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3 years ago

Does anyone know this answer to this questions

Mathematics

1 answer:

7nadin3 [17]3 years ago

4 0

ANSWER

-4.0

EXPLANATION

The given trigonometric equation is

$\tan \: 45 \degree - 10 \: \cos \: 60 \degree$

From special angles or using the unit circle.

$\tan \: 45 \degree = 1$

$\cos \: 60 \degree = \frac{1}{2}$

We make the substitution to get:

$1 - 10 ( \frac{1}{2} ))$

This simplifies to:

$1 - 5 = - 4$

Hence the correct answer is -4.0

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Please help asapppp!!!!

Pavlova-9 [17]

Answer:

The only option 3 is correct

Step-by-step explanation:

See the given diagram.

1. ∠ D = ∠ B {Since AB ║ DE and DB is transverse line. So, they are alternate angles.}

So, ∠ D = 43° ≠ 28°

2. Now, ∠ A = ∠ CED {Again they are alternate angles}

⇒ ∠ A = ∠ CED = 180° - ∠ CEF = 180° - 152° = 28° ≠ 43°.

3. Again, ∠ ACD = 180° - ∠ ACB = ∠ A + ∠ B = 28° + 43° = 71°.

4. ∠ BCE = ∠ ACD {Vertically opposite angles}

⇒ ∠ BCE = 71° ≠ 109°

Therefore, the only option 3 is correct. (Answer)

7 0

3 years ago

Use mathematical induction to prove the statement is true for all positive integers n. 1^2 + 3^2 + 5^2 + ... + (2n-1)^2 = (n(2n-

Charra [1.4K]

Answer:

The statement is true is for any $n\in \mathbb{N}$ .

Step-by-step explanation:

First, we check the identity for $n = 1$ :

$(2\cdot 1 - 1)^{2} = \frac{2\cdot (2\cdot 1 - 1)\cdot (2\cdot 1 + 1)}{3}$

$1 = \frac{1\cdot 1\cdot 3}{3}$

$1 = 1$

The statement is true for $n = 1$ .

Then, we have to check that identity is true for $n = k+1$ , under the assumption that $n = k$ is true:

$(1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}$

$\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}$

$\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}$

$k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot (2\cdot k +1)^{2} = (k+1)\cdot (2\cdot k +1)\cdot (2\cdot k +3)$

$(2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)$

$k\cdot (2\cdot k - 1)+3\cdot (2\cdot k +1) = (k + 1)\cdot (2\cdot k +3)$

$2\cdot k^{2}+5\cdot k +3 = (k+1)\cdot (2\cdot k + 3)$

$(k+1)\cdot (2\cdot k + 3) = (k+1)\cdot (2\cdot k + 3)$

Therefore, the statement is true for any $n\in \mathbb{N}$ .

4 0

3 years ago

Find two positive numbers satisfying the given requirements. The product is 432 and the sum of the first plus three times the se

kogti [31]

Answer:

Step-by-step explanation:

Let the two positive integers be x and y.

If their product is 432, then

xy = 432 ......... 1

Also if the sum of the first plus three times the second is a minimum, then;

p(x) = x + 3y

From 1;

y = 432/x ..... 3

Substitute 3 into 2;

p(x) = x+3y

p(x)= x + 3(432/x)

p(x) = x + 1296/x

Since the expression is at minimum when dp(x)/dx = 0

dp/dx = 1 + (-1296)/x²

dp/dx = 1 -1296/x²

0 = 1 -1296/x²

0 = (x²-1296)/x²

cross multiply

0 = x²-1296

x² = 1296

x = √1296

x = 36

Since xy = 432

36y = 432

y = 432/36

y = 12

Hence the two positive numbers are 36 and 12

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3 years ago

Jon buys 3 shirts for 20

grin007 [14]

Answer:

Step-by-step explanation:

he would have to pay 60 dollars but I don't really understand your question

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3 years ago

Read 2 more answers

How many solutions exist for |1/2x + 1| = 5?

swat32

Answer:

Two, 8 and -12

Step-by-step explanation:

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3 years ago