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3 years ago

Find x. Round your answer to the nearest tenth of a degree.

Mathematics

1 answer:

viktelen [127]3 years ago

3 0

Answer: x=52.6°

Step-by-step explanation:

To find the value of x, we have to use our SOHCAHTOA. We can eliminate sine and cosine because both uses hypotenuse, which is not labelled. Therefore, we use tangent.

$tan(x)=\frac{17}{13}$

To find x, we want to use inverse tangent.

$x=tan^{-1}(\frac{17}{13} )$ [plug into calculator]

$x=52.6$

Now, we know that x=52.6°.

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As we know that the standard equation of circle is ${\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}$ , where r is the radius of circle and centre at (h,k) 

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2 years ago

A total of 1 232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russ

ElenaW [278]

Answer:

$n(S\cap F \cap R)=7$

Step-by-step explanation:

The Universal Set, n(U)=2092

$n(S)=1232\\n(F)=879\\n(R)=114$

$n(S\cap R)=23\\n(S\cap F)=103\\n(F\cap R)=14$

Let the number who take all three subjects, $n(S\cap F \cap R)=x$

Note that in the Venn Diagram, we have subtracted $n(S\cap F \cap R)=x$ from each of the intersection of two sets.

The next step is to determine the number of students who study only each of the courses.

$n(S\:only)=1232-[103-x+x+23-x]=1106+x\\n(F\: only)=879-[103-x+x+14-x]=762+x\\n(R\:only)=114-[23-x+x+14-x]=77+x$

These values are substituted in the second Venn diagram

Adding up all the values

2092=[1106+x]+[103-x]+x+[23-x]+[762+x]+[14-x]+[77+x]

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3 years ago

Keenan currently does a total of 8 pushups each day. He plans to increase the number of pushups he does each day by 2 pushups un

Viefleur [7K]

Answer:

Step-by-step explanation:

Given that

Current count of pushups = 8

Number of increase in pushups each day = 2

The desired pushup goal on daily basis = 30

Days require = x= ?

as we can conclude the number of pushups would increase by following sequence

8, 10, 12, 14, 16, ......30

Now as we can be the number of pushups by a constant number each day it means this sequence is arithmetic.

First term of our sequence is X1 and the final term is Xn, and the difference between two consecutive terms (Common Difference) is 2.

X1 = 8

Xn = 30

d = 2

Using the formula of nth term for arithmetic sequence

Xn = X1 + (n-1)d

Substituting the values

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So, it means on the 12th day he will have to do 30 pushups if he starts from 8 and increase 2 pushups each day.

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