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natta225 [31]
2 years ago
11

Logarithms - Please Help!!!

Mathematics
1 answer:
shusha [124]2 years ago
3 0

Answer:

log 4(b)

Step-by-step explanation:

Use the log law 1 / log b(a) = log a(b)

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
H over 3 plus 16 equals 18
3241004551 [841]

Answer:

If you're looking for H it could be 6

Step-by-step explanation:

bc 6/3+16=18 so 6/3=2 so 2+16=18

3 0
3 years ago
Read 2 more answers
Please answer this asap for 15 pt
crimeas [40]

Answer:

Step-by-step explanation:

what is question that you whant my to answer

6 0
3 years ago
Pls find the blank space. <br><br>the first answer will get marked brainliest​
True [87]

Step 1

Anything divided by one gives itself.

\frac{1}{8}=-8\text{ and }\frac{-8}{1}=\frac{-12}{48}

8

1

=−8 and

1

−8

=

48

−12

Step 2

Convert -8−8 to fraction -\frac{64}{8}−

8

64

.

\frac{1}{8}=-\frac{64}{8}\text{ and }\frac{-8}{1}=\frac{-12}{48}

8

1

=−

8

64

and

1

−8

=

48

−12

Step 3

Compare \frac{1}{8}

8

1

and -\frac{64}{8}−

8

64

.

\text{false}\text{ and }\frac{-8}{1}=\frac{-12}{48}false and

1

−8

=

48

−12

Step 4

Anything divided by one gives itself.

\text{false}\text{ and }-8=\frac{-12}{48}false and −8=

48

−12

Step 5

Reduce the fraction \frac{-12}{48}

48

−12

to lowest terms by extracting and canceling out 1212.

\text{false}\text{ and }-8=-\frac{1}{4}false and −8=−

4

1

Step 6

Convert -8−8 to fraction -\frac{32}{4}−

4

32

.

\text{false}\text{ and }-\frac{32}{4}=-\frac{1}{4}false and −

4

32

=−

4

1

Step 7

Compare -\frac{32}{4}−

4

32

and -\frac{1}{4}−

4

1

.

\text{false}\text{ and }\text{false}false and false

Step 8

The conjunction of \text{false}false and \text{false}false is \text{false}false.

\text{false}false

Hint

Do the arithmetic.

Solution

\text{false}false

4 0
2 years ago
Read 2 more answers
Y= -2(x - 1)^2 + 8 the answer
Dahasolnce [82]
Y = (-2x +2)^2 +8
(-2x^2 +4) +8
-2x^2 +12
8 0
3 years ago
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