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2 years ago

HELP!!!!! FAST PLEASE!!!!

1 answer:

7 0

Think of the right triangle formed by the ladder, the height of the upper end of the ladder and the distance of the bottom of the ladder from the wall.

Then x = 6 ft and the hyp is 10 ft. The trig function cos theta equals "adj side" / hyp, so, in this case,

cos theta = 6/10 = 0.6. Use the arccos x function on your calculator to find the angle x:

x = 0.927 (radians) = 53.1 degrees.

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Anyone knows how to do questions 7 and 8? 15 pts!!

Oksi-84 [34.3K]

7) Certainly there is a typo in the statement, just see that the expression of item (ii) is different from that of item (i). Probably the correct expression is: $2x^2-4x+5$ . With this consideration, we can continue.

(i) Let E the expression that we are analyzing:

$E=2x^2-4x+5\\\\ E=2x^2-4x+2-2+5\\\\ E=2(x^2-2x+1)-2+5\\\\ E=2(x-1)^2+3$

Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.

(ii) Manipulating the expression:

$2x^2+5=4x\\\\ 2x^2-4x+5=0$

So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.

8) Let E the expression that we want to calculate:

$E=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)+1\\\\ E-1=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)$

Multiplying by (2-1) in the both sides:

$(2-1)(E-1)=(2-1)(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ (E-1)=\underbrace{(2-1)(2+1)}_{2^2-1}(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ (E-1)=\underbrace{(2^2-1)(2^2+1)}_{2^4-1}(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ ...$ Repeating the process, we obtain: $...\\\\ E-1=(2^{32}-1)(2^{32}+1)\\\\ E-1=2^{64}-1\\\\ \boxed{E=2^{64}}$

3 0

3 years ago

Read 2 more answers

A^2+b^2+c^4=2020. Yes

pychu [463]

Answer:

yes

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

There is a fire in the third floor of a building, 22 feet above the ground. The fire truck has a 16-foot tall ladder on top, and

Over [174]

Answer: Yes the ladder will reach the fire

Step-by-step explanation: Please refer to the attached diagram for details.

The fire is at point A, while the top of the truck is at point C. The fire is actually burning at 22 feet off the ground, but because the fire truck itself is already 6 feet off the ground, the point that would serve as the base of the building would be 16 feet from the third floor (which is 22 feet minus 6 feet). Hence, point A to point B is 16 feet. So we need to calculate if line AC (from the truck to the fire at the third floor, labeled as b) shall equal the length of the ladder which is 16-foot long.

The angle of the ladder with the top of the truck is 75 degrees. Therefore,

Sin 75 = opposite/hypotenuse

Sin 75 = 16/b

By cross multiplication we now have

b = 16/Sin 75

b = 16/0.9659

b = 16.56

If the distance from A to C is 16.56 feet, then the 16-foot long ladder would reach the fire.

8 0

2 years ago

Leo has 11/3 cups of sugar. He uses 3/4 cups of sugar in a recipe. How much sugar does Leo have left?

Evgesh-ka [11]

It is 35/21 it shows that is can turn into a mixed number as well

7 0

3 years ago

What is the value of x?

nikklg [1K]

It took me a minute, but I understand what it wants you to do.

a^2+b^2=c^2

Find the missing length on that one triangle to the left.

62^2+b^2= 99.2^2

Square the numbers.

3844+b^2= 9840.64

Subtract 3844 on both sides.

b^2= 5996.64

Square root it.

b= 77. 437975 round down to b= 77.4

Now, we can find the length of the other missing side. (x+2)

77.4^2+b^2= 112^2

5990.76+b^2= 12,544

Subtract 5990.76 on both sides.

b^2= 6553.24

Square root it.

b= 80.952085, round to b=81

Now, plug that in.

(x+2)= 81

Subtract 2 on both sides.

x=79 (about)

I hope this helps! Make sure to check my work.
~kaikers

4 0

3 years ago