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3 years ago

1 ln(1) + 2 ln(2) + 3 ln(3) + ⋯ + 10 ln(10)

Mathematics

1 answer:

Lapatulllka [165]3 years ago

6 0

Answer:

$\ln(1\cdot2^{2} \cdot3^{3}\cdot4^{4} ...\cdot10^{10} )$

Step-by-step explanation:

By logarithm rules

$\ln1+2\ln2+3\ln3+....+10\ln10\\\ln1+\ln2^2+\ln3^3+....\ln10^{10}\\\ln(1\cdot2^{2} \cdot3^{3}\cdot4^{4} ...\cdot10^{10} )$

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Hello there ^ _ ^ Can you help me please ? Please explain how you find the answer. Thanks!

ziro4ka [17]

It's C because for the perpendicular line, you need to construct cross points to draw it through.

- you start by drawing a random circle with F as the center, just as long as it intersects line DE
- Then you use the intersections of that circle to draw new circles starting at F.
- These new circles intersect at F and another point below DE.
- You draw the perpendicular line through F and the other point.

8 0

3 years ago

Maci and I are making a small kite. Two sides are 10". Two sides are 5". The shorter diagonal is 6". Round all your answers to t

Art [367]

Answer:

A. 4".

B. Approximately 9.54".

C. Approximately 13.54".

Step-by-step explanation:

Please find the attachment.

Let x be the distance from the peak of the kite to the intersection of the diagonals and y be the distance from the peak of the kite to the intersection of the diagonals.

We have been given that two sides of a kite are 10 inches and two sides are 5 inches. The shorter diagonal is 6 inches.

A. Since we know that the diagonals of a kite are perpendicular and one diagonal (the main diagonal) is the perpendicular bisector of the shorter diagonal.

We can see from our attachment that point O is the intersection of both diagonals. In triangle AOD the side length AD will be hypotenuse and side length DO will be one leg.

We can find the value of x using Pythagorean theorem as:

$(AO)^2=(AD)^2-(DO)^2$

$x^{2}=5^2-3^2$

$x^{2}=25-9$

$x^{2}=16$

Upon taking square root of both sides of our equation we will get,

$x=\sqrt{16}$

$x=\pm 4$

Since distance can not be negative, therefore, the distance from the peak of the kite to the intersection of the diagonals is 4 inches.

B. We can see from our attachment that point O is the intersection of both diagonals. In triangle DOC the side length DC will be hypotenuse and side length DO will be one leg.

We can find the value of y using Pythagorean theorem as:

$(OC)^2=(DC)^2-(DO)^2$

Upon substituting our given values we will get,

$y^2=10^2-3^2$

$y^2=100-9$

$y^2=91$

Upon taking square root of both sides of our equation we will get,

$y=\sqrt{91}$

$y\pm 9.539392$

$y\pm\approx 9.54$

Since distance can not be negative, therefore, the distance from intersection of the diagonals to the top of the tail is approximately 9.54 inches.

C. We can see from our diagram that the length of longer diagram will be the sum of x and y.

$\text{The length of the longer diagonal}=x+y$

$\text{The length of the longer diagonal}=4+9.54$

$\text{The length of the longer diagonal}=13.54$

Therefore, the length of longer diagonal is approximately 13.54 inches.

3 0

3 years ago

7. Subtract the polynomials: 5x2 + 4x + 1 and x2 + 3x - 4

Colt1911 [192]

Answer:

4x²+x+5.

Step-by-step explanation:

5x²+4x+1-(X²+3x-4).

5x²+4x+1-x²-3x+4.

5x²-x²+4x-3x+1+4.

4x²+x+5.

3 0

3 years ago

Read 2 more answers

Dimensions of a Box A large plywood box has a volume of . Its length is ft greater than its height, and its width is ft less tha

cupoosta [38]

Answer:

Few things are missing, they are volume of the box is 180 feet cube. Length is 9 feet greater than its height, and weight is 4 feet less than its height.

Step-by-step explanation:

Given, the volume of the box, V = 180 feet cube

Let the height of the box, h = x feet

Therefore, length is, l = ( 9+x ) feet

And width is, b = ( x-4) feet

so volume of the box is

V = l x b x h

$180= (x+9) \times (x-4) \times (x)$

$x^3 +5x^2-36x -180 =0$

Factorizing we get

(x+5)(x-6)(x+6)=0

Therefore,

x = -5, -6, 6

Now since the height of the box cannot be negative, so taking the positive value of x, we get

Height of the box, h = x = 6 feet

Length , l = ( 9+x ) = 9+6 = 15 feet

Width , b = ( x-4) = 6-4 = 2 feet

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3 years ago

Which

Vedmedyk [2.9K]

Answer:

The answer is D: lll and IV only

Step-by-step explanation:

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3 years ago