 0

True because for ex).
2.31~2
2.31~2.3
Both the whole number and the nearest tenth were rounded down.

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What is the positive slope of the asymptote of (y+11)^2/100-(x-6)^2/4=1? The positive slope of the asymptote is .

VladimirAG [237]

Answer:

the positive slope of the asymptote = 5

Step-by-step explanation:

Given that:

$\frac{(y+11)^2}{100} -\frac{(x-6)^2}{4} =1$

Using the standard form of the equation:

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}= 1$

where:

(h,k) are the center of the hyperbola.

and the y term is in front of the x term indicating that the hyperbola opens up and down.

a = distance that indicates how far above and below of the center the vertices of the hyperbola are.

For the above standard equation; the equation for the asymptote is:

$y = \pm \frac{a}{b} (x-h)+k$

where;

$\frac{a}{b}$ is the slope

From above;

(h,k) = 11, 100

$a^2$ = 100

a = $\sqrt{100}$

a = 10

$b^2 =4$

b = $\sqrt{4}$

b = 2

$y = \pm \frac{10}{2} (x-11)+2$

$y = \pm 5 (x-11)+2$

y = 5x-53 , -5x -57

Since we are to find the positive slope of the asymptote: we have

$\frac{a}{b}$ to be the slope in the equation $y = \pm \frac{10}{2} (y-11)+2$

$\frac{a}{b}$ = $\frac{10}{2}$

$\frac{a}{b}$ = 5

Thus, the positive slope of the asymptote = 5

8 0

3 years ago

I need help with Precal asap !!!! I’ll mark u as brainliest, please if you don’t know the correct answer don’t write down.

Amanda [17]

Answer:

Equation 1: r = 4 +( 3 * cos theta )

Equation 2: r = sqrt ( 5² * sin(2 theta) )

Step-by-step explanation:

GRAPH 1:

The first graph is a dimpled limacon.

General equation for dimpled limacon:

r = a + b cos theta ∴ if dimple is along the x- axis

r = a + b sin theta ∴ if dimple is along the y-axis

y-intercept : { a, -a } = { 4, -4 } ∴ the points at which limacon intersects y-axis

Negative side of x-axis = ( a – b ) ⇒ 1

Positive side of x-axis = ( a + b ) ⇒ 7

Subtract the value of a from sum of a and b to find b:

b = 7 – 4 ⇒ 3

Equation1: r = 4 +( 3 * cos theta )

GRAPH 2:

The second graph is a lemniscates.

General equation for lemniscates is:

r² = a² cos(2theta) ∴ if petals of graph are on coordinate axis

r² = a² sin(2 theta) ∴ if petals of graph are not on coordinate axis

now, according to the graph:

a = 5 ⇒ a² = 25

angle of graph: cos2θ, simply divide 360° by 2:

$\frac{360}{2}$ ⇒ 180°

The petals cannot be on coordinate axis, we start from 45° and then the next petal will be on:

45° + 180° = 225°

Since the graph is not on the coordinate axis, so

r² = 5² sin(2 theta) ⇒ r = sqrt ( 5² * sin(2 theta) )

Equation 2: r = sqrt ( 5² * sin(2 theta) )

6 0

3 years ago

Solve 821 x 54 using an area model.

IRISSAK [1]

Check the image below for your answer. Hope this helped!

8 0

4 years ago

Read 2 more answers

Which graph represents an exponential function

luda_lava [24]

Y=ab with a x overtop

3 0

3 years ago

Is it possible to form a triangle with the given side lengths? If not explain why not.

Brut [27]

Answer:

d. no; 0.7+1.4=2.1 is the answer...

because for forming a triangle the sum of two sides should be greater than the third side always.

while in this case it is equal so it is not possible to form a triangle...

4 0

3 years ago