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V125BC [204]
3 years ago
7

15^2x=36 write the equation in logarithmic form.

Mathematics
1 answer:
marusya05 [52]3 years ago
5 0

X=log36/(2*log15)
X=aprox 0.6616
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Determine if the given set is a subspace of set of prime numbers P 2. Justify your answer. The set of all polynomials of the for
devlian [24]

Answer:

All polynomials of the p=at² where a is in R is a subspace Pn for an appropriate value of n do not fulfill the condition and hence do not form the subspace

Step-by-step explanation:

Check attachment

7 0
3 years ago
Find the co-ordinate of the image of the point A (3, -2) when it is reflected on the line x=0 and then rotated about origin thro
Luba_88 [7]

Answer:

Step-by-step explanation:

Rotations are easy when its multiples of 90 degrees; 90,180,270,360. Treat them like they’re a complex number like [x+yi]*i=[-y,xi] so rotating by 90 degrees and 180 is i squared [-1]! So [-3,2] rot90 is [-2,-3].

Reflection about the y=x line is change places. [x.y]=[y,x].

So [-2.-3] reflected about the y=x line is [-2.-3]=[-3.-2],

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5 0
3 years ago
Mrs. Benson has graded 46 math assignments but has 80% of the assignments left to grade. Mrs. Benson has how many math assignmen
timofeeve [1]

Mrs. Benson has 184 math assignments left to grade.

<u>Step-by-step explanation:</u>

Here we have , Mrs. Benson has graded 46 math assignments but has 80% of the assignments left to grade.We need to find Mrs. Benson has how many math assignments left to grade. Let's find out:

Let total Number of math assignments be x , So According to question 46 math assignments are graded & 80% are left i.e.

⇒ x = 46+\frac{80x}{100}

⇒ x -\frac{80x}{100}= 46

⇒ \frac{100x-80x}{100}= 46

⇒ \frac{20x}{100}= 46

⇒ \frac{x}{5}= 46

⇒ x=230

Now , Assignments left to grade is :

⇒ 230-46

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Therefore , Mrs. Benson has 184 math assignments left to grade.

4 0
3 years ago
Find the slope of the tangent line to the given polar curve at the point specified by the value of θ
MariettaO [177]

The given curve has equation

<em>r(θ)</em> = 9 + 8 cos(<em>θ</em>)

and its derivative is

d<em>r</em>/d<em>θ</em> = -8 sin(<em>θ</em>)

When <em>θ</em> = <em>π</em>/3, we have <em>r</em> (<em>π</em>/3) = 13, and d<em>r</em>/d<em>θ</em> (<em>π</em>/3) = -4√3.

Differentiate these with respect to <em>θ</em> :

d<em>y</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)

d<em>x</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ</em>) sin(<em>θ</em>)

In polar coordinates, we have

<em>y(θ)</em> = <em>r(θ)</em> sin(<em>θ</em>)

<em>x(θ)</em> = <em>r(θ)</em> cos(<em>θ</em>)

and when <em>θ</em> = <em>π</em>/3, we have <em>y</em> (<em>π</em>/3) = 13√3/2 and <em>x</em> (<em>π</em>/3) = 13/2.

The slope of the tangent line to the curve is d<em>y</em>/d<em>x</em>. By the chain rule,

d<em>y</em>/d<em>x</em> = d<em>y</em>/d<em>θ</em> • d<em>θ</em>/d<em>x</em> = (d<em>y</em>/d<em>θ</em>) / (d<em>x</em>/d<em>θ</em>)

d<em>y</em>/d<em>x</em> = (d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)) / (d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ</em>) sin(<em>θ</em>))

When <em>θ</em> = <em>π</em>/3, the slope is

d<em>y</em>/d<em>x</em> = (-4√3 sin(<em>π</em>/3) + 13 cos(<em>π</em>/3)) / (-4√3 cos(<em>π</em>/3) - 13 sin(<em>π</em>/3))

d<em>y</em>/d<em>x</em> = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

d<em>y</em>/d<em>x</em> = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

<em>y</em> - 13√3/2 = -1/(17√3) (<em>x</em> - 13/2)

<em>y</em> = -(<em>x</em> - 338)/(17√3)

4 0
2 years ago
Write an equation based on the graph. Please help 15 points!
nignag [31]

Answer should be:

y = -3x - 3

5 0
2 years ago
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