How do you solve this problem?
1 answer:
Answer: 2.5722 .
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Explanation:
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log(base "
" of 19 = y ? ; Solve for "y" ;
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^ (y) = 19 ; Solve for "y" ?
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Take the "ln" (that is, "natural logarithm", of both sides:
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ln [ ^ (y) ] = ln 19 ;
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y * ln = ln 19 .
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Use "3.1416" as an approximation for: " " ;
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y * ln (3.1416) = ln 19 ;
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Divide EACH side of the equation by: " [ ln (3.1416) ]" ; to isolate "y" on one side of the equation; and to solve for "y"; (Use a calculator to do this) ;
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y * ln (3.1416) / [ ln (3.1416) ] = ln 19 / [ ln (3.1416) ] ;
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y = ln 19 / [ ln (3.1416) ] ;
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y = 2.5721639670047041 ;
→ round to nearest 4 (FOUR) decimal places;
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→ y = 2.5722 .
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_____________________________________________________
Explanation:
_________________________________________________
log(base "
__________________________________________________
__________________________________________________
Take the "ln" (that is, "natural logarithm", of both sides:
__________________________________________________
ln [
__________________________________________________
y * ln
__________________________________________________
Use "3.1416" as an approximation for: "
__________________________________________________
y * ln (3.1416) = ln 19 ;
__________________________________________________
Divide EACH side of the equation by: " [ ln (3.1416) ]" ; to isolate "y" on one side of the equation; and to solve for "y"; (Use a calculator to do this) ;
_________________________________________________________
y * ln (3.1416) / [ ln (3.1416) ] = ln 19 / [ ln (3.1416) ] ;
________________________________________________________
y = ln 19 / [ ln (3.1416) ] ;
_______________________________________________________
y = 2.5721639670047041 ;
→ round to nearest 4 (FOUR) decimal places;
_______________________________________________________
→ y = 2.5722 .
________________________________________________________
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B, C, E, F
<h2>Explanation:</h2>In this problem, we have the following equation of a line written in Standard form:
So we need to choose the equations that has the same solutions as this equation. If we multiply each equation by a constant term and find the same solution as the given equation, then they will have the same solution. This is only true fro options B, C, E and F.
Option B.
So we get the same given equation. This option is valid!
Option D.
So we get the same given equation. This option is valid!
Option E.
So we get the same given equation. This option is valid!
Option F.
So we get the same given equation. This option is valid!
For the other options, there is no any constant term that multiplies both sides of the equation and gives us the same given equation.
<h2>Learn more:</h2>About this subject: brainly.com/question/8810210
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Answer:
Verified
Area = 13.12 square units.
Step-by-step explanation:
Let the given points / vertices of the parallelogram be represented as follows:
A(2,-1,1),
B(5, 1,4),
C(0,1,1),
D(3,3,4)
In vector notation, we can have;
A = 2i - j + k
B = 5i + j + 4k
C = 0i + j + k
D = 3i + 3j +4k
One of the ways to prove that a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.
(i) Now, let's find the various sides of the assumed parallelogram. These sides are:
AB = B - A = [5i + j + 4k] - [2i - j + k] <em>open the brackets</em>
AB = 5i + j + 4k - 2i + j - k <em>collect like terms and solve</em>
AB = 5i - 2i + j + j - k + 4k
AB = 3i + 2j+ 3k
BC = C - B = [0i + j + k] - [5i + j + 4k] <em>open the brackets</em>
BC = 0i + j + k - 5i - j - 4k <em>collect like terms and solve</em>
BC = 0i - 5i + j - j + k - 4k
BC = -5i + 0j - 3k
CD = D - C = [3i + 3j +4k] - [0i + j + k] <em>open the brackets</em>
CD = 3i + 3j + 4k - 0i - j - k <em>collect like terms and solve</em>
CD = 3i - 0i + 3j - j + 4k - k
CD = 3i + 2j + 3k
DA = A - D = [2i - j + k] - [3i + 3j +4k] <em>open the brackets</em>
DA = 2i - j + k - 3i - 3j - 4k <em>collect like terms and solve</em>
DA = 2i - 3i - j - 3j + k - 4k
DA = - i - 4j - 3k
AC = C - A = [0i + j + k] - [2i - j + k] <em>open the brackets</em>
AC = 0i + j + k - 2i + j - k <em>collect like terms and solve</em>
AC = 0i - 2i + j + j + k - k
AC = - 2i + 2j +0k
BD = D - B = [3i + 3j + 4k] - [5i + j + 4k] <em>open the brackets</em>
BD = 3i + 3j + 4k - 5i - j - 4k <em>collect like terms and solve</em>
BD = 3i - 5i + 3j - j + 4k - 4k
BD = - 2i + 2j + 0k
(ii) From the results in (i) above, it has been shown that;
AB is equal to CD, and that implies that AB is parallel to CD. i.e
AB = CD => AB || CD
<em>Also,</em>
AC is equal to BD, and that implies that AC is parallel to BD. i.e
AC = BD => AC || BD
(iii) Therefore, ABDC is a parallelogram since its opposite sides are equal and parallel.
(B) Now let's calculate the area of the parallelogram.
To calculate the area, we find the magnitude of the cross product between any two adjacent sides.
In this case, we choose sides AC and AB.
Area = | AC x AB |
Where;
AC X AB = i(6 - 0) - j(-6 - 0) + k(-4 -6)
AC X AB = 6i + 6j - 10k
|AC X AB| =
|AC X AB| =
|AC X AB| =
|AC X AB| = 13.12
Therefore the area is 13.12 square units.
PS: The diagram showing this parallelogram has been attached to this response.
