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Serjik [45]
4 years ago
15

Stan invests $5000, some at 6% interest and the rest at 4.5% interest. If x is the amount he invests at 6%, then the amount inve

sted at 4.5% can be expressed as
A) .045x.
B) 10.5x.
C) 5000 - x.
D) 5000 + x.
Mathematics
1 answer:
Bumek [7]4 years ago
8 0
Let's say that Stan invested $1500 at 6%.  To find how much he invested at 4.5% would be 5000 - 1500 = $3500.  Now we have a pattern.  Now let's say stan invested x dollars. Even though it is unknown, we can set up how much is left.  So subtract x from 5000 or 5000 - x which is C
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Let u,v,wu,v,w be three linearly independent vectors in R7R7. Determine a value of kk, k=k= , so that the set S={u−3v,v−2w,w−ku}
11Alexandr11 [23.1K]

Answer:

1/6

Step-by-step explanation:

For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.

C1a + C2b + C3c = 0

From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)

The values in parenthesis are the ccoefficients of w, v and u respectively.

On writing this vector as a linear combination, we will have;

C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)

0-2C2+C3 = 0........ 1

-3C1+C2 = 0 ........... 2

C1-kC3 = 0 ….......... 3

From equation 2, 3C1 = C2

Substituting into 1, -2(3C1)+C3 = 0

-6C1+C3 = 0

-6C1 = -C3

6C1 = C3.…..4

Substitute 4 into 3 to have

C1-k(6C1) = 0

C1 = k6C1

6k = 1

k = 1/6

Hence the value of k for the set of vectors to be linearly dependent is 1/6

6 0
3 years ago
Use an addition property to solve for c.
NeX [460]

Answer:

"C" =14

Step-by-step explanation:

14+(-12)=-12+c

-12+c=14+(-12)

-12+c=14-12

-12+c+12=2+12

c=14

8 0
3 years ago
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Answer:

12, 72, 180

Step-by-step explanation:

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3 years ago
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A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
Vlad1618 [11]

Answer:

Reaches a maximum height of 235.00 feet in 3.75 seconds.

Step-by-step explanation:

The height of the boulder, h,  in feet after t seconds is given by the function is given by :

h=-16t^2+120t+10 .....(1)

For maximum height, put \dfrac{dh}{dt}=0

i.e.

\dfrac{d(-16t^2+120t+10)}{dt}=0\\\\-32t+120=0\\\\32t=120\\\\t=3.75\ s

Put t = 3.75 in equation (1). So,

h=-16(3.75)^2+120(3.75)+10\\\\h=235\ \text{feet}

So, the boulder's maximum height is 235 feets and it takes 3.75 s to reach to its maximum height.

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These are parallel lines

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