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3 years ago

Use the change of base rule to find the logarithm to four decimal places

Mathematics

1 answer:

Bond [772]3 years ago

6 0

Answer:

1.7059

Step-by-step explanation:

$\log_{9}{(42.45)}=\dfrac{\log{(42.45)}}{\log{(9)}}\approx\dfrac{1.62788}{0.954243}\\\\\approx 1.7059$

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Find the area of the given triangle to the nearest square unit. Angle a= 30 degrees, b=10, angle B=45 degrees

storchak [24]

Answer:

$A=34\ units^2$

Step-by-step explanation:

Suppose we have a general triangle like the one shown in the figure.

We know the angle A, the angle B and the length b.

$A = 30\°\\\\B = 45\°\\\\b = 10$

By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.

$A + B + C = 180\\\\30 + 45 + C = 180$

We solve the equation and thus we find the angle C.

$C = 180 - 30-45\\\\C = 105$

We already know the three triangle angles.

Now we use the sine theorem to calculate the sides c and a.

The sine theorem says that:

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

Then

$\frac{sin(30)}{a}=\frac{sin(45)}{10}$

$\frac{sin(30)}{\frac{sin(45)}{10}}=a$

$a=7.071$

Also

$\frac{sin(105)}{c}=\frac{sin(45)}{10}$

$\frac{sin(105)}{\frac{sin(45)}{10}}=c$

$c=13.660$

Finally, we use the Heron formula to calculate the triangle area

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Where s is:

$s=\frac{a+b+c}{2}$

Therefore

$s=\frac{7.071+10+13.660}{2}$

$s=15.37$

$A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}$

$A=34\ units^2$

3 0

3 years ago

One exterior angle of a regular polygon measures 97°. What is the measure of one interior angle?

3241004551 [841]

Hello :) = Merhaba :)

Answer:

Step-by-step explanation:

The total angle of a polygon and its external angle must be 180°.

So the inner angle of this polygon:

180 - 97 = 83° would.

NOTE: I'm not American. I'm just a Turk who wants to help you. So if my sentences are wrong, please forgive me.

<em><u>#Cevapistevereyim</u></em>

Başarılar :) = Achievements :)

4 0

3 years ago

A vendor sold 15 hotdogs diring a football game.If the ratio of hotdogs to hamburgers sold was 3:2 how many hamburgers did the v

algol13

10 hamburgers were sold

4 0

3 years ago

−3 1/3 ÷ 9= What I need it now!

Contact [7]

Step 1. Convert 3 1/3 to improper fraction.

- 3 * 3 + 1/3 ÷ 9

Step 2. Simplify 3 * 3 to 9

-9 + 1/3 ÷ 9

Step 3. Simplify 9 + 1 to 10

-10/3 ÷ 9

Step 4. Use this rule: a ÷ b/c = a * c/b

-10/3 * 1/9

Step 5. Use this rule: a/b * c/d = ac/bd

-10 * 1/3 * 9

Step 6. Simplify 10 * 1 to 10

-10/3 * 9

Step 7. Simplify 3 * 9 to 27

-10/27

8 0

3 years ago

Last year at a certain high school, there were 125 boys on the honor roll and 80 girls on the honor roll. This year, the number

Elodia [21]

Answer:

6.8% decrease

Step-by-step explanation:

a drop of 8% means that only 92% of 125 boys remained on honor roll from last year; .92 x 125 = 115

a drop of 5% means that only 95% of 80 girls remained on honor roll from last year; .95 x 80 = 76

total number of students on honor roll last year = 125 + 80 = 205

total number of students on honor roll this year = 115 + 76 = 191

percent of change = (191 - 205) ÷ 205 = -14/205 = -.068

-.068, which represents a 6.8% decrease

3 0

2 years ago