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3 years ago

4x + 5 is greater than 11

Mathematics

1 answer:

erastova [34]3 years ago

8 0

Answer:

if your asking if x is greater than 11 it will be false

Step-by-step explanation:

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What is the antiderivative of sin^2(x)cos^2(x)?

marin [14]

Answer:

$\frac{x}{8}-\frac{\sin(4x)}{32}+C$

Step-by-step explanation:

[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]

Recall that we can express the squared trig functions in terms of cos(2x). That is,

$\cos(2x)=2\cos^2x-1 \\ \cos(2x)=1 - 2\sin^2x.$

And so inverting these,

$\cos^2x=\frac{1}{2} (1+\cos2x) \\ \sin^2x=\frac{1}{2} (1-\cos2x)$ .

Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

$\sin^2x \cdot \cos^2x =\frac{1}{2} (1-\cos2x) \cdot \frac{1}{2} (1+\cos2x) = \frac{1}{4}(1-\cos^2(2x)).$

Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).

$\cos(2x)=2\cos^2x-1 \Rightarrow \cos(4x)=2\cos^2(2x)-1 \Rightarrow \cos^2(2x) = \frac{1}{2}(1+\cos(4x))$

So then,

$\sin^2x \cdot \cos^2x = \frac{1}{4}(1-\cos^2(2x)) = \frac{1}{4}(1-\frac{1}{2}(1+\cos(4x))) = \frac{1}{4}(1-\frac{1}{2}-\frac{1}{2}\cos(4x))=\frac{1}{8}(1-\cos(4x)).$

This is now integrable (phew),

$\int \sin^2x\cos^2x \ dx = \int \frac{1}{8}(1-\cos(4x)) \ dx = \frac{1}{8} \int (1-\cos(4x)) \ dx = \frac{1}{8}(x-\frac{1}{4}\sin(4x))+C.$

7 0

2 years ago

Find the length of a diagonal of a rectangle if the length of the rectangle is 24 cm and its width is 10 cm. A) 22 cm B) 26 cm C

xz_007 [3.2K]

Answer:

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem:

$hypotenuse^2=leg^2+leg^2$

We have

$leg=24cm,\ leg=10\ cm,\ hypotenuse=d$

Substitute:

$d^2=24^2+10^2\\\\d^2=576+100\\\\d^2=676\to d=\sqrt{676}\\\\d=26$

5 0

2 years ago

Read 2 more answers

Given that<br>9^-1/2 = 27^1/4 ÷ 3^x+1<br>Find the exact value of x.

nexus9112 [7]

Answer:

Find the exact value using trigonometric identities.

Exact Form: x=34

Decimal Form: x=0.75

Step-by-step explanation:

5 0

2 years ago

HEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPP will mark brainlest

Pepsi [2]

Answer:

She sold 39 tall candies and 52 short candies

Step-by-step explanation:

x is all the tall candies

y is all the short candies

x+y=91

8x+5y=572

Use the method of Substitution to find out both x and y.

x=91-y

8(91-y)+5y=572

728-8y+5y=572

728-3y=572

3y=156

y=52

x+52=91

x=39

8 0

2 years ago

What is represented by p v q?

Stella [2.4K]

$\lor$ is the logical or/disjunction symbol. $p\lor q$ means " $p$ or $q$ ". Disjunction is commutative, which means $p\lor q$ is equivalent to $q\lor p$ .

So if $p$ represents $x$ and $q$ represents $x>3$ , then $p\lor q\equiv q\lor p$ means $x>3$ or $x$ .

4 0

3 years ago