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9966 [12]
3 years ago
9

Simplify. -sqrt m^4n^7

Mathematics
1 answer:
Delvig [45]3 years ago
3 0

Answer:

-m^2 |n|^3 sqrt(n)

Step-by-step explanation:

-sqrt( m^4n^7)

We know that sqrt(ab) = sqrt(a) sqrt(b)

-sqrt(m^4) sqrt(n^7)

The sqrt(m^4) = m^2

The sqrt(n^7) = sqrt(n^6) sqrt(n) = |n|^3 sqrt(n)  We take the absolute value because if n is negative, n^6 is postive, but n^3 is negative

-sqrt(m^4) sqrt(n^7)

-m^2 |n|^3 sqrt(n)


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Given that A=27, B=43 and c=17, solve triangle ABC to the nearest hundredth
katrin2010 [14]
When we are given 3 sides, we try to solve the angles first by using the
law of cosines
cos (A) = [b^2 + c^2 - a^2] / (2 * b * c)
cos (A) = [43^2 + 17^2 -27^2] / (2 * 43 * 17)
cos (A) = [1,849 + 289 -729] / <span> <span> <span> 1,462
</span></span></span>cos (A) = 1,409 / 1,462
cos (A) = <span> <span> <span> 0.96374829001368
Angle A = 15.475

Now that we have one angle, we next can use the
Law of Sines
sin(B) / side b = sin(A) / side a
sin(B) = sin(A) * sideb / sidea
</span></span></span><span>sin(B) = sin(15.475) * 43 / 27
</span><span>sin(B) = 0.26682 * 43 / 27
sin (B) = </span><span>0.424935555555</span>
Angle B = 25.147 Degrees
Remember the arc sine (<span>0.424935555555) also equals </span> <span> <span> <span> 154.85

</span></span></span>Finally, calculating the third angle is quite easy
Angle C =  180 - Angle (A) - Angle(B)
Angle C =  180 - 15.475 - 154.85
Angle C =  9.675

Source:
http://www.1728.org/trigtut2.htm


6 0
3 years ago
2. A lunch stand makes s.75 profit on each chef's salad and $1.20 profit on each Caesar salad. On a typical weekday, it sells be
kow [346]

Let's let

<u>x = the number of chef salads, x>=0</u>

<u>y = the number of Caesar salads, y>=0</u>

The constrains are:

40 <= x <= 60

35 <= y <= 50

x + y <= 100

The objective function here is F(x, y) = 0.75x + 1.20y

The corner points are (40, 35),  (60, 35), (60, 40), (50, 50) and (40, 50).

F (40, 35) = 0.75*40 + 1.20*35 = $72

F (60, 35) = 0.70*60 + 1.20*35 = $84

F (60, 40) = 0.75*60 + 1.20*40 = $93

F (50, 50) = 0.75*50 + 1.20*50 = $97.50

F (40, 50) = 0.75*40 + 1.20*50 = $90

Thus, we conclude to maximize the profit 50 Chef and 50 Caesar salads should be prepared.

8 0
4 years ago
What is the perimeter of a triangle measuring 3 on each side?
ANTONII [103]
Add them all up.
A triangle has 3 sides, and you said each side is 3. So:
3+3+3 = 9
8 0
3 years ago
Read 2 more answers
Rudi bought 12.5 yards of fabric to make pillows. Each pillow requires 1.75 yards of fabric. Use compatible numbers to estimate
Ipatiy [6.2K]
Hi there!

Using compatible numbers it would be:

12 ÷ 2 = 6.

Now when you divide it, the answer would be close to 6.

So, 12 ÷ 2 = 6 would be using compatible numbers.

Hope this helps ;)
8 0
3 years ago
Read 2 more answers
The equation $(x - 7)^2 + (y + 13)^2 = 12$ represents a circle. What is its radius?
miskamm [114]

Answer:

<h3>2√3</h3>

Step-by-step explanation:

The standard equation of a circle is expressed as;

(x-a)²+(y-b)² = r² where;

(a, b) is the center of the circle

r is the radius of the circle

Given the equation (x - 7)^2 + (y + 13)^2 = 12

On comparing;

r² = 12

Take the square root of both sides

√r² = √12

r = √12

r = √4*3

r = 2√3

Hence the radius of the circle is 2√3

7 0
3 years ago
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