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Dmitry_Shevchenko [17]
2 years ago
15

Need help , asap - 20 points .

Mathematics
1 answer:
Olin [163]2 years ago
4 0

Answer:

C

Step-by-step explanation:

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List the following numbers in order from least to greatest. a) 3.5× 10/3 B) 3.5× 10-2 C) 5.3 × 10/3
Crazy boy [7]

Answer:

3.5*10^{-2}, 3.5*10^3, 5.3*10^3

B, A, C

Step-by-step explanation:

This is scientific notation. The numbers 3.5 * 10^3\\3.5 *10^{-2}\\5.3 * 10^3 can be ordered least to greatest by looking at their digits and exponents. Since a -2 as an exponent is present, this means this is a small decimal and is the least. 3.5 and 5.3 have the same exponent of 3 but 5.3 is greater than 3.5 so its the greatest. The order is

3.5*10^{-2}, 3.5*10^3, 5.3*10^3

5 0
2 years ago
Determine the measure of ∠Q, rounded to the nearest tenth of a degree.<br> images attached.
const2013 [10]

Answer:

D

Step-by-step explanation:

Using the Sine rule in Δ QRS , that is

\frac{q}{sinQ} = \frac{r}{sinR} , that is

\frac{15}{sinQ} = \frac{12}{sin50.1} ( cross- multiply )

12× sinQ = 15 × sin50.1° ( divide both sides by 12 )

sinQ = \frac{15sin50.1}{12} , thus

Q = sin^{-1} ( \frac{15sin50.1}{12} ) ≈ 73.5° ( to the nearest tenth )

8 0
3 years ago
Find the equation of the directrix of the parabola x2=+/- 12y and y2=+/- 12x
PIT_PIT [208]

Answer:

  1. x^2 = 12 y equation of the directrix y=-3
  2. x^2 = -12 y equation of directrix y= 3
  3. y^2 = 12 x   equation of directrix x=-3
  4. y^2 = -12 x equation of directrix x= 3

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

  1. x^2 = 12 y
  2. x^2 = -12 y
  3. y^2 = 12 x
  4. y^2 = -12 x

For each part the value of directrix will be different.

For x²  = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay  eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x²  = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay  eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y²  = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax  eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y²  = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax  eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3

5 0
3 years ago
Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery.
Sonja [21]

Answer:

  27 years

Step-by-step explanation:

The formula for the number of payments can be used:

  N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03

There will be a couple thousand dollars left after the 27th payment.

The winnings will last 27 years.

5 0
3 years ago
If both the length and width of a rectangle are doubled, how is the area of the rectangle changed?
Law Incorporation [45]

Answer:

B) The area is four times larger

Step-by-step explanation:

A=LW

2*2*A=2L2W

4A=2L2W

Therefore, the area is four times larger

7 0
2 years ago
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