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3 years ago

Determine the relationship between the two vecors

Mathematics

1 answer:

asambeis [7]3 years ago

6 0

Answer:

Step-by-step explanation:

Since there exists a scalar

(namely

λ=a⋅b

) such that

b=λa

, the directions of the two vertices are the same (they are collinear). This implies that

|a⋅b|=|a||b|

So,

|a|=|(a⋅b)b|=|a||b||b|

which implies that

|b|=1

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The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T min

Maslowich

Answer:

67.3°C

Step-by-step explanation:

A = 25, T(0) = 100, T(1) = 90, find T(4)

dT/dt = -k(T - A)

d(T - A)/dt = -k(T - A)

d(T - A)/(T - A) = -k dt

ln(T - A) = lnC - kt

$T(t) -A=Ce^{-kt}\\T(t) = A + Ce^{-kt} = 25 + Ce^{-kt}\\T(0) = 25 + C = 100\\C=75$

$T(t) = 25 + 75e^{-kt}\\T(1) = 25 + 75e^{-k} = 90\\75e^{-k} = 65\\e^{-k} = \frac{65}{75}, k = ln\frac{75}{65} = 0.1431\\T(t) = 25+75e^{-0.1431t}\\T(4) = 25+75e^{-0.1431\times4} = 67.3$

4 0

2 years ago

Help me with this question? What is 8% of 85?

natta225 [31]

X = 8% * 85

x = 8/100 * 85

x = 0.08 * 85

Multiply 0.08 and 85.

x = 6.8

6.8 is 8%<span> of 85.</span>

3 0

3 years ago

Read 2 more answers

What number should replace the question mark?

TiliK225 [7]

Answer:

Just a guess but I think 5

Step-by-step explanation:

The top right square on all boxes is the difference of the second box and the first box which equals the third box. This rule is applied to all of the other boxes so if I'm not wrong the question mark should be 5

3 0

3 years ago

Read 2 more answers

Darius is a graphic designer he makes a sign for a company that has a width of 2 feet and a length of 2 feet 6 inches the compan

Sav [38]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

Width of the sign made by Darius initially = 2 feet

Length of the sign = 2 feet 6 inches

Dimension of the flyer are 10 inches by 8 inches. Since, in original sign the measure of length is greater, therefore, the length of flyer is 10 inches and its width is 8 inches.

In order to find the scale factor we must convert the lengths and widths to same units. Lets convert the length and width of sign into inches.

Since, 1 feet = 12 inches

Length of the sign = 2 feet 6 inches = 2(12) + 6 inches = 30 inches

Width of the sign = 2 feet = 2(12) inches = 24 inches

Now we can find the scale factor by either comparing the lengths or widths of both the designs. Scale factor will be equal to the ratio of corresponding lengths/widths.

So, the scale factor would be:

Length of Flyer : Length of Sign

= 10 inches : 30 inches

= 1 : 3

= $\frac{1}{3}$

This shows, the length of flyer is $\frac{1}{3}$ times as that of the sign. So, the scale factor that Darius must use is $\frac{1}{3}$ . The length and width of the flyer are $\frac{1}{3}$ as that of the sign.

The same scale factor would result if we would have used the ratio of widths instead of the lengths.

Scale Factor = Width of Flyer : Width of sign

= 8 : 24

= 1 : 3

Therefore, Darius must type the scale factor of $\frac{1}{3}$ in his computer to get the size of the flyer.

7 0

3 years ago

What number is 9 more than 45

MissTica

Its 54
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8 0

3 years ago

Read 2 more answers