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baherus [9]
3 years ago
6

Find the slope of the line through (-9, -19) and (-2,-5),

Mathematics
2 answers:
svetoff [14.1K]3 years ago
8 0

Answer:

Find the slope of the line through (-9, -19) and (-2,-5),

-3 over-10

son4ous [18]3 years ago
5 0

Answer:

Slope is 2

Step-by-step explanation:

(-9, -19) and (-2,-5)

m=(y2-y1)/(x2-x1)

m=( -5 + 19)/( -2 + 9)

m = (14)/(7)

m = 2

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Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4
arsen [322]

we are given

R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k

now, we can find x , y and z components

x=cos(8t),y=sin(8t),z=8ln(cos(t))

Arc length calculation:

we can use formula

L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt

x'=-8sin(8t),y=8cos(8t),z=-8tan(t)

now, we can plug these values

L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt

now, we can simplify it

L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8sec(t) dt

now, we can solve integral

\int \:8\sec \left(t\right)dt

=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|

now, we can plug bounds

and we get

=8\ln \left(\sqrt{2}+1\right)-0

so,

L=8\ln \left(1+\sqrt{2}\right)..............Answer

5 0
3 years ago
A college dorm refrigerator measures 18.5 cm by 32 cm 12.2 cm. What is the volume of the collage dorm refrigerator
valina [46]

Answer:

722.24 cm

Step-by-step explanation:

The volume formula is L X W X H = V  so using that information we can do 18.5 times 32 times 12.2 which gives us 722.24 cm.

6 0
2 years ago
Do one of the​ following, as appropriate.​ (a) Find the critical value z Subscript alpha divided by 2​, ​(b) find the critical v
aliya0001 [1]

Answer:

t=\pm 2.95

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The t distribution or Student’s t-distribution is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.  

Data given

Confidence =0.99 or 99%

\alpha=1-0.99=0.01 represent the significance level

n =16 represent the sample size

We don't know the population deviation \sigma

Solution for the problem

For this case since we don't know the population deviation and our sample size is <30 we can't use the normal distribution. We neeed to use on this case the t distribution, first we need to calculate the degrees of freedom given by:

df=n-1=16-1=15

We know that \alpha=0.01 so then \alpha/2=0.005 and we can find on the t distribution with 15 degrees of freedom a value that accumulates 0.005 of the area on the left tail. We can use the following excel code to find it:

"=T.INV(0.005;15)" and we got t_{\alpha/2}=-2.95 on this case since the distribution is symmetric we know that the other critical value is t_{\alpha/2}=2.95

8 0
3 years ago
Tell whether −2 is a solution of the inequality. 8−2x&lt;12
kolbaska11 [484]

Answer:

No

Step-by-step explanation:

8−2x<12

Subtract 2 from each side

8-8−2x<12-8

-2x <4

Divide each side by -2, remembering to flip the inequality

-2x/-2 >4/-2

x > -2

Is -2 a solution

-2 >-2

This is false, it is equal

5 0
3 years ago
If x=82902, what is... x*6930+93945*x/7?
olganol [36]

Answer: 1194677035.714285

Step-by-step explanation:

= {(82902 * 6930)+(93945*82902)} / 7

= (574510860 + 7788228390) / 7

= 8362739250 / 7

= 1194677035.714285

3 0
3 years ago
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