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Mathematics

1 answer:

pychu [463]3 years ago

3 0

An equation in point-slope form that passes through point P(a,b) is as follows:

y-b=m(x-a) where m=slope, a,b are coordinates of point P.

For a line to pass through P(4,-8)
the equation will look like:
y-(-8) = m(x-4)
simplify left side
y+8=m(x-4)

The given equation has a slope of m=-1/2, so the slope of a line perpendicular to it has a slope of -1/m = -1/(-1/2)=+2

Now go through the answer choices:
a. y+8=2(x-4) => passes through P(4,-8) and has a slope of 2. so TRUE
b. y-4=2(x+8) => has a slope of 2, but passes through (-8,4), which is not P so FALSE
c. y+8=(1/2)(x-4) => passes through P(4,-8), but has the wrong slope (a reflection, not perpendicular) so FALSE
d. y-8=(1/2)(x+4) => passes through a wrong point (-4,8) and has the reflected slope (not perpendicular) so FALSE

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Which of the following expressions could be used to find the area of the larger rectangle? 3(64 mm2) 9(64 mm2) 9(32 mm2) 3(576 m

kari74 [83]

Answer:

$9(64)\ mm^{2}$

Step-by-step explanation:

we know that

The area of rectangle is equal to

$A=bh$

In this problem we have

the larger rectangle

$b=48\ mm$

$h=12\ mm$

substitute

$A=48*12=(4*4*3)(4*3)=(3*3)(4*4*4)=9(64)=576\ mm^{2}$

4 0

3 years ago

After sitting on a shelf for a while, a can of soda at room temperature (73 F) is placed inside a refrigerator and slowly cools.

Alona [7]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling here:

$T(t)=T_s+(T_0-T_s)^{-kt$

where T(t) is the temp of something after a certain amount of time, t, has gone by; Ts is the surrounding temp, and T0 is the initial temp. k is the constant of cooling. We need to first solve for this using the information given. Filling in what we know:

$53=35+(73-35)^{-35k$ which can simplify a bit to

$53=35+(38)^{-35k$ and $18=38^{-35k$

Take the natural log of both sides:

$ln(18)=ln(38)^{-35k$

Taking the natural log allows us to pull that exponent down out front:

$ln(18)=-35k*ln(38)$

and now we can divide both sides by ln(38) to get

-35k = .794585 so

k = -.023

Now that have the value for k, we can go on to solve the rest of the problem which is asking us the temp of the soda after 70 minutes. Filling in using the k value and the new time of 70 minutes:

$T(t)=35+(38)^{70(-.023)$ and