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Naddik [55]
3 years ago
9

Find all the values of k so that the given points are 29 square units apart. (-5, 5) and (k,0).

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
7 0
Distance formula between 2 points (x1,y1) and (x2,y2)

D=\sqrt{(x1-x2)^{2}+(y1-y2)^{2}}

D=29 and one point is (-5,5) and the other is (k,0)
sub

29=\sqrt{(-5-k)^{2}+(5-0)^{2}}
29=\sqrt{(-5-k)^{2}+(5)^{2}}
square both sides
841=(-5-k)^{2}+(5)^{2}
841=(-5-k)^{2}+25
minus 25 both sides
816=(-5-k)^{2}
square root both sides don't forget positive and negative roots
+/-4√51=-5-k
add 5 to both sides
5+/-4√51=-k
times -1 both sides
-5+/-4√51=k




the possible values for k are
k=-5+4√51 or k=-5-4√51

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A small theater had 6 rows of 26 chairs each. An extra 9 chairs have just been brought in. How many chairs are in the theater no
Andrej [43]

Answer:165

Step-by-step explanation:

6•26 = 156. 156+9=165

6 0
3 years ago
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Write an equation of the line with the given properties. Your answer should be written in standard form.
Vanyuwa [196]

Given:

The slope of the line is m=0.

The line passes through the point P(-9,-3).

To find:

The equation of the line in standard form.

Solution:

Standard form of a line is:

Ax+By=C

The slope intercept form of the line is

y-y_1=m(x-x_1)

Where, m is the slope and (x_1,y_1) is the point on the line.

It is given that the slope of the line is 3 and it passes through the point (-9,-3), so the equation of the line is

y-(-3)=0(x-(-9))

y+3=0

y=-3

Therefore, the standard form of the given line is y=-3.

7 0
3 years ago
Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br
Lina20 [59]

Answer:

The differential equation for the amount of salt A(t) in the tank at a time  t > 0 is \frac{dA}{dt}=12 - \frac{2A(t)}{500+t}.

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t

where, \text{R}_i_n = concentration of salt in the inflow \times input rate of brine solution

and \text{R}_o_u_t = concentration of salt in the outflow \times outflow rate of brine solution

So, \text{R}_i_n = 4 lb/gal \times 3 gal/min = 12 lb/gal

Now, the rate of accumulation = Rate of input of solution - Rate of output of solution

                                                = 3 gal/min - 2 gal/min

                                                = 1 gal/min.

It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

So, \text{R}_o_u_t = concentration of salt in the outflow \times outflow rate of brine solution

             = \frac{A(t)}{500+t} \text{ lb/gal } \times 2 \text{ gal/min} = \frac{2A(t)}{500+t} \text{ lb/min }

Now, the differential equation for the amount of salt A(t) in the tank at a time  t > 0 is given by;

= \frac{dA}{dt}=12\text{ lb/min } - \frac{2A(t)}{500+t} \text{ lb/min }

or \frac{dA}{dt}=12 - \frac{2A(t)}{500+t}.

4 0
3 years ago
Find the greatest common factor of 27, 9, and 45.
Anna [14]

Answer:

9

Step-by-step explanation:

hope that this is helpful.

3 0
3 years ago
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F(x) =17x and g(x) = 4x. Find f(x)-g(x) when x=3
bogdanovich [222]

Answer:

39

Step-by-step explanation:

f(x)=17x

f(3)=17(3)

f(x)=51

g(x)=4x

g(3)=4(3)

g(x)=12

f(x)-g(x)

51-12= 39

8 0
3 years ago
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