Can someone please help me answer this.

GenaCL600 [577]

To solve this problem, we need to know the formula for the nth term of an arithmetic sequence. The formula is $a_{n}$ = t₁ + (n-1)d, with $a_{n}$ being the nth term, t₁ being the first term, and d being the distance between terms. Now we can substitute values to figure out what $a_{n}$ is. When substituting, the equation becomes:

$a_{n}$ = 12 + 29(-6)
$a_{n}$ = -162

That means that the 30th term in this arithmetic sequence is -162.

8 0

3 years ago

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I need help finding the values of the last boxes shown in the image.

Bingel [31]

The volume of the region R bounded by the x-axis is: $\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}$

<h3>What is the volume of the solid revolution on the X-axis?</h3>

The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

In the graph, the given straight line passes through two points (0,0) and (2,8).

Therefore, the equation of the straight line becomes:

$\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}$

where:

(x₁, y₁) and (x₂, y₂) are two points on the straight line

Thus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:

$\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}$

y = 4x

Now, our region bounded by the three lines are:

y = 0
x = 2
y = 4x

Similarly, the change in polar coordinates is:

x = rcosθ,
y = rsinθ

where;

x² + y² = r² and dA = rdrdθ

Now

rsinθ = 0 i.e. r = 0 or θ = 0
rcosθ = 2 i.e. r = 2/cosθ
rsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)

⇒ r = 0 to r = 2/cosθ
θ = 0 to θ = tan⁻¹ (4)

Then:

$\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}$

$\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}$

Learn more about the determining the volume of solids bounded by region R here:

brainly.com/question/14393123

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5 0

2 years ago

The scatter plot shows the systolic blood pressure of people of several different ages. The equation represents the linear model

elena-14-01-66 [18.8K]

Answer: 95 mm Hg

Step-by-step explanation:

Given: The equation represents the linear model for the data is

$y=x+95$

Since, age is an independent quantity whereas blood pressure is dependent quantity.

Thus, y represents the the systolic blood pressure of people of several different ages (x).

Now, the age of new born baby =0

Substitute x=0 in the equation , we get y=95

Hence, The systolic blood pressure of new born baby = 95 mm hg

5 0

3 years ago

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Bla lee la. la la lee bla

eimsori [14]

Answer:laaa vidas so las vi vi ras ony laa viras so las vi vi ras

Step-by-step explanation:laaaa vidas so las vi vi ras boty hastice hastice sola vi vi rasss*birb falling*

6 0

3 years ago

Sadie finished her math test in sixteen minutes less than three times the amount of times it took her friend Laura to finish.if

amid [387]

Answer:

Sadie took 47 minutes to finish her test.

Step-by-step explanation:

Let Laura's time be x minutes.

Then we have:

x + 3x - 16 = 68

4x = 84

x = 21 minutes.

So Sadie took 3(21) - 16 = 63-16

= 47 minutes.

3 0

3 years ago