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2 years ago

4. Which of the following is an arithmetic sequence?A. 4, 1, -2,-5, -8 B.4,-12, 36, -108

Mathematics

2 answers:

katrin2010 [14]2 years ago

6 0

A is an arithmetic sequence since the common difference is -3 while B is a geometric sequence and depends on multiples

Zolol [24]2 years ago

4 0

A is the answer :) it goes my increments of -3

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Martin decided to buy 2 bags of grapes weighing 5 and two-thirds pounds each, instead of the 3 bags weighing 4 and one-fifth pou

Juli2301 [7.4K]

Answer: He ended up with about 1 pound less grapes

Step-by-step explanation:

2 bags of grapes weighing 5 and two-thirds pounds each will give a total weight of:

= 2 × 5 2/3

= 2 × 17/3

= 34/3

= 11 1/3 pounds

3 bags weighing 4 and one-fifth pounds each, will give a weight of:

= 3 × 4 1/5

= 3 × 21/5

= 63/5

= 12 3/5

He ended up buying lesser grapes. This was about 12 3/5 - 11 1/3 = 1 4/15 less. This means that he ended up with about 1 pound less grapes

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In △ABC, m∠A=39°, a=11, and b=13. Find c to the nearest tenth.

Talja [164]

For this problem, we are going to use the <em>law of sines</em>, which states:

$\dfrac{\sin{A}}{a} = \dfrac{\sin{B}}{b} = \dfrac{\sin{C}}{c}$

In this case, we have an angle and two sides, and we are trying to look for the third side. First, we have to find the angle which corresponds with the second side, $B$ . Then, we can find the third side. Using the law of sines, we can find:

$\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{B}}{13}$

We can use this to solve for $B$ :

$13 \cdot \dfrac{\sin{39^{\circ}}}{11} = \sin{B}$

$B = \sin^{-1}{\Big(13 \cdot \dfrac{\sin{39^{\circ}}}{11}\Big)} \approx 48.1$

Now, we can find $C$ :

$C = 180^{\circ} - 48.1^{\circ} - 39^{\circ} = 92.9^{\circ}$

Using this, we can find $c$ :

$\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{92.9^{\circ}}}{c}$

$c = \dfrac{11\sin{92.9^{\circ}}}{\sin{39^{\circ}}} \approx \boxed{17.5}$

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8 0

2 years ago

A cone and a cylinder have equal radius, r, and equal altitudes, h. If the slant height of the cone is l, then the ratio of the

77julia77 [94]

Given:

radius of cone = r

height of cone = h

radius of cylinder = r

height of cylinder = h

slant height of cone = l

Solution

The lateral area (A) of a cone can be found using the formula:

$A\text{ = }\pi rl$

where r is the radius and l is the slant height

The lateral area (A) of a cylinder can be found using the formula:

$A\text{ = 2}\pi rh$

The ratio of the lateral area of the cone to the lateral area of the cylinder is:

$\pi rl\text{ : 2}\pi rh$

Canceling out, we have:

$\begin{gathered} =\frac{\pi rl}{2\pi rh} \\ =\text{ }\frac{l}{2h}\text{ or l:2h} \end{gathered}$

Hence the Answer is option B

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8 months ago

4. Which of the following is an arithmetic sequence?A. 4, 1, -2,-5, -8 B.4,-12, 36, -108​

4. Which of the following is an arithmetic sequence?A. 4, 1, -2,-5, -8 B.4,-12, 36, -108