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Suppose you deposited $100 in a savings account 3 years ago. The simple interest rate is 3.2 %. The interest that you earned in

astraxan [27]

It's not compounded interest, you just get $3.20 every year.
$100 * 0.032 = $3.20
$3.20 * 3 years = $9.60

7 0

3 years ago

Consider the planes 4x+3y+4z=1 and 4x+4z=0. (A) Find the unique point P on the y−axis which is on both planes. ( 0 equation edit

Nana76 [90]

Answer:

Step-by-step explanation:

A) From the order of the exercise we already know that the intersection points lies on the Y-axis, so its coordinates are P(0;y;0). In order to find it, we only need to substitute the equation 4x+4z=0 into the equation 4x+3y+4z=1. Then,

1=4x+3y+4z = 3y + (4x+4z)= 3y+0.

From the expression above it is easy to obtain that y=1/3, and the intersection point is P(0;1/3;0).

B) To obtain the parallel vector to both planes we use the cross product of the normal vector of the planes.

$\left[\begin{array}{ccc}i&j&k\\4&3&4\\4&0&4\end{array}\right] = 12i-0j+12k$

As we want a unit vector, we must calculate the modulus of u:

$|u|=\sqrt{12^2+0^2+12^2} = \sqrt{2\cdot 12^2}=12\sqrt{2}$ .

Thus, the wanted vector is $\frac{u}{12\sqrt{2}}$ . Therefore,

$u = \frac{1}{\sqrt{2}}i-\frac{1}{\sqrt{2}}k = \frac{\sqrt{2}}{2}i-\frac{\sqrt{2}}{2}k$ .

C) In order to obtain the vector equation of the intersection line of both planes, we just need to put together the above results.

$r = \frac{1}{3}j +\lambda \left( \frac{\sqrt{2}}{2}i- \frac{\sqrt{2}}{2}k \right)$

where $\lambda$ is a real number.

8 0

4 years ago

Suppose two telephone poles are 60 ft apart and the length of the wire between the poles is 61 ft. If the lowest point of the wi

Brut [27]

Answer:

H=22.5ft

Step-by-step explanation:

According to the graph, we must find y to determine the height at which the rope must be placed so that the lowest point of the rope is 17 ft high .

applying the pythagorean theorem

$h^{2}=x^{2} +y^{2}\\y^{2}=h^{2} -x^{2}\\y^{2}=30.5^{2} -30^{2}\\ y^{2}=930.25-900\\y=\sqrt{30.25}=5.5ft$

then H=17ft+5.5ft=22.5ft

5 0

4 years ago

What’s 9/10x7=hbbbdndjfkfkgjgjtjtjggjg

GaryK [48]

6.3 is the answer fujrtijdsbrhhcjsrhrhrhrhdbd

6 0

4 years ago

Read 2 more answers

Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream

irina1246 [14]

So this is a solution problem the answer is 3/4 cups or 75% milk and 1/4 cups or 25% cream, here's why:

m = milk

c = cream

m + c = 1

This is because when you add milk and cream then you get one cup of solution

.02m + .18c = .06

When you add together the percentages the goal is to have .06 or 6%

100m + 100c = 100

2m + 18c = 6

I do this to make it easier to solve

200m + 200c = 200

-200m - 1800c = -600

The "m's" cancel out

-1600c = -400

c = 1/4 or .25 or 25%

Now we add c back in

m + 1/4 = 1

Solve for m

m = 3/4

Thus: 3/4 milk and 1/4 cream

4 0

3 years ago