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2 years ago

Evaluate the expression. −8²=__

Mathematics

1 answer:

Vikentia [17]2 years ago

4 0

It would equal 64 because -8 pounds o the power of 2 would be 64

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Evey month the bank withdraws $15 from netsy checking account as a service fee . Betsy had budgeted $75 for the next few fees se

Nadusha1986 [10]

15x≤75
x<span>≤5
</span>service fee will be covered for 5 months

3 0

2 years ago

The position vector for a particle moving on a helix is

topjm [15]

Answer:

a) 25.15

x = 1

y = t

z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)

c) (x,y) = (1, -2pi)

Step-by-step explanation:

First lets calculate the velocity, that is, the derivative of c(t) with respect to t:

v(t) = (-sin(t), cos(t), 2t)

The velocity at t0=4pi is:

v(4pi) = (0, 1, 8pi)

And the speed will be:

s(4pi) = √(0^2+1^2+ (8pi)^2) = 25.15

The tangent line to c(t) at t0 = 4pi has the parametric form:

(x,y,z) = c(4pi) + t*v(4pi)

Since

c(4pi) = (1, 0, (4pi)^2)

The tangent curve has the following components:

x = 1

y = t

z = (4pi)^2 + t *(8pi) = 4pi(4pi + 2t)

The intersection with the xy plane will occurr when z = 0

This happens at:

t1 = -2pi

Therefore, the intersection will occur at:

(x,y) = (1, -2pi)

6 0

2 years ago

Yertle the turtle and his 362 turtle buddies went swimming in 3 different ponds. if the same number of turtles swim in each pond

konstantin123 [22]

There are 363 turtles (including yertle)
there are 3 different ponds and the same # in each pond. you simply divide the number of turtles by 3 because there are 3 different ponds.

363/3=121
there 121 turtles in each pond

8 0

2 years ago

A line that passes through the point (4, 2) and has the slope of -3/2

mash [69]

The answer is: y = -3/2 x + 8

Graph:

To find the answer we use the formula;

y-y1 = M1 (x - x1)

y-2 = -3/2 (x-4)

When fully solved: the answer is:
y = -3/2 x + 8

8 0

2 years ago

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

zepelin [54]

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

As we know the given points

Center = (5, -4)

and

Point on circle = (-3,2)

The distance between point on circle and center will give us the radius of circle

So,

The formula for distance is:

$\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10$

The standard form of equation of circle is:

$(x-h)^{2}+(y-k)^{2}=r^{2}$

where h and k are the coordinates of the center. So putting in the value:

$(x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100$

8 0

2 years ago