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ICE Princess25 [194]
3 years ago
6

What is the value of the expression 5³√-27+4√25

Mathematics
1 answer:
MakcuM [25]3 years ago
8 0

Answer:

669.51905283  or 375 √3 + 20

Step-by-step explanation:

Raise 5 to the power of 3

125√27 + 4√25

Rewrite 27 as 3²·3

Factor 9 out of 27

125√9(3) + 4√25

Rewrite 9 as 3²

125√3²·3 + 4√25

Pull terms out from under the radical

125(3√3) + 4√25

Multiply 3 by 125

375√3 + 4√25

Rewrite 25 as 5²

375√3 +4√5²

Pull terms out from under the radical, assuming positive real numbers

375√3 + 4 · 5

Multiply 4 by 5

375 √3 + 20

Exact form: 375 √3 + 20

Decimal form: 669.51905283

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A small island is 3 kilometers from the nearest point p on the straight shoreline of a large lake. if a woman on the island can
yKpoI14uk [10]
The distance walked will be (12-x) km
the distance rowed will be (9+x²) km
A] The function T(x) will be given by:
Time=distance/speed
thus we shall have:
T(x)=[√(9+x²)]/2.5+(12-x)/4

B] To get the distance x=c that minimizes the time travel, we differentiate the above.
T'(x)=(1/2.5)[1/(2.5√9+x²)*2x-1/4]
this should give us 0 for x=c, thus
c/[2.5*√(9+c²)]-1/4=0
⇒c/[2.5*√(9+c²)]=1/4
c/√(9+c²)=2.5/4
squaring both sides we get:
c²/(9+c²)=5/8
8c²=5(9+c²)
8c²=45+5c²
3c²=45
c²=15
c=3.87 km

c] The least travel time is
T(c)=[√(9+c²)]/2.5+(12-c)/4
this will give us:
T(c)=[√(9+3.87²)]/2.5+(12-3.87)/4
T(c)=3.9999209~4 hours

d] The second derivative will be:
T"(x)=1/[2.5√(9+x²)]-x²/[2.5(9+x²)^(3/2)]
but
x=c=3.87
T"(x)=0.01668 hours/ mile²
Given that T(c)=0, while T(x)<0 for x<c and T(x)>0 for x>c proves that T(x)  decreases for x<c and increases for x>c, so there is a minimum at x=c


4 0
3 years ago
Write an equation of the line that passes through (0,-5) and (-5,-5)
nikitadnepr [17]
-5- -5=0 which leads to slope of zero. (0, -5) is the y-intercept so it is Y= -5
6 0
3 years ago
If a line crosses the y-axis at (0,1) and has a slope of 4/5, what is the equation of the line ?
stepladder [879]
The slope intercept form of a line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).  We are given that the slope is 4/5 and the point (0,1) so we know m=4/5 and b=1 so:

y=4x/5+1  now to rearrange into standard form ax+by=c

y=(4x+5)/5

5y=4x+5

5y-4x=5

So the answer is D.

However, by convention, in standard form, the equation is usually expressed with a positive coefficient for x.

5y-4x=5 SHOULD be expresses so the x has a positive coefficient, divide both sides by -1 and you have the technically correct form:

4x-5y=-5

Apparently whomever/whatever posed this question to you was unaware of this convention :P
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3 years ago
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A pizza buffet has prepared 15 pizzas to place on the line at the beginning of lunch at 11:00 a.m. The equation used to describe
Anit [1.1K]

Answer:

B. Every 16 minutes, 22 more pizzas were set out on the buffet.

Step-by-step explanation:

At 11:00 am, x would be equal to 0, and there would be 15 pizzas on the buffet line. Then, every 8 minutes, 11 more pizzas are added to the buffet line. So in 16 minutes, 22 pizzas will be added to the buffet.

\frac{16}{8} =2\\(11)(2) = 22

7 0
2 years ago
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