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3 years ago

In TUV below, find m T to the nearest degree

Mathematics

2 answers:

Andre45 [30]3 years ago

7 0

Answer:

T = 88 degrees to the nearest degree

Step-by-step explanation:

To find the measure of the angle T, we can use the cosine rule

We have the formula as;

t^2 = u^2 + v^2 - 2uv Cos T

t = 8.1

u = 7.1

v = 4.2

8.1^2 = 7.1^2 + 4.2^2 - 2(7.1)(4.2) cos T

-2.44 = -59.64 cos T

cos T = (2.44)/(59.64)

T = arc cos (2.44/59.64)

T = 87.66

to the nearest degree, this is 88 degrees

iren [92.7K]3 years ago

3 0

Answer

The guy above me is correct but I'm gonna explain it better

Step-by-step explanation:

Step ONE 1.- Arrange the equation: Choose an equation from the LAW OF COSINES.

8.1^2= 7.1^2 + 4.2^2 - 2(7.1)(4.2) COS(T)

Step 2- Solve

65.61= 68.05-59.64 x COS(T)

Step 3- Inverse Operation (SUBTRACT: 65.61-68.05)

65.61= 59.64 x COS(T)

-68.05

INVERSE OPERATION AGAIN (DIVIDE: -2.44/59.64)

-2.44/59.64= COS(T)

INVERSE OPERATION ONE LAST TIME

WE MUST GET THE "T" ALONE SO WE MUST MOVE THE "COS" TO THE OTHER SIDE "COS^-1 (Cos (x))

Cos ^-1 (-.04)= (T)

87.707= T

ROUND: ROUND 87.707 TO THE NEAREST DEGREE.

88 = T

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Answer:

12x=4y........................................

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3 years ago

Sheila bought some rose plants and sunflower plants.There were 35 rose plants than sunflower plants.If the ratio of the rose pla

DENIUS [597]

So assuming that youmeans there were 35 MORE rose plants than sunflower seeds, then

Rose:Sunflower =8:3

rose=sunflower+35
therefor

8 units=rose
3 units=sunflowers

rose-35=sunflower
8unit-35=3unit
5unit-35=0
5unit=35
therefor
35=5unit
divide by 5
7=1unit

so 8 units of roses

7 times 8=56

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4 years ago

The speeds of vehicles traveling on a highway are normally distributed with an unkown population mean and standard deviation. A

Maksim231197 [3]

Answer:

The 90% confidence interval would be given by (60.09;69.91)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X =65$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9 represent the sample standard deviation

n=11 represent the sample size

2) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=11-1=10$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,10)".And we see that $t_{\alpha/2}=1.81$

Now we have everything in order to replace into formula (1):

$65-1.81\frac{9}{\sqrt{11}}=60.09$

$65+1.81\frac{9}{\sqrt{11}}=69.91$

So on this case the 90% confidence interval would be given by (60.09;69.91)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

3 0

3 years ago

Answer ASAP. Please give correct answer. (Involves a bunch of circles and trig identities)

iren [92.7K]

Answer:

45.40

Step-by-step explanation:

First of all, the shape of rope is not a parabola but a catenary, and all catenaries are similar, defined by:

y=acoshxa

You just have to figure out where the origin is (see picture). The hight of the lowest point on the rope is 20 and the pole is 50 meters high. So the end point must be a+(50−20) above the x-axis. In other words (d/2,a+30) must be a point on the catenary:

a+30=acoshd2a(1)

The lenght of the catenary is given by the following formula (which can be proved easily):

s=asinhx2a−asinhx1a

where x1,x2 are x-cooridanates of ending points. In our case:

80=2asinhd2a

40=asinhd2a(2)

You have to solve the system of two equations, (1) and (2), with two unknowns (a,d). It's fairly straightforward.

Square (1) and (2) and subtract. You will get:

(a+30)2−402=a2

Calculate a from this equation, replace that value into (1) or (2) to evaluate d.

My calculation:

a=353≈11.67

d=703arccosh257≈45.40

7 0

3 years ago

What is the slope of a line whose graph contains the points (−2,−6)<br><br> and (0,0)<br><br>?

torisob [31]

Answer:

It’s D

Step-by-step explanation:

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3 years ago